Robert Dalling, Physics Teacher at Louisiana School of Math, Science, and the Arts www.lsmsa.edu

www.lsmsa.edu teacher Robert Dalling's Physics Lectures (see also www.ushumans.net)

Mechanical Work and Energy

We all know that it takes energy to do work such as climbing stairs or walking up a hill. In physics, we say that mechanical work W is done when a force F is applied through a distance x.

W = F · x.

Mechanical Work = force times the distance through which it is applied.

When speaking, the phrase "mechanical work" is usually shortened to "work," but the physics term “work” has a more specific meaning than does the English word “work.” Work has units of force times distance, which is Newton · meters or Joules. (This unit is named after James Prescott Joule (1818-1889) who found that heat was a form of energy.) Force F and displacement x are both vectors but work is a scaler. When the force and displacement vectors do not lie along the same line then work is determined from the component of the force that points in the direction of the displacement. In this case the vector dot product is used.

W = F · x = F x cos θ,

where θ is the smallest angle between the F and x vectors when they are placed tail to tail.

Work results only from the part of the force pointing in the direction of the movement. Notice that when there is a 90° angle between the F and x vectors then cos θ = 0 and no mechanical work is done. For example, if you carry a weight along level ground then the angle between the displacement and the force of gravity will be 90° and no mechanical work will be done. Notice also that if the displacement x is zero, then the work done W = Fx is also zero. For example, no mechanical work is done when pushing against a wall that doesn't move. In one more case, carrying an object up a hill and then back down a hill results in a net work of zero.

Since work is the product of force and displacement, a specific amount of work can be done by either a large force applied through a small distance or by a much smaller force applied through a much larger distance. For example, the same work is done by a 100-Newton force moving through a distance of 1 meter as by a 1-Newton force moving through a distance of 100 meters.

When doing a pushup or a pull-up, the mechanical work done is W = Fx. We know we are doing work because we feel the force in our arms as we push through the distance x. We also do work when we lift a mass up to a certain height. Our back tells us that more work is done when raising a large mass than a small one.

Example:

The work done in lifting a 10 kg (22 pound) baby from the ground to your hip, which is 1.0 meter high, is given by

W = Fx = mgx = ( 10 kg )( 9.8 m/s² )( 1.0 m ) = 98 Nm = 98 Joules = 98 J.

CQ: What work is done by a force F = 167 N applied through a distance of 6 meters?

W = Fx = 1000 J.

CQ: What work is done by a force F = 167 N applied through a distance of 6 meters when there is a 45° angle between the Force and displacement vectors? W = F x cos θ = 70 J.

Example:

What work do you do when pushing a 10-kg box 3 meters on level ground across the carpet which has μ_K = 0.9?

W = Fx = μ_Kmgx = ( 0.9 )( 10 kg )( 9.8 m/s² )( 3m )= 58.8 J.

What work does the force of gravity do on the box? The answer is zero because there is a 90° angle between the gravitational force vector and the displacement vector x. What work does friction do on the box? Suppose the box is pushed along the positive x axis. Then the displacement is in the positive direction but the frictional force points in the negative-x direction. There is a 180° angle between these two vectors, so the works done by friction is

W = Fx cos θ = μ_Kmgx cos( 180 ) = ( 0.9 )( 10 kg )( 9.8 m/s² )( 3m )( -1 ) = -58.8 J.

Example.

What work is done by the engine to drive (push) a 2000-kg car 1000 meters when the coefficient of friction is 0.9?

W = Fx = μ_Kmgx=( 0.9 )( 2000 kg )( 9.8 m/s² )( 1000 m ) = 1.3 x 10⁷ J.

A person can do work in 100-Joule amounts while machines do work in one million Joule sizes.

Example:

Let’s calculate the mechanical work done when the applied force is not wholly in the direction of motion. What mechanical work is done when we pull a child 10m in a wagon using a force of F = 50 N directed at an angle 20° above direction of motion?

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When we calculate work, the angle θ is the smallest angle between the force and displacement vectors when placed tail to tail. We have

W = F x cos θ = ( 50 N )( 10 m )( cos20 ) = 470 J.

Example:

What is the mechanical work done against the gravitational force when carrying a 10-kg baby up a 10-meter long incline that has an angle of 5.7°. The F gravity vector points downward. The displacement vector points up the incline. The plane is inclined at an angle θ above the positive x axis. The smallest angle between x and F is then θ + 90°. Since cos( θ + 90 ) = sin( θ ), the smallest angle between x and F in this case becomes sin( θ ). But Lsin θ = 10 sin( 5.7 ) = 1, which is the 1-meter vertical lift. This means that we are lifting the same vertical distance of 1 meter as in the earlier problem in which the baby was lifted straight up into the air without the benefit of a ramp.

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We do the same mechanical work against gravity whether lifting straight up or traveling along an inclined hill. For conservative forces in general, the work done is independent of the path. The incline allows a smaller force but over a larger distance. Our knees and back tells us its easier to carry the mass up the incline than it is to lift it straight up the vertically-edged end of the ramp.

Student:

Try some of Joseph W. Howard’s sample problems involving work

Power

The same amount of work is done whether we lift an object slowly or quickly. Power P is a measure of the time rate at which work is done,

P = W / t.

Power = work / time = work done divided by the time taken to do the work.

Since W = Fx, power can be written as

P = Fx/t = Fv.

Power = forces times speed.

More power is needed to lift quickly or go straight up a hill then to follow a winding path, less power expended in walking up a less-steep incline. A screw is an inclined plane twisted in a circle.

Power has units of energy per unit time or Joules per second J/s. The combination J/s has been named after James Watt. One Watt = 1 J/s and 1 hp = 746 Watts.

CQ: What power is done when a mother lifts her 10-kg baby through a distance of one meter in one second?

P = W/t = Fx/t = mgx/t = ( 10 kg )( 9.8 m/s² )( 1 m ) / 1 s = 98 Watts.

Example:

Suppose that one person carries a mass up an inclined plane in 10 seconds while another lifts the mass straight up to the same height in 2 seconds. Who does the most work? They do equal work. Who expends more power? The lifter.

Example:

A 200- hp car engine does work at the rate ( 200 hp )( 746 W/hp ) = 14,920 J/s. At what speed could this engine raise the car vertically? Solving P = Fv = mgv for v gives

v = (14920 J/s ) / [( 2000 kg )( 9.8 m/s2 )] = 0.76m/s = 1.7 mph.

This would be the vertical speed at which this car could move straight upward. The car seems to have a lot of power but it could manage only a 1.7 mph upward speed. Rather than trying to climb straight up, we drive up less steep roads. The engine of a car does work against air friction. The engine also does work against ground friction at the rate P = Fv =μ_Kmgv. This heats the tires and scrapes rubber off them. (By the way, where does all the rubber go from the mountains of tires that are worn out each year? Down the drain and into our sewage treatment plants.)

The car is using 15,000 watts, the power consumption of our civilization is about 10 trillion watts, and the operation of a person requires about 100 watts, which is about the same power as is consumed by a light bulb.

Student.

Here is a list of the power produced by various processes.

Example:

A person eating 2,500 Calories per day, is operating on a power of

P = W / t = ( 2500 Cal/day )( 4187 J/Cal )( 1 hr/3600 s )( 1 day/24 h ) = 120 watts,

where we used the conversion factor: One Calorie = 1000 calories = 4187 Joules. A person can obtain this amount of energy by eating two or three pounds (one kilogram) of bread or three kilograms (6.5 pounds) of potatoes per day. Within the consumer, the energy of food is stored in fat that contains 270 Calories per ounce. This chemical energy is put to use one ATP molecule at a time.

Student:

Louis A. Blomfield explains what can be done with 60 watts.

Efficiency is defined to be work out / work in = useful output / input. Some efficiencies (from Priest page 39) include the following.

Device Converts Efficiency

Fluorescent lamp electrical to light 20%

car engine chemical to heat/thermal to mechanical 25%

steam turbine thermal to mechanical 47%

Home oil furnace chem to thermal 65%

Electric generator mechanical to electrical 99%

Conservation of energy

The total work done by a varying force is equal to the area under the F-x graph. For example, the force of a spring varies as F = -kx. The area under this straight line graph has the shape of a triangle. Since the area of a triangle is half the rectangular area of kx by x, we have

W_s = U_s = ½kx².

The work done in stretching or compressing a spring by a distance x is equal to one-half the spring constant k times the square of the distance. The work done is stored in the spring as energy U_s.

|-------relaxed length-------|

∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂

|– compressed length –|

ℓℓℓℓℓℓℓℓℓℓℓℓℓℓℓℓℓℓ

...................................|–x–|

Suppose an un-stretched spring is placed on a table and against a wall. If a mass is placed next to this un-stretched spring, nothing happens. But if work is done to compress the spring a distance x before it is placed next to a mass, when the spring is released it will apply a force through a distance x to propel the mass. The work initially done to compress the spring had been stored as energy U_s in the spring, and this energy was later used to do work on the mass. It is said that the compressed spring has stored, potential energy that can be later reclaimed.

As we throw a rock, we feel the force of our muscles as we push the rock through a distance. The force is accelerating the rock from an initial speed of zero up to a final speed v that occurs as the rock leaves our hand. When we substitute F=ma into the equation for work, we get

W = Fx = (ma)x.

In the case of a constant force producing a constant acceleration, we know that the distance the rock travels while we are pushing it will be x = ½ a t². The above equation for work is then

W = Fx = (ma)x = (ma)( ½ a t² ) = ½m(at)².

But a = vt, so this can be written

W = ½mv².

The quantity ½mv² is termed kinetic energy which is the “energy of motion.” Initially, the kinetic energy of the rock was zero. The work done on the rock by applying a force through a distance has changed the kinetic energy of the rock. It takes work, which is a force applied through a distance, to change the speed of a mass. We then have

W = Fx = ΔK.E. = Δ( ½mv² ),

where

K.E. is the kinetic energy, ½mv².

Kinetic energy is the “energy of motion.” This means that motion is another way to store energy. The motion of a spinning mass similarly stores energy.

The expression for kinetic energy can also be obtained from the motion equation

v² = vo² + 2ax.

Substituting a = F/m, we get

v² - vo² = 2ax = 2(F/m)x

½mv² - ½mv_o² = Fx.

Which can be written as

ΔKE = Fx = W.

It takes work to increase the kinetic energy of a mass. The reverse is also true. A mass in motion can do work, as in bending metal or in driving uphill against gravity and friction. As a car travels up a hill, its speed is decreasing because work is being done against the gravitational force. As a car travels, it is also doing work against the frictional force.

Example:

Calculate the kinetic energy of the Lunar Prospector spacecraft (m = 160 kg) hitting the moon at a speed of 1.7 km/s.

KE = ½mv²= ( 0.5 )( 160 kg )( 17,000 m/s )² = 2.3 x 10¹⁰ Joules.

CQ:

Using typical values for mass ans speed, calculate the kinetic energy of a person who is running. For a person of mass m = 60 kg (132 pounds) running at a speed of 4 m/s (9 mph), we get

KE = ½mv²= ( 0.5 )( 60 kg )( 4 m/s )² = 480 Joules.

The total energy of a system is conserved. That is, it never changes. The energy might be converted from one form to another. If a compressed spring is released to propel a mass up a hill, then the system contains work, kinetic energy, gravitational potential energy, and the elastic potential energy of the spring. As in this situation, the answer to most every problem in the textbook is

W + ΔKE + ΔU_g + ΔU_s = 0

“Work plus the change in kinetic energy plus the change in gravitational potential energy plus the change in elastic potential energy = 0.” You will get the right answer to each homework problem if you begin with this equation. Sometimes, the problem doesn’t involve one of the types of energy so that term can be omitted.

If work W = Fx = ½kx² is done to compress a spring then energy U_s is stored in the spring. That stored energy can be used to do work on a mass as the spring-force is applied through a distance. The energy stored in the spring is being converted into the energy of motion of the propelled mass. Energy is converted from one form to another. Work changes energy from one form into another. In this situation, the initial work of compressing the spring was stored as energy in the spring and then became the energy of motion of the mass. The sequence of events were W = Fx = ½kx² = Fx = ½mv².

The work done to lift a mass against the gravitational force through a distance h is

W_g = Fx = mgh.

The raised mass now possesses stored, gravitational potential energy just as the spring possessed stored energy in the previous example. If the raised mass is released, its stored, gravitational potential energy is converted into the energy of motion ½mv². The gravitational force is doing work = Fx on the mass as it falls through a distance x. In this case, the sequence of energy conversions were W = Fx = mgh = ½mv².

The falling mass might land on an empty soda can. The can becomes dented as its resisting force is applied through a distance. (The resisting force of the can is not linear.)

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The work done in raising the mass was stored as gravitational potential energy that was converted to the kinetic energy of motion of the falling mass and then used to apply a force through a distance while bending the metal of the can. It takes energy to bend metal. Lifting the rock twice as high requires twice the work and doubles the stored or potential energy which later becomes twice the kinetic energy and does twice the damage to the can upon impact.

The bending of metal in a car collision is the same process. In a car collision, damage is done by the kinetic energy, which increases with the square of the speed of the car. Doubling the speed quadruples the damage. Increasing the speed from 10 to 80, increases the damage by a factor of 64.

Gravitational potential energy is measured relative to a freely chosen origin of the coordinate system. Only changes in height matter.

This energy of position is called “potential energy” because the raised mass has the potential to do mechanical work, such as might change the energy of motion of the mass or bend metal if dropped onto a can.

Energy is conserved. The energy existing in the universe today is the same energy (about 10⁶⁸ Joules) that comprised the Big Bang. There are many forms of energy, but the total energy contained in the universe never changes. Energy is not created or destroyed but it can be converted from one form into another. Some forms of energy include chemical, heat, light, motion (½mv²), and position (mgh). Energy is stored in a battery or in a dammed river, and it is stored in a stretched spring, rubberband, sling shot, or bow that will launch an arrow. This is called stored or potential energy because it has the potential to do work or be turned into another form.

Eienstein’s equation, E = mc², showed us that mass is just another way to store energy. The energy forming the atoms of your body existed at the moment of the Big Bang and was a part of the Big Bang.

Do work to lift water uphill, we will have W = Fx = mgh, and energy will be stored in the raised water. The stored gravitational potential energy (mgh) can be later converted into the energy of motion (½mv²) as the raised water flows downhill. In the operation of an overshot waterwheel, this kinetic energy is used to turn a stone that is grinding grain or to turn a saw that is cutting wood. Water from a small creek is collected in a pond through the night and then through the day, it is allowed to fill buckets at the top of a vertical, rotating wheel. The weight of the water forces the wheel to rotate as the water falls. Overshot waterwheels are more expensive to build than are undershot wheels in which water current strikes the bottom of a vertical, rotating paddlewheel forcing it to spin. The paddles partially dip into the water as the wheel spins. The paddled wheel could also be oriented horizontally. In Cathedral, Forge, and Waterwheel: Technology and Invention in the Middle Ages by Frances and Joseph Gies (1995, HarperPerennial, New York), the Gies show that an overshot waterwheel produces eighty to one-hundred-twenty times the power of an animal-turned mill and ten to twenty times the power of an undershot wheel. You can see animations of various water wheels and mills at the Old Sturbridge Village website (click education, for teachers, classroom materials, and then mills and waterpower). You can also go directly to http://www.osv.org/education/WaterPower.

Windmills, sailing ships, and undershot waterwheels directly use the motion of the stream. The current speed is decreased as some of its energy is used to spin the sail or mill. If the sail or mill took all the energy from the current, the current would then pile up and stop flowing. This would end the power source. Calculations show that the maximum power is transferred to the paddles or sails when 59% of the current’s energy is converted into sail or mill motion.

The Gies explain that the horizontal waterwheel was probably invented in Armenia around the year 200 bc. At that time, the Chinese began using water power to rotate the upper grinding stone, while the Romans began using animals for this purpose. Waterwheels east of Persia were typically horizontal but were vertical west of Persia. Persians invented a horizontal windmill in the seventh century ad. The use of vertical windmills had made its way to Europe in the twelfth century ad. In vertical windmills, the wind is caught edge-on in pinwheel fashion so the entire building or at least its roof frequently has to be turned toward the wind. By the sixteenth century, some manufacturing cities in Holland contained hundreds of windmills. Today, Europe is generating 30 megawatts of electrical power from wind-powered generators. This is 75% of the world’s total. Europe plans to obtain 5% of its energy supply from the wind by the year 2010 and 20% by 2020. Half of the electrical energy usage in Navara Spain today is obtained from the wind. The U.S. is obtaining 10 megawatts of power from the wind.

Example:

The stored chemical potential energy of gasoline is 40 mega-joules per liter. How far can a liter of gas take a 2000-kg car when doing work against a frictional force of 0.65 times the car's weight? The frictional force is F = μ_Kmg = ( 0.65 )( 2000 kg )( 9.8 m/s² ) = 12,740 Newtons. The work done against the frictional force is W = Fx, so

x = W / F = ( 40x10⁶ J/L )( 1 L ) / 12740 N = 3140 meter = 3 km.

Example:

Try the NASA exercise of measuring the frictional force on a coasting car of known weight to estimate the energy content of a gallon of gasoline. The answer is that the energy content of each gallon is equivalent to that of 50 pounds of dynamite.

Example:

Lift a 10-kg mass up a height h of one meter. We saw above that,

W = Fx = mgh = ( 10 kg )( 9.8 m/s² )( 1 m ) = 98J.

The mechanical work done resulted in gravitational potential energy. When the mass is released, it gains speed as it falls. What is its speed when it reaches the ground? The stored, gravitational potential energy (mgh) will be converted into kinetic energy:

mgh = ½mv².

In this equation, we cancel m and then solve for

v = √(2gh) = 4.4 m/s.

This problem was solved using conservation of energy considerations. This procedure is simpler than using the motion equations of previous chapters, where we used

h = ½at²,

t = √ (2h/g)

and then

v = at = gt = (g)(√(2h/g)) = √(2hg2/g) = √(2gh).

As the mass falls from y = h down to y = 0, its total energy is constant

Total energy E = kinetic energy plus gravitational potential energy = mgy + ½mv².

At the top of the motion, where y = h, all the energy is potential. When halfway to the ground, its gravitational potential energy of position is U_g = 98/2 J and its kinetic energy of motion is KE = 98/2 J. At the instant just before hitting the ground, the gravitational energy of the mass is zero and its total energy is all kinetic energy, KE = 98 J and U_g = 0.

Birds and airplanes do work to increase their height above the ground, which is gravitational potential energy, and then convert that energy U_g = mgh into kinetic energy by diving downward. A fly knows this, too, and will often take a diving motion to increase its speed.

A pendulum is mass tied to a string attached to a support. Work W = Fx is done to raise the mass. The work done is independent of the path. The work energy is stored as gravitational potential energy U_g = mgx stored in the mass. When you release the raised mass, the pendulum swings back and forth. As it swings, its total energy E = KE + U_g is oscillating between being entirely potential energy U_g at the top of the swing to being entirely kinetic energy KE at the bottom of the swing. In addition, the pendulum is doing work against air friction and against friction at the slightly-moving pivot point. This is heating the mass and the air through which it is moving. Eventually, the pendulum comes to a stop as do all Earth-bound contraptions. (This is the reason that perpetual motion machines never work.) The work done in initially raising the mass was stored as gravitational potential energy and then oscillated between U_g and KE while doing work against friction. When it had stopped moving, all of the work done in initially raising the mass has gone into heat energy and raised the temperature of the mass and air.

As an engineless roller coaster moves around a track, its speed increases as it moves downward and decreases as it moves upward. Its total energy E = KE + U_g is constant but its potential energy U_g and kinetic energy KE are continually changing. As U_g goes up, KE goes down. Either might change in time or distance as shown in the following plot.

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A mass can also oscillate from side to side along the inside surface of a bowl. Work must first be done to lift the block up one side of the bowl. The raised mass then possesses stored gravitational potential energy due to its height above the ground. If the mass is then released, it will slide down the surface of the bowl, exchanging its gravitational potential energy for the kinetic energy of motion. The mass gains speed, reaches the bottom of the bowl, and then moves up the opposite side of the bowl. Just as occurs in the pendulum, the energy mixture alternates between potential and kinetic. As the mass moves, it is doing work against friction and so will eventually stop moving. Skateboaders move within a bowl-shaped ramp.

Example:

The speed of a ball increases as it rolls down an inclined plane.

Example:

The speed, kinetic energy, gravitational potential energy, normal force, and acceleration change as a mass slides along hills.

Example:

Gravitational potential is converted into kinetic energy of motion as a skier slides down a hill.

As a bullet is being propelled down a barrel, the expanding gas of the gunpowder explosion is supplying a force F that does work on the bullet. This force is decreasing with distance during the gas expansion. A longer gun or canon barrel allows the expanding gas to do work through a greater distance and hence result in a higher kinetic energy for the bullet.

When a bullet is shot into a box of sand, its speed and kinetic energy continually decrease as it does work (W = Fx) at a known rate while boring into the sand. By measuring the bored distance, the initial kinetic energy can be calculated.

Student:

Try some of Glenbrook’s energy problems and think about their energy barcharts.

Student:

Discuss the flow of energy in these systems by Judson Wagner.

Example:

When a pendulum string is blocked by a peg.

Meteorites bore into the earth during a collision but their typically approach speed of 50,000 mph is so great that the asteroid is usually heated, melted, and vaporized during the collision. As the crater is formed (from a Science Fair paper by Kristyn Rodzinyak), material is ejected outwards, traveling hundreds of kilometers in the largest collisions. By the way, meteorites are more frequently microscopic in size. These create havoc with spacecraft and space-born instruments.

Student:

Calculate the energy and power of an asteroid hitting the Earth. Here is an animation of a meteor hitting the ocean near New York City. Here is an animation of a tsunami propagating away from a meteor impact

Comets sometimes collide with the Earth. Here is an animation of the KT-impact that may have caused the extinction of the dinosaurs. Throughout the surface of the Earth, a buried layer of iridium, which is a component of comets, has been found that dates to the time of this impact and the disappearance of the dinosaurs. (Could it instead be that alien sports hunters used iridium bullets to wipe out the dinosaurs!) Scientists estimate that the energy from this collision was about 10,000 times larger than the energy from all of the world's nuclear weapons. About once per year, a much smaller but still massive 20,000-ton asteroid burns up in the atmosphere. In the year 1908 an extensive forest area of Siberia was damaged by an explosion of unknown origin, speculations concerning its cause range from antimatter to asteroid impacts.

When asteroids having a diameter of one kilometer (0.6 mile) or more collide with the Earth, the collision might throw enough dust into the air to cause darkness for over a year. In addition, several years would elapse before the dust would settle back to the ground and stop blocking sunlight. The darkness and cold would cause the death of many plants and in turn, result in the death of the animals that eat the plants–and in the animals that eat these animals. Such a sequence of events might lead to the extinction of a large portion of the species of life on the Earth. In fact, there have been five such extinctions where 50% to 90% of the Earth's species have suddenly disappeared. (Visit here for lists and video of today’s endangered species. Visit here for an international comparison of numbers of endangered species.) These extinctions may be due to asteroid or comet collisions or they may be due to rapid changes in climate.

A flexible golf club also stores energy that results in a higher speed for the ball being hit by a golfer. The golfer applies a force though a distance to do work on the accelerating club. The impact of the club deforms the ball, which briefly stores elastic energy.

During part of each stride, a running Cheetah stores some energy in its flexible spine. This energy is released during the right portion of each stride to enable the Cheetah to run faster than any other animal. They run as fast as 30 m/s (70 mph).

Grasshoppers, fleas, and locusts and such store energy by stretching the rubber-like protein called reslin. It takes some time for this stretch to occur, so the animal must pause between jumps. The time required varies from 0.1 to 20 seconds, depending on the species. When the stretch is complete, the energy is released all at once in as little as 0.006 seconds, launching the animal into the air. Locusts leave the ground at 3.2 m/s = 7.2 mph and jump through a range of r = Vo²/g sin(2θ) = 1 meter. It can jump 0.5 meter vertically, which is about the same height attained by a person. The locust jumps at an angle of 45° to maximize its range.

Demonstration:

Hold two unequally-sized, elastic spheres touching together with the smaller one above the larger one and then drop both at the same instant. When the two hit the ground the upper ball will bounce extra high. During the collision at the ground, the surface of the both balls are elastically deformed slightly at their point of contact, storing elastic energy. This energy gives the upper ball an extra kick that increases its kinetic energy. This is also a model of the supernova explosion that ejects a star’s outer surface during a rebounding oscillation.

A spinning wheel stores rotational energy. (This is the purpose of a mechanical flywheel.) After work is done to get a heavy wheel spinning, the wheel can be stopped, for example, by pressing a metal bar against it. The metal bar will heat up as the wheel slows, converting the rotational energy into thermal or heat energy within the bar. The rotational energy of the spinning wheel can instead be converted into linear kinetic energy. If a tire is spinning in midair on a stick poked through its central axis and then the wheel is placed with its tread against the ground, that rotational energy will be converted into kinetic energy ½mv² as the wheel begins rolling along the ground.

When we sit in a playground swing, how do we get it to move and oscillate? We first lean back, lowering our head while raising our feet. We have raised our center of mass by pulling down on the rope, applying a force through a distance. We do work to raise our center of mass and increase our gravitational potential energy. We repeatedly do a bit of work at the right time within each oscillation and build the amplitude of our swing.

Similarly, primates swinging through the trees do a bit of arm work W = Fx to raise their center of mass when passing through the lowest part of their arc and then drop their center of mass when grasping a branch for a moment at the top of their swing. They sort of throw themselves more quickly through the trees. The arm work increases their speed.

We see that there are many forms of energy. Physicist Richard Feynman said that “it’s hard to say what is energy, but it occurs in many forms.” He said this is similar to the way in which a child might place some blocks under the bed, some in a covered box, and some on the couch. We can run around the room counting the blocks and we can move some from one place to another to change the individual counts, but the total block count does not change.

Energy is used to do work against friction. Air resistance occurs as a moving object collides with pieces of air. The collision increases the speed and kinetic energy of the air pieces but decreases the speed and kinetic energy of the moving object. Car tires get hot doing work against ground friction. Suppose we stir a bowl of water for a few minutes. This increases the kinetic energy of the pieces of water and increases the temperature of the water. Do you believe that shaking a can of sand for a few minutes will heat the can? When we throw mud or spaghetti against a wall, all of the kinetic energy is converted into the energy of sound and heat. The total amount of energy is always conserved, but energy can be converted into many different forms.

CQ:

Discuss work to increase the kinetic energy of pitched ball and of a swung bat. Discuss the flow of energy as the bat hits the ball and then as the ball flies through the air.

Example:

Let’s consider energy and work as a spring launches a mass up a frictional hill.

Example:

Light has energy also. Suppose a cubical box having sides of length 1-meter is lined with inward-facing mirrors. If a light bulb is placed in this box, turned on, and then turned off, will the insides of the box remain lit? Each reflection absorbs some light energy, say 1%. After one bounce the remaining light energy is 0.99 of original. After two bounces, it is (0.99)(0.99)=0.99², and after n bounces, a fractional amount (0.99)ⁿ of the energy remains. For n = 10000 bounces, 0.99¹⁰⁰⁰⁰ = 2.2 x 10^-44 will be the fraction of remaining energy. This is an exponential decrease in remaining light. Since light moves at the speed c = 3x10⁸ m/s, it reflects 3x10⁸ times per second in this cubicle box. The fraction (0.99) raised to the 3x10⁸ power is pretty close to zero. All of the light is absorbed within a fraction of a second.

In the Force Chapter, we saw that basic physics is all that is needed to model complicated systems composed of many interacting parts. Here are some examples from the

Lawrence Berkeley Laboratory Visualization Group, The Taiwan National Center for High-Performance Computing, and the Theoretical & Computational Fluid Dynamics Laboratory.

Energy and our body

The operation of our hearts, livers, muscles, and brains and such require energy at a rate of about 100 watts–even while a person is motionless. How much power is one hundred watts? It is the power needed to lift fifty kilograms up a distance of two meters every second–or in the old-fashioned English units, one hundred pounds being lifted six feet every second. It would be difficult to keep up that pace of mechanical work for very many minutes. What do we do with our 100 watts? In Table 2 of the report Basal Metabolic Rate in Man, J.V.G.A. Durnin explains that

25% of our energy is used by muscles and the heart

19% brain (independent of concentration level)

27% liver and spleen

10% kidneys

19% heating, digesting and all else.

ATP molecules are energy packets that power much of an operating creature. As these molecules are either constructed or utilized, about one-third of the involved energy is released as unused or waste heat. Have you noticed that you are warmed just after eating? Energy is being released as the molecules of ingested food are being broken down. (By the way, plants obtain their energy from the sun, and hence, so do the creatures that eat plants.) We are also warmed while exerting ourselves because of the energy lost as ATP is providing the energy needed for a specific task. This becomes heat that must be radiated away from our surface. (Architects plan for people to provide one-fourth of the heating in a high-occupancy building.) For example, when an animal synthesizes glucose to store energy in a molecule of ATP, 30% of the reaction’s energy is lost as heat to the surrounding materials; when a muscle contracts by using the energy stored in ATP, only 30% of the available energy goes into the motion of the muscle while the remainder is lost as heat A creature’s heat retention increases with its volume while its heat loss increases with its surface area. The larger the creature, the more numerous are its cells, and the more energy that creature will need. Metabolism is the total of all chemical processes occurring within an organism.

Since each liter of oxygen reacting with body fat releases 20,000 Joules of energy (see page 15 of Alexander), metabolism is measured by measuring oxygen intake while a masked animal–for example, an elephant– is doing various activities. (The mouth and nose are covered so that oxygen is inhaled only through a meter-equipped tube.) Langman reports that the energy per second used in walking is maximum at about 1 m/s in both elephants and humans. (Some anthropologists have postulated that our first bi-pedal ancestors lost their hair because walking generates a lot of heat, as each of us knows.) Metabolism can also be measured in the physics lab by surrounding a “volunteer” with ice and measuring the resulting amount of ice that has been melted into water. Across many species, the surface area of animals varies as the 0.63 power of their body mass, and their basal or resting metabolic rate varies as the 0.75 power of body mass, which is Kleiber’s law. The Science Magazine discusses other scaling laws. Radhakrishnan also has a comparison of the energy used by swimming, flying, and running animals.

Space-walking astronauts are necessarily equipped with their own oxygen supply, making the rate at which they breathe oxygen readily and continually measured while they go about their activities. J M. Waligora and D.J. Horrigan discuss the measured heart rates and calculated metabolic rates of the Apollo 15 Commander during EVA-1.

In their report The mechanics of six-legged runners, Full and Tu explain that despite differences in body form, the mass-specific energy (0.9J/kg*m) that an animal uses to move a given distance is the same for cockroaches, ghost crabs, mammals and birds. Similarities in force production, stride frequency and mechanical energy production during locomotion suggest that there may be common design constraints in terrestrial locomotion that scale with body mass and are relatively independent of body form, leg number and skeletal type.

Chemical reactions are always temperature dependent. Biochemical reaction rates (metabolic rates) increase by 10% with every 10-Centigrade-degree increase in temperature. (When we have a fever, our temperature raises by 1° Centigrade.) Since metabolic rates decrease by 30% per Centigrade degree, hibernating animals lower their body temperature. Since our metabolic rate increases after a protein-rich meal, we feel warmer after eating.

In the year 1919, J. Harris and F. Benedict published their report A biometric study of basal metabolism in man. They measured the age, height, weight, and basal metabolic rate of a large number of persons and then fit the data with the so-called Harris-Benedict Equation. The basal energy needed for men is

66.5 + (13.75 x weight in kg) + (5.003 x height in cm) - (6.775 x age),

66.5 + (6.25 x body weight in lbs.) + (12.71 x height in inches) - (6.775 x age in years).

For women it is

655.1 + (9.563 x weight in kg) + (1.850 x height in cm) - (4.676 x age),

655.1 + (4.35 x weight in lbs.) + (4.699 x height in inches) - (4.676 x age in years).

Your daily activities require perhaps 20% of this amount, so that your daily caloric needs are 1.2 times your basal rate. The calculator linked at Cornell University Pediatric Critical Care includes the extra energy needed per day while you are sick. Notice that it takes extra energy to rebuild tissue while recovering from a sunburn, which is why a sunburn makes us tired.

People weighing 120 to 150 pounds need only 1300 to 1600 Calories per day, while a person weighing 200 pounds needs 3400 Calories per day. As weight decrease, so does the amount of energy needed to sustain that diminishing weight–making weight loss increasingly difficult. Food labels in the U.S. say that an average person needs to eat about 2,000 Calories/day (10.5 million J/day), but the average person in the U.S. eats 3,600 Calories per day. On the average, those of us in the U.S. should eat about half as much as we are eating. A restaurant-sized plate of food provides a day’s worth of energy in a single meal. About 80% of the trouble with our weight is due to portion sizes–the lack of exercise accounts only for the remaining 20% of the problem’s cause.

Using the values for your height and age, you can choose how much you want to weigh by eating the number of calories indicated by this formula. No matter what your starting weight is, after some months you would weigh the amount given. The amount we eat is five times more influential on our weight than is our activity.

Remember that one “Big C” Calorie = 1000 “Little C ” calories, and that one “Big C” Calorie = 4,187 Joules but one “Little C ” calorie = 4.187 Joules. We store an energy of 270 “Big C” Calories = 1,130,000 Joules per ounce of fat (4,300 Calories per pound). Each day, we eat about 10 handfuls of food, and each handful averages 200 calories. There is a factor of only 2 to 5 (rarely 10) in calories per handful (or gram, ounce, pound, or ton) between low and high calorie foods. We get a day’s supply of energy by eating either one pound of meat or 6 pounds of potatoes. The U.S. Department of Agriculture lists the caloric, fat, and nutritional contents of most every food. By the way, here is a very long list of the ingredients in tobacco cigarettes, including everything except nicotine.

Reducing food intake by 1000 Calories per day, results in a weight loss of

(1000 Cal/day)(1 ounce/270 Cal)(30 day/month)(1 lb/16 ounces) = 7 lb/month.

This means that a person will lose 7 pounds per month by dropping 1,000 Calories per day. Or, in the other direction, I would gain only 7 lbs per month (84 pounds per year) if I eat two pints of ice cream per day instead of just one.

Example:

If your normal energy usage is 2500 Cal/day, how long do you have to diet at 2000 Cal/day to lose 10 lbs (4.5 kg)? This is a decrease of 500 Calories per day. The number of Calories in 10 pounds of fat is

(270 Cal/ounce)(16 ounce/lb)(10 lb) = 43200 Calories.

To lose 10 pounds, the number of dieting days is then

( 43200 Cal ) / ( 500 Cal/day ) = 87 days, which is an eternity.

Muscles usually work slowly for many minutes. They use oxygen to retrieve stored energy from fat. Anaerobic muscles are used for short bursts of work and get energy without using oxygen, instead converting glucose to lactic acid. In fish, for example, some muscles provide sustained swimming while anaerobic muscles provide short bursts of speed.

We saw above that the construction of ATP is 70% efficient and that the conversion of its energy into muscular motion is 30% efficient. The product of these two efficiencies is 21%, showing that the efficiency of our body to convert food into mechanical-muscular work is about 20% at most.

After eating 500 Calories (2,100,000 J), which is 2 handfuls of food or 2 candy bars, how much work can we do? We will be able to convert about 20% of that energy, which is 100 Calories (400,000 J) into mechanical-muscular work.

Example:

How far will 100 Calories (400,000 J) enable us to push a 10-kg (22 lb) block along a carpeted floor whose coefficient of friction is 0.9? The work done against friction is

W = Fx = μ_Kmgx = 400,000 J.

Solving, we get x = 4,500 m. Do you believe that? Try to put yourself in this place and imagine the difficulty of pushing 22 lbs for 4.5 km–yet that requires only 500 Calories of energy input and 100 Calories of work output.

Example:

A 68 kg person might take one minute to walk up stairs that rise ten meters in elevation. The work done per minute is then W/t = mgh / t = ( 6664 J/min )( 1 Calorie / 4187 J ) = 1.6 Cal / min. This is a devilish amount of work If the efficiency of the person is just 10%, than he or she will burn 10 times that many Calories, or 16 Cal/min. This is about the same value obtained through oxygen-intake measurements as reported by the Amateur Athletic Foundation in their table of “calories used per minute by a 150 pound (68 kg) person doing various activities.” This shows that all of the energy is accounted for and that the entire process–from food to muscle to motion–is quantitatively understood.

Example:

How far can a person (m = 65 kg or 143 lb) vertically climb with 100 Calories (400,000 Joules) of energy?

W = Fx = mgh gives h = 628 meters = 2000 feet.

It takes a lot of exercise to burn just 500 Calories. Remember that we turn at best one-fifth of the energy content of food into usable mechanical work.

Students:

Bring in a food wrapper and convert the Calories indicated on its label to hours spent swimming and running and such. For example, the label on a can of spinach says that there are

( 45 Cal/ Serving )( 3.5 Servings / ounce ) = 11 Cal / ounce.

But we have a 20% efficiency in converting this input energy to muscular-mechanical work. Using the results of the previous examples, an ounce of spinach would enable us to climb a vertical distance of ( 0.2 )( 2000 feet )( 11/100 ) = 44 feet.

A candy bar having 250 Calories per 2.5 ounces, which is 100 Calories/ounce, would enable us to climb ( 100/ 11 )( 44 feet ) = 400 feet. How far would a spinach-flavored candy bar enable you to climb?

Many sources list the measured energy usages for various activities. The Harvard School of Public Health website has a table of “Energy requirements of common daily activities” such as playing the piano or vacuuming and a table of “Time for an Average 150 lb Adult to Burn 150 Calories” while walking or mowing the lawn and such activities. On page 93 of Medical Physics, Cameron shows that we lose weight by attending lectures while awake. the National Institutes of Health on-line publication Fitness and Exercise has a table of calories burned during various tasks.

Alexander shows that it takes 150 joules/meter to walk 1 m/s and 300 J/m to walk at 2 m/s. Above that speed it takes less energy per meter to instead run. It takes 300 J/m to run at a speed of 2 m/s or nnn to run at a speed of 4 m/s. More distance covered means more total energy used at the higher speed. When running, we kind of bounce a springy foot off the ground by temporarily storing and retrieving energy in and from tendons. Cheetahs and greyhound dogs store and retrieve energy in their backbones.

Alexander shows that the metabolic rate while running equals the metabolic rate while standing + cv, where c is a constant. The units of c are energy cost per meter, which differs for each species. The ratio c/m is found to be proportional to mass to the two-thirds power.

Animals run in dynamically similar manner when they have similar Froude numbers, which is the combination N_F = v²/(gl) where l = leg length. Animals change from walking to running at a Froude number of one half.

Our legs sort of act as a pendulum when we swing them forward. Since the period of a pendulum is T = 2π √(l/g), a person having legs of length l = 1 meter will have a natural period of T = 2 seconds. Children have shorter legs (smaller l) and have to run to keep up with an adult who is walking. When your walking speed exceeds one step per two seconds, which is 2-2.5 m/s or 4.5 - 5.5 mph) then you'll have to begin running, which lifts a leg rather than letting it swing. (A tree-swinging primate is also a pendulum.) Our slightly bent-while-running legs enable us to run faster because our legs have less rotational inertia.

Large animals use straighter, stiffer legs to directly support their large weight. Small animals can crouch while they run because they have less weight to support.

When an animal jumps, it does work by pushing against the ground through a distance. This work increases the kinetic energy of the animal. This kinetic energy ½mv² is converted to gravitational potential energy mgh as the animal rises to a height h. We have W = Fx = ½mv² = mgd. When a person jumps, the speed with which he or she leaves the ground is typically v = 3 m/s and the height attained is h = 0.45 m.

L. Gladney discusses the work, power, and trajectory of a jumping flea. A flea (m = 450 micrograms) accelerates by pushing against the ground for 0.001 s. This acceleration of 100g gives it a launch speed v > 1.6 m/s, which makes for a strong wind as it leaves the ground. The flea then rises to a height of h = 0.035 m, which is 100 times its height. Leg muscle is known to develop a power of 60 W/kg. Here is a video of a jumping flea.

Biologist measure forces and energies in every species. Here are a few reports. In the report Inexpensive Load Carrying by Rhinoceros Beetles, Roger Kram of the University of California at Berkeley describes the measured energy consumption of beetles. Gary Ritchison of Eastern Kentucky University plots energy usage versus body weight in various species of birds in the report Avian Energy Balance & Thermoregulation.

The oxygen usage of an 87 gram fish shows that is uses 10 milliwatts when still and 60 milliwatts when swimming at a speed of 0.64 m/s. The speed-burst of the fish occurs as it pushes a mass of water equal to three times its own mass. In this action-reaction situation, the pushed water is angled mostly backward and moves at one-third the forward speed of the fish.

Example.

Let’s discuss the flow of energy that occurs as a pole vaulter runs, sticks, rises, and falls. Chemical energy is stored within the pole vaulter. As she begins running, she is using her leg muscles to push against the ground, increasing her speed. Stored chemical energy is being converted into kinetic energy. A 65-kg person running at 10 m/s has kinetic energy ½mv² = 3250 Joules. She then places the pole into a catcher and begins exchanging kinetic energy for the gravitational potential of her rising position. As the pole is being bent, it is storing elastic potential energy. At this time, portions of the initial energy have been converted into both gravitational and elastic potential energy. When her trajectory has reached about half of its maximum height, the pole has ben bent by a maximum amount and its stored energy begins to go into increasing her gravitational potential energy by a larger amount than would have been possible without this added boost. Her maximum height is reached as all of the elastic energy has been converted into gravitational potential energy. A 65-kg person that is 5.1 meters above the ground has potential energy mgh = 3250 Joules. The stored, gravitational potential energy of the vaulter is converted back into kinetic energy during the fall, and this energy is converted into the potential energy of the compressed cushion. At last, the energy has been converted into heat within the cushion–plus a tiny amount of sound energy. Our hearing is very sensitive. The energy content of a year’s worth of spoken words would boil about one cupful of water.

Going backwards, the energy that enabled the pole vaulter to run and jump came from the conversion of chemical energy that had been stored in a few grams of peas that had been earlier eaten. The energy content of a gram of peas, or most any vegetable, is about one Calorie = 4,187 Joules per gram. Only 10% of the food’s energy was converted into useful muscle motion. To do 3250 Joules of mechanical work, a person must eat ( 3250 Joules / 4,187 J/g ) / ( 0.1 efficiency ) = 7.8 grams of peas. That is, the person consumed 7.8 grams of peas that had a total energy content of 32,500 Joules and converted 3250 of those Joules into energy of motion. The person stores the chemical energy of the peas as ATP molecules within cells. About one-third of the chemical energy of the pea material is lost to heat within the person during the assembly of ATP molecules and only one-third of the energy successfully stored in ATP molecules is converted into useful mechanical motion. The rest of the energy dissipates as the heat that warms us when we eat and when we run.

The pea plant converts received sunlight energy into stored, chemical energy. About 10% of the sunlight energy received is converted into stored, chemical energy. The plant received 325,000 Joules of sunlight energy and converted 10% of that, which is 32,500 J, into stored chemical energy. Sunlight energy is a by-product of the fusion of four hydrogen nuclei into two helium nuclei. (By the way, the proper mis-pronunciation of “helium nucleus,” is “helius nucleum.”) About 4.1x10^-12 Joules of energy are released by the fusion of four hydrogen nuclei. The energy received by the pea plant occurs when the energy of 325,000 Joules / ( 4.1x10^-12 Joules / 4 hydrogen nuclei ) = 8x10¹⁵ hydrogen nuclei is entirely converted into sunlight. In his equation E = mc², Einstein showed that mass is just another form of stored energy. The energy released during fusion had been stored as some of the mass of the hydrogen nuclei.

We see that the flow of energy for the pole vaulter includes conversions of mass energy, fusion energy, light energy, chemical energy of peas and ATP molecules, kinetic energy of motion, potential energy stored in the springy pole, gravitational potential energy, another round of kinetic energy and then potential energy in the springy cushion, and finally some heat and sound energy.

Chemical processes involve the electrical force among atoms. Electrical energies are many orders of magnitude greater than the energy of motion of a person. The energy needed to drive the electrical interactions of the molecules within each cell is much more than the energy needed to mechanically move the entire person. The chemical energy contained in a few grams of peas enable a 65-kg person to run and jump. We see that chemical-electrical processes involve much more energy than is involved in the motion of a person. When mechanically moving the body, about 50 Joules per second is the maximum mechanical work per second that a person can sustain for several minutes, but the electrical-chemical processes occurring among the molecules of our cells use energy at the rate of 100 Joules per second. Our 2-watt heart does a billion Joules of work in a lifetime.

The most important point of the physics course is that the universe consists of little besides the flow of energy. Every biological, chemical, and physical process involves the flow of energy. Energy is hard to define or to picture, but we see that energy appears in many forms and that every process involves the flow of energy from one form to another.

Energy sources for our civilization

Einstein found that mass is a lot of stored energy: E = mc², where the speed of light c = 3 x 10⁸ m/s. Mass-energy is taken up or given off during nuclear reactions. For example, four hydrogen atoms are crushed together in the center of a star by the weight of the rest of the star matter above. The mass of a hydrogen atom is 1.67345 x 10^-27 kg, and the mass of a helium atom is 1.64647 x 10^-27 kg. Comparing these two numbers, we see that helium has less mass then did the four hydrogen atoms. It’s convenient to specify mass in Atomic Mass Units (AMU), where 1 u = 1.660566x10^-27 kg. The periodic table contains masses given in AMU. The lost mass is then

m_final - m_initial = mass of helium atom + mass of two more electrons - 4 ( mass of 1 proton plus 1 electron)

= [4.00260 + 2(0.000549) - 4( 1.007276 + 0.000549 )]u = 0.02762 u.

= ( 0.02762 u )( 1.660566x10^-27 kg / u ) = 4.6 x 10^-29 kg.

The mass difference is released energy

E = mc² = ( 4.6 x 10^-29 kg )( 3 x 10⁸ m/s)² = 4.1 x 10^-12J per fusion reaction.

The power output of the sun is 3.9 x 10²⁶ watts. How many kg/s of hydrogen is being fused?

( 3.9 x 10²⁶ J/s )( one fusion / 4.1 x 10^-12 J )( 4 hydrogen atom/fusion )( 1.67345 x 10^-27 kg/hydrogen atom ) = 6.4 x 10¹¹ kg-hydrogen/s.

The mass of the sun is 2 x 10³⁰ kg, not all of which is hydrogen. If it were then the sun would last

( 2 x 10³⁰ kg ) / ( 6.4 x 10¹¹ kg-hydrogen/s ) = 3.1 x 10¹⁸ seconds = 10¹¹ years.

This is 100 billion years, but the sun will last about one-tenth this time.

To provide today's global power usage of 12 x 10¹² J/s would require

( 12 x 10¹² J/s ) / ( 4.1 x 10^-12 J per fusion reaction ) = 2.9 x 10²⁴ fusions/second, and

(2.9 x 10²⁴ fusions/second)(4.6 x 10^-29 kg/fusion) = 0.00013 kg/s = 4100 kg / year.

This is the energy equivalence of the lost fuel mass of 4100 kg, which is a fraction of about 0.027/4 = 0.007 of the initial deuterium mass that was 4100 kg / 0.007 = 600,000 kg. That is, starting with 600,000 kg of deuterium, the fusion process will result in a loss of 4100 kg per year which releases enough energy to power our global civilization.

There are many fusion reactions. To provide power for our global civilization, a promising reaction involves the fusion of deuterium with tritium. Deuterium is a hydrogen atom that has two neutrons instead of one (it’s often called- “heavy water”), tritium has three neutrons. One in 6,000 hydrogen atoms is deuterium. There are 30 grams of deuterium per cubic meter of seawater and fusing this deuterium with tritium gives as much energy as is obtained from 240 tons of coal.

The Palo Verdes nuclear powered electrical generating plant produces 1500 megawatts of energy–enough for 1 million people to have 1500 watts each to continually run a stove. Since we don’t run stoves simultaneously nor continually, 1500 megawatts is enough power for 5 million people through average day. Nuclear powered electrical generating plants convert a portion of the mass of uranium or plutonium fuel into energy. A nuclear plant generates 1500 megawatts of power from a piece of uranium that is the size of a basketball. It is mind boggling that so much energy can come from such a small amount of material.

Meanwhile a coal-fired plant burns one or two trainloads coal per day (100-200 train-car-loads, each holding ninety tons of coal) and so emits a great deal of pollution into the air. One quarter of the energy used by such a plant involves the transportation of the coal to the plant. According to the Union of Concerned Scientists, each of the 600 coal-fired, 500-megawatt plants in the U.S. burn about 1.4 million tons of coal per year, see here.

A pea-sized piece of uranium runs a nuclear-powered submarine for a few years. One scientist calculated that a grain-sized amount of nuclear fuel would power an automobile for 100 years. Can you imagine not having to stop for gas in your entire lifetime and not generating a lifetime of pollution from the combustion of gasoline in your car?

In the U.S., electrical generating plants that burn coal or natural gas produce half the greenhouse gasses emitted into the atmosphere, and automobiles produce another quarter of those gases. Through the last couple decades, U.S. plants have been switching from coal to natural gas. This has increased the demand for natural gas, whose price has tripled in the last few years. How do the damages caused by fossil-fuel-fired and nuclear-fired power plants historically compare?

The International Atomic Energy Agency reports that as of January 2006, there are 443 nuclear power plants in operation with a total capacity of 370 gigawatts and there are 24 nuclear power plants are under construction. The agency reports the number of nuclear reactors in each nation. The International Atomic Energy Agency reports that the percentage of electricity generated by nuclear power is about 20% in the U.S. but 80% in France. There are 17 nations who have a larger nuclear percentage of electrical energy generation than occurs in the U.S. The agency’s 2003 report Energy, Electricity and Nuclear Power Estimates for the Period up to 2030 shows the percentage of electricity generated by nuclear power in various nations, see Figure 1 in this report. Scientists and engineers in France are experimenting with nuclear waste in a search for ways to recycle that waste. The U.S. wants to pile it up in Nevada at the rate of several truckloads per year (not trainloads per day). Radiation is the evil word in monster movies and in commercials with influential movie stars. The nuclear fear that exists in U.S. does not occur in France.

In the energy crises of the 1970s, the U.S. was importing 30% of the oil it was using. At that time, politicians made much noise about the dire consequences of this foreign reliance. What has been the result of their speeches? Today, the U.S. imports 60% of the oil it uses. Our political and corporate leaders could not be doing us worse. The nation has had no energy plan to prepare us for the future. Why have we not incorporated passive solar collection into every home and placed solar-powered water heaters on every rooftop? Why isn’t there a wind-powered electrical generator on every rooftop? The Solar Cooking Archive explains how to cook food using sunlight.

Is nuclear energy evil or does it solve our energy and war problems? We better investigate our options thoroughly because much is at stake. If we don’t investigate thoroughly then we might make the wrong choice and end up causing unnecessary harm to the lives and environment we are trying to protect.

As the nuclear reactions comprising radiation take place in the interior of the Earth, the Earth is heated by the mass-energy being released. Without the heating from this radiation, the Earth would cool off in 20 million years, but it has been kept warm through 4.5 billion years. Volcanoes get their heat energy from the radiational heating of the earth’s interior. Wooden homes have less radiation than do homes made of earthen brick which naturally contains radiation. Underground heat also powers geysers such as Old Faithful. The heat of the earth’s interior can also be tapped to power steam turbines that in turn generate electricity, as is done in geothermal plants. In fact, any temperature difference can be tapped as an energy source, including the difference in temperature between the ocean depths and surface. Such a tap is to be built off Hawaii.

France and other nations harness the energy of ocean currents by using tidal generators. The Bay of Fundy in Canada has tides that move through a vertical distance of 17 meters. These tides are caused by a resonance with the periodically recurring pull of the moon, sort of like the way a person in a bathtub can make the water slosh back and forth. A tidal generator has been built there. There are a variety of renewable energy sources, including solar energy.

The Sun powers the Earth’s life and its weather

Since energy is about all there is to the universe, it is worth a day of class time to explain the big picture of energy. The Sun converts energy stored as mass into motion, heat, and light energy. Sunlight spreads out in all directions. The Earth receives two-billionths of the Sun’s light, and of this received energy, 23% evaporates water to drive the Earth’s water cycle 2 3, 1% drives the winds, and 0.023% powers photosynthesis and all life on Earth. Plants are stored sun-energy. Some animals eat the resulting plants while other animals eat the animals that eat the plants. The plant and animal foods we eat provides the energy needed to breathe, walk, think, love, learn, enjoy, and talk. Fossil fuels result from buried plant and animal remains. The electrical energy used in our homes and factories is converted fossil fuel, water, and wind energy, all of which are stored sun-energy. In addition to these energy sources, nuclear powered electrical generating plants convert energy that had been stored as mass. Our civilization runs off all this energy. Each home today uses about one thousand times the energy used in a home just two centuries ago. When people successfully harness fusion power, the power available to each home will soon be 1,000 times as much as we have today. With megawatts of power available to each home, machines can combine carbon and hydrogen and such to make edible organic chemicals and even change “lead into gold.” With such power available to civilization, will anyone work in a factory? What will life be like?

About 0.0023% of sunlight striking the earth powers photosynthesis and all life on Earth. Of the sunlight falling on the Earth that is absorbed by plant life, about 10% of this energy is later consumed by herbivorous animals, such as rabbits, and 10% of that energy is consumed by the first layer of carnivorous animals, such as coyotes. About 10% of that energy is consumed by the next layer of carnivorous animals, such as mountain lions. In summary, about 10% of the energy of each tropic layer powers the next higher level. The sun is the source of all of this energy.

The surface of the Earth is heated by the sun. If the Earth did not have an atmosphere, then its surface temperature would vary through day and night time extremes, as does that of the moon. The Earth’s atmosphere absorbs and holds a sufficient portion of this energy to keep the average surface temperature at about 283 K or 15̊C (59̊F). The equilibrium temperature of the atmosphere depends on the chemicals contained within it and also on the number and type of clouds.

The Earth's outer atmosphere, above the clouds and weather, receives an energy of 1360 W/m² from this sunlight for a total of twenty million-billion watts. This is equivalent to 200 million-million, 100-watt light-bulbs and is 20,000 times as much power as the 12 trillion watts used by our entire civilization of six billion persons–or 100,000 times the power used by the people of the United States. (For further comparison, a single hurricane generates ten times the power used by the United States while a one-megaton nuclear bomb would supply only one-ten-thousandth of the U.S. needs.)

Portions of this energy are reflected, transmitted, or absorbed. About 200 W/m² reaches the ground in mid latitudes on cloudless days averaged over 24 hours through the year. The sunlight hitting any particular spot on the surface of the Earth varies with latitude 2 and by the minute, day, and month. NASA calculates that each square centimeter of surface area absorbs four times as much sunlight energy during long summer days as occurs during short, winter days when the sun is low. This uneven, solar heating and the rotation of the Earth drives the winds around the Earth.

Energy from the sun drives the weather and the seasons. To see the cause of the seasons, imagine the Sun and the Earth as two spheres placed on a table, each with a line painted around its center or equator. The Earth is placed to the right of the Sun. The center line of the Sun is parallel to the table top but the Earth must be tilted so that its center line points upward by twenty-three degrees from the horizontal table top. The Earth's axis remains tilted this way as it orbits the Sun. Light coming from the Sun always shines more directly onto the equatorial region but glances along the polar regions. One pole is tilted toward the Sun but the other is tilted away from it. This makes the regions near the equator warmer than the polar regions. Six months later, the Earth has traveled halfway around the Sun. In terms of our table-top model, we would slide the Earth around the Sun, being careful not to change the orientation of the Earth's center line, until it is on the left side of the Sun. The pole which had been tilted toward the Sun is now tilted away from it. This means that each pole drastically cools for a few months of each year while it is receiving no sunlight. The north pole receives no sunlight at all around January, while the south pole is in the dark around June.

Climate

The equilibrium temperature of the surface also depends on its reflectivity because water, land, snow, and desert each absorb and reflect differing portions of incident energy. Climate varies through the millennia because continental positions vary as plate tectonics carry the plates sometimes to polar and sometimes to equatorial latitudes. (See here for more about geological and astronomical factors in the climate of the Earth.)

As air circulates around the planet, it cools whenever it moves into a sunless, polar region and heats while in daylight, especially whenever it travels near the equator. The same thing happens to ocean water as it travels around the planet, moving between equatorial and polar regions. Water circulates around the world’s oceans following paths largely determined by the current positions of the continents. Circulation patterns change as the positions of the continents change. When ocean currents flow from the equator toward the poles, they carry heat that warms the poles (air movements have a smaller role in moving heat from the equator toward the poles). The ability of ocean currents to move equatorial heat pole-ward changes as the location and shape of the continents change through time.

The Earth’s climate is also affected by the number of volcanoes around the world that are active at the same time. In the year 1815, a large volcano threw a lot of dust into the atmosphere that in turn blocked enough sunlight to cancel that year's summer. Larger volcanoes can cause several summers to be skipped and trigger a glacial advance, as has occurred in the past. In the Philippines in 1991, the volcanic eruption of Mt. Pinatuba released dust that blocked enough sunlight to cool the Earth's air by 0.5 centigrade degree (one degree Fahrenheit). A very large volcanic eruption that occurred 71,000 years ago may have caused a six-year-long winter and triggered a 1,000-year-long ice age.

The Earth’s climate is first of all driven by the Sun. Variations in the energy output of the Sun have been directly measurable for only the last twenty years. Satellites have found a 0.1% change. The Sun's magnetic activity varies with an eleven-year cycle and also a 100,000-year cycle. Mukul Sharma found the longer cycle when studying changes in the amount of radioactive beryllium-10, which has a 1.5-million-year half-life, produced on the Earth by cosmic rays. This amount depends both on the magnitude of the Earth’s magnetic field and on the magnetic activity of the Sun.

Several astronomical factors affect the Earth's climate. The 23-degree tilt of the Earth relative to its orbital plane results in the yearly seasonal changes with which we are all familiar. But the tilt of the Earth varies between 21.5 and 24.5 degrees on a 41,000-year cycle. The elliptical orbit of the Earth around the Sun slowly alternates between being more circular and less circular, and this 100,000-year cycle changes the distance of Earth's closest approach to the Sun and so changes the maximum amount of received sunlight. All these cycles are simultaneously occurring. Sometimes their effects cancel, sometimes they combine into a heating trend, and sometimes the combine into a cooling trend. The Earth’s temperature necessarily follows the net effect, but these astronomical variations alter only slightly the amount of received sunlight. Asteroid and comet collisions can instantly and drastically alter the Earth's climate.

When asteroids having a diameter of one kilometer (0.6 mile) or more collide with the Earth, the collision might throw enough dust into the air to cause darkness for over a year. (Click here for a video of a 1.5 kilometer wide satellite passing near the Earth.) In addition, several years would elapse before the dust would settle back to the ground and stop blocking sunlight. The darkness and cold would cause the death of many plants and in turn, result in the death of the animals that eat the plants–and in the animals that eat these animals. Such a sequence of events might lead to the extinction of a large portion of the species of life on the Earth. In fact, there have been five such extinctions where 50% to 90% of the Earth's species have suddenly disappeared. (Visit here for lists and video of today’s endangered species. Visit here for an international comparison of numbers of endangered species.) These extinctions may be due to asteroid or comet collisions, or they may be due to rapid changes in climate.

The total amount of water on the Earth has changed little through time. It is mainly found in the oceans or locked up in glacial ice, only 3% is held within rivers. But scientists have found that the sea level rises and falls through time as the volume of the Earth’s glaciers change due to global temperature changes. (The height of the sea is also affected by the volume of the oceanic ridges.) As glaciers appear, grow in time, and then melt and disappear, the Earth's ocean level rises and falls. Whenever there are large glaciers then there will be less water in the oceans. As glaciers have advanced and retreated, the ocean levels have been found to raise and lower by a 300-yard (300 meter) vertical distance. It has risen by 120 meters (120 yards) in the last 20,000 years. When the glaciers melt, a lot of water is temporarily held in many lakes. These lakes occasionally burst free, releasing huge torrents that create instant canyons. About 8,000 years ago, a single Canadian lake-burst released enough water to raise the level of the ocean by 20 to 40 cm (4 to 8 inches).

The glaciation found today in the northern and southern poles developed through two different continental movements: the separation of the Antarctic continent and the joining of North and South America. About thirty-six million years ago, the continents of South America and Australia separated from the Antarctic continent, which then drifted toward the southern pole. In addition, a circumpolar oceanic current developed that allows little equator-to-pole heat movement. The polar location of the Antarctic continent and the circumpolar oceanic current both enabled the southern ice cap to develop. The glacier of Antarctica averages 6,500-feet in thickness (2,000 meters) and account for 90% of all glacial volume. Greenland’s glacier accounts for another 9% of the total volume and mountain-top glaciers account for the remainder. The amount of water held in these glacial regions can be found here. (For a 3-D view of the Martian polar ice cap, see here.) Mile-thick glaciers can not form on top of the ocean surface. The sea-ice found at the North Pole of the Earth is only three meters (ten feet) thick. During the summer, it becomes 30-centimeters (one-foot) thinner. The sea-ice at the southern pole is only half that thick because it spreads more easily across the wide-open ocean. For more information, visit the NASA websites here and here. The NOAA website has an animation of the changes in sea-ice thickness through the last fifty years. Many other animations are here. You might also like to check the webcams placed at the north pole, see here, and the south pole, see here. The amount of sea-ice occurring at the north pole was indirectly enhanced by the joining of the North and South American continents, which happened about three million years ago, see here. When these two joined, they blocked an east-west flowing ocean current. The gulf stream that developed in its place carries moisture-laden air that increases precipitation near the north pole.

In the last two million years there have been about twenty cycles of glacial advance and retreat. These cycles have roughly followed a 100,000-year period and may be related to the 100,000-year cycle in the Sun’s magnetic activity. Within this more-lengthy period occurs shorter cycles of glaciation. In Northern Europe, some of these have been dated to 75, 65, 59, 40-29, 19-13, and 11-7.5 thousand years ago. Some relatively recent, large temperature changes occurred about 14,000, 11,500 and 7,600 years ago. Smaller and more recent changes include a warmer period during the years 900 to 1200 ad and a cooler period from 1450 to 1850, during which time Holland's canals and London's Thames river would freeze–the last time was in 1814. In the sixteenth century, Spanish Conquistadores encountered snow in Mississippi.

During a glacial maximum or “ice age,” summer temperatures are ten to twenty degrees Fahrenheit (five to ten degrees Celsius) colder than they are now. Four of the ice ages that occurred in the last one million years–the Nebraskan, Kansan, Illinoian, and Wisconsinan–were named for the most southerly advance of year-round ice. Sometimes the northern, year-round glacial region extends down to Britain and Kansas, while at other times there is no region of year-round ice anywhere on the planet. Since there is less year-round ice today, we are living in a relatively mild phase of an ice age. You can see the glacial retreat during from 18,000 to 8,000 years ago in the Midwestern U.S. by visiting here or here for the North America retreat. For an overview and movies, see here.

The last glacial advance began 130,000 years ago, peaked 20,000 years ago when one-third of the Earth's land was covered by ice, and has been in a steady decline since that time. This glacial extreme created a land bridge between North America and Asia and allowed many groups of us humans to migrate from Asia into the Americas. As the glacier retreated, the land bridge became submerged under the ocean. This process can be seen in the video Postglacial Flooding of the Bering Land Bridge: A Geospatial Animation made by the Institute of Arctic and Alpine Research at the University of Colorado. This video is available at their website. The institute also shows a plot of sea level changes through the last 20,000 years here. Rising ocean levels submerge flat islands and cause higher, coastal land to be stranded out at sea, as was the case for Britain. Visit here to see the ocean rise from ten to five thousand years ago, stranding Britain out to sea. In the distant future, the ocean level will again fall and Britain will rejoin the continent. The sea level changes with the Earth’s temperature.

For most of the Earth's history, the average year-round temperature throughout the planet was about 70 degrees Fahrenheit (20 degrees centigrade). There were no areas of year-round ice because wintertime temperatures were not much less than summertime temperatures. In fact, with no polar continents it didn't often get cold enough to snow even during the winter–as occurs today. Under those conditions, each region of the Earth received similar amounts of rainfall so that there were no extensive desert areas. Today, the deserts of the Earth cover about 20% of the surface area and reduce the amount of available farm land. During much of the past, the lack of desert regions meant that a larger portion of the Earth's surface could have been farmed (except that no humans were yet there to do the farming). Today’s year-round temperature is not so comfortable because we are in the middle of an ice age. We might be stuck with this cold weather, with regions of glaciers and deserts, for as long as Antarctica is parked over the south pole and for as long as there is decreased heat flow from the equator to the poles.

We see that there are a large number of variables affecting the Earth’s climate and temperature and that all these variables are simultaneously occurring. Each variable is at some time trying to cool the Earth while at other times it is trying to warm the Earth. If enough of the variables are in a warming phase then the Earth's temperature will increase, otherwise it will decrease; sometimes a temporary balance exists. About ten astronomical cycles are simultaneously contributing to the heating and cooling of the Earth. The two main factors are the heat output of the sun and the heat-holding properties of the Earth’s atmosphere, which raises the Earth’s surface temperature by fifty degrees Fahrenheit (twenty-degrees Celcius) as explained here. In addition, the reflective and absorptive properties of land, sea, and sky change as continents drift from equatorial to polar locations, as ocean currents allow or do not allow heat movement from the equator toward the poles, as the amount of cloud cover and the proportions of desert- and ice-covered land changes, as the number of dust-emitting volcanoes changes, as the chemical composition of the atmosphere changes and as manmade chemicals are added to the atmosphere. See here for an inventory of greenhouse gas emissions and sinks. For information about worldwide carbon dioxide emission, visit here.

Through the last few centuries of industrialization, we humans have been altering the chemical composition of the atmosphere sufficiently to change its absorptive and reflective properties. Many man-made chemicals, from carbon-dioxide to soot, are contributing to global warming. A presentation of the factors in global warming, including a plot of “Atmospheric Carbon Dioxide Concentrations From Ice Cores 1734 - 1983," is given here.The NASA/Goddard Space Flight Center, the SeaWiFs Project and ORBIMAGE, and the Scientific Visualization Studio have created the video SeaWiFS: NASA Carbon Cycle Initiative showing the seasonal changes in global atmospheric carbon-dioxide levels along with changes through the last fifty years and the last one thousand years. To view the clip online, visit here and search for SeaWiFS: NASA Carbon Cycle Initiative. Visit here to see a comparison of snow-accumulation with and without a doubling of the atmospheric carbon-dioxide level.

We don’t want to make a too-hasty conclusion about manmade global warming, but at the same time there is no reason to gamble needlessly with the Earth's ecological balance. Recent and cautionary data obtained from glacial drilling experiments show that a global transition from cooling to warming can occur in a time-span of just a few decades. Our environmental impact could go as far as to cause a massive extinction of species. Will the next generation of citizens decide to end pollution by requiring that each factory, home, and car emit nothing at all into the environment? Scientists and engineers would be thrilled to tackle the problem of designing factories, cars, and homes this way. Are factory owners willing to add to the original cost of building a plant and are consumers willing to pay more for products, or should we just spoil our own environment while we are here? Zero-emission designs mean that each factory will collects its waste products for use by other industries and that cars will have both a fuel tank and a waste tank. Can you design a tank that collects the exhausts of an automobile engine, and can these exhausts be exchanged at the gas station for further processing? By the way, our car engines consume about fifteen pounds of atmospheric oxygen to burn each pound of gasoline. The combustion products consist of water, carbon dioxide, nitrogen and nitrogen oxides. The atmosphere consists mostly of nitrogen (78%), oxygen (21%), and small amounts of argon, carbon-dioxide, and other gases (1%).

After talking about the effects of humans on our own environment, let’s talk about the direct effects of our environment on our size, shape, and color such that we are most able to remove excessive heat or cold. A warm object cools by releasing heat through its surface. An object retains warmth if it has lots of volume but little surface area. For this reason, the size and shape of humans varies with climate. At the warm, sunny equator we are tall and thin so that we are more easily cooled. In polar areas, we retain more heat by being shorter and rounder so that we have more volume and less surface area. We humans are also found to have darker colored skin when living near the equator and lighter colored skin when living near the poles. Dark skin helps reflect sunlight–especially ultraviolet light–while light skin absorbs more sunlight. Light skin is needed to avoid the rickets caused by low sunlight–as occurs in northern, cloud-filled latitudes. The color of our skin shows our relationship to the Earth and its latitudes. One anthropologist made a globe of the Earth with each region colored like that of local human skin. Humans are also about 10% smaller in height and size whenever we live in year-round highly-humid locations because the decreased sweat evaporation makes a larger volume harder to cool.

Energy use in the home, factory, nation, and planet-wide civilization

Our global civilization operates on 12 trillion watts, about one-quarter of this is used in each of China, the U.S., Europe, and the rest of the world. U.S. energy sources, consumption, history, and future are discussed by the Energy Information Agency (EIA) of the Department of Energy. Here is their overview. The World Energy Council has information about energy. Greg Bothun of the University of Oregon has lectures and weblinks for his online course in renewable energy sources. Gordon Aubrecht of Ohio State University is the author of Energy. His website has numerous facts about energy and society. The Departement de Recherche sur la Fusion Controlee has an overview of totals for each of today’s possible energy sources, see also here.

Energy used in a U.S. home:

50% heating

20% water heater

5% for each of cooking, cooling, tv, clothes washer/dryer, fridge/freezer, lights and misc appliances

You can reduce your home energy costs by half by making simple changes in lighting, heating, and cooling. A home energy audit analyzes your existing energy use and recommends changes. Audits are available online here. Enter your zip-code so that the program can look up your climate. You can tailor the audit by entering your home dimensions, window dimensions, and the number and type of lights and such. Here is another home energy audit. There are numerous, simple things that can be done to reduce the nation’s total home energy usage.

Notice that 20% is used in water heaters. Water heaters in the U.S. are keep water heated 24-hours per day though it is used only for a couple hours per day. Commonly in Europe, water is heated only on demand. Compare the energy consumption of U.S. and European water heating approaches. The European Union’s SAVE II Project promotes energy efficiency in circulation pumps, especially in domestic heating systems. See also, Technical Study on Improving on Electric Water Heater Efficiency for the Australian Greenhouse Office by Energy Partners in association with Sustainable Solutions Pty Ltd and The University of New South Wales, May 2000. The energy consumption of household appliances is discussed in the 2003 report Cool Appliances, Policy Strategies for Energy Efficient Homes by the International Energy Agency.

Energy use in U.S. by industry:

20% residential

15% commercial

40% industrial

25% transportation (of this 50% is autos, 15% trucking, rest is bus and plane and train and boat and such)

The consumption of each sector is further categorized here. How do these figures compare to the case found in Europe? See also Changes in Residential Energy Consumption Patterns and Future Trend in Japan. The Web Japan Gateway for all Japanese Information includes the report Electric Energy Consumption by Industry (F.Y.1986-2004). The Canadian Industrial Energy End-Use Data and Analysis Centre has information about energy in Canada.

The EIA report Energy Imports, Exports, and Net Imports 1949-2004 shows our energy trend. The EIA Country Analysis Briefs (and here) compare the production and consumption of energy in various countries. Which European nations are net energy importers and which are exporters, and what are the sources of energy? The EIA’s Country Analysis Brief for the European Union has the answer.

In the article Locomotion: Dealing with friction, see here, V. Radhakrishnan of the Raman Research Institute discusses the energy needed to move cars, planes, and boats and such. He compares power versus speed for many types of vehicles and shows that transportation by water is the most efficient.

Electrical generation in the U.S.

(1970)

45% coal

15% oil

20% natural gas ( these first 3 produce half the CO₂ and other greenhouse gases that block reradiation of absorbed heat from Earth back into space at lower, more-infrared wavelengths)

15% hydro

5% nuclear

(2000)

23% coal

12% oil

20% gas

these three fossil fuels account for 80%

3% hydro

8% nuclear

34% geothermal, wood, waste, liquified natural gas

The U.S. is importing one-third of the energy and two-thirds of the oil that it is consuming.

Tips for using less gasoline in order to reduce pollution

The main way to reduce your gasoline usage is to buy and use a car that gets at least 50 miles per gallon of gasoline. (Phil Fraundorf estimates that a gallon of gasoline contains as much energy as needed for a person to do 300,000 pushups.) The money you will spend each year on gas will be $2,100 at 20 mpg but only $850 at 50 mpg. When driving 15,000 miles per year and paying $2.85 per gallon of gas, the difference between a car that gets 20 mpg and one that gets 30 mpg amounts to $700 per year, or $2,850 extra in fuel costs in just four years. The difference between a car that gets 20 mpg and one that gets 50 mpg amounts to $1300 per year, or $5,200 extra in fuel costs in four years. Gas expense/year is

( price/gallon * miles driven/year ) / mpg.

If you don’t know what your gas mileage is, see what it is for other people driving the same car that you own by visiting here.

Certain European cars get great gas mileage. For example, Daimler-Chrysler's Smart Car gets 70 miles per gallon in a 3-cylinder, non-hybrid and has been sold in Europe for many years but not in the U.S. The Zap corporation is now beginning to import these cars into the U.S. You might also like to look at the Canta that is made in the Netherlands.

You can effectively reduce the price of gasoline by changing your driving habits.

Save $0.20 per gallon by not driving ten miles per hour over the speed limit. Due to air and ground friction, fuel economy decreases rapidly at speeds above 60 mph. Each 5 mph over 60 mph is like paying an additional $0.10 per gallon for gas. Drive at a steady speed rather than at a varying speed. Use your overdrive gear and cruise control.

Save 5% to 10% of fuel in city traffic by anticipating the traffic situation ahead of you so that you have to start and stop less often. Since half the fuel is being used to accelerate your car from a stop, try to accelerate less often and only moderately rather than quickly.

Avoid unnecessary idling. Unnecessary idling translates to 0 mpg, wastes fuel, costs money, and pollutes the air. If waiting for more then a couple minutes in a drive-up lane, turn off the engine. Most vehicles do not need to be warmed up.

Use a carpool, take the bus, or ride a bike. You can cut your weekly fuel costs in half and save wear on your car if you take turns driving with other people. Combining errands means you travel less total miles.

Check for faulty oxygen sensor. If it’s bad and so replaced, you’ll save 40%, which is like paying $1.71 per gallon rather than $2.85 per gallon. A clogged air or oil filter decreases your mileage by 10%. When needing a tune-up, your gas mileage decreases by 4%. Carrying an extra one hundred pounds of stuff in the trunk will reduce your fuel economy by 1 to 2%. Using the wrong oil decreases gas-mileage by 1%-2%.

Improperly inflated tires decrease gas-mileage by 3%. Under-inflated tires can lower gas mileage by 0.4 percent for every 1 psi drop in pressure of all four tires. Properly inflated tires are safer and last longer. Car manufacturers state safe tire pressures in a label in the door or inside the gas cap cover. If the label lists a psi range, use the higher number in order to maximize fuel efficiency.

For more information, you might like to visit here, here, and here. See here for international gas prices and profits. The EIA report Motor Vehicle Mileage, Fuel Consumption, and Fuel Rates, Selected Years, 1949-2003 shows how car and truck gas mileage has changed through the years.

From a news report:

The EPA first began testing vehicle fuel economy in 1977. The test assumes drivers won't go over a maximum speed of 56 mph in the city and 60 mph on the highway and that drivers won't speed up more than 3.3 mph per second. Many highways now have higher speed limits and acceleration is 8.4 mph per second among faster drivers.

Review

Every phenomena and process in the universe involves energy and the conversion of energy from one form to another. Energy and force are the two most all-encompassing aspects of physics. Each citizen needs a working knowledge of these two fundamental quantities.

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