Chapter 7: Energy

Why does one get tired pushing against a stationary wall when no work is done on the wall?

Although no work is done on the wall, work is nevertheless done on internal parts of your body.

What famous equation y Albert Einstein describes the relationship between mass and energy?

E=mc ^2

When the velocity of an object is doubled, by what factor is its momentum changed? By what factor is its kinetic energy changed?

If the velocity is doubled, the kinetic energy is quadrupled.

An inefficient machine is said to "waste energy." Does this mean that energy is actually lost? Explain.

No, whatever energy is "wasted" is converted to thermal energy.

Why does the force of gravity do work on a car that rolls down a hill but no work when it rolls along a level part of the road?

On the hill there is a component of gravitational force in the direction of the car's motion. This component of force does work on the car. But on the level, there is no component of gravitational force along the direction of the car's motion, so the force of gravity does no work in this case.

You and a flight attendant toss a ball back and forth in an airplane in flight. Does the KE of the ball depend on the speed of the airplane? Carefully explain.

The KE of the tossed ball relative to occupants in the airplane does not depend on the speed of the airplane. The KE of the ball relative to observers on the ground below, however, is a different matter. KE, like velocity, is relative

Consider a ball thrown straight up in the air. At what position is its kinetic energy at a maximum? Where is its gravitational potential energy at a maximum?

The ball is at it's maximum KE when it reaches the middle of it's fall and right before it hits the ground. It's maximum PE is when it reaches the top of it's trajectory.

When a jumbo jet slows and descends on the approach to landing, there is a decrease in both its kinetic and potential energy. Where does this energy go?

The energy turns into heat, or thermal energy.

At what point in its motion is the KE of a pendulum bob at a maximum? At what point is its PE at a maximum? When its KE is at half its maximum value, how much PE does it have relative to its PE at the center of the swing?

The maximum KE of a pendulum bob is in the middle of its swing, while the maximum of PE is at the top of its swing. When KE is half it's maximum value, PE is half it's maximum value.

Suppose that you and two classmates are discussing the design of a roller coaster. One classmate says that each summit must be lower than the preceding one. Your other classmate says this is nonsense, for as long as the first one is the highest, it doesn't matter what height the others are. What do you say?

The second classmate is right, because as long as the first hill is the highest- the others can be any size.

Two people who weigh the same climb a flight of stairs. The first person climbs the stairs in 30 s, and the second person climbs them in 40 s. Which person does more work? Which uses more power?

They both do the same amount of work, but the person who climbed in less time (30 s) used more power.

When a rifle with a longer barrel is fired, the force of expanding gases acts on the bullet for a longer distance. What effect does this have on the velocity of the emerging bullet?

When a rifle with a long barrel is fired, more work is done as the bullet is pushed through the longer distance. A greater KE is the result of the greater work, so of course, the bullet emerges with a greater velocity.

Does the International Space Station have gravitational PE? KE? Explain.

Yes to both, relative to Earth, because work was done to lift it in Earth's gravitational field and to impart speed to it.

If your momentum is zero, is your kinetic energy necessarily zero also?

Yes, if your momentum is zero- your kinetic energy is zero as well.

A car has the same kinetic energy when traveling north as when it turns around and travels south. Is the momentum of the car the same in both cases?

Yes, momentum is a vector.

Why do you do no work on a 25 kg backpack when you walk a horizontal distance of 100 m?

You do no work because the backpack moves relative to you.

Your friend says that one way to improve air quality in physics is to have traffic lights synchronized so that motorists can travel long distances at constant speed. What physics principle supports this claim?

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Someone who wants to sell you a Superball claims that it will bounce to a height greater than the height from which it is dropped. Can this be?

It's not possible because the conservation of energy wouldn't allow it.

Two lumps of clay with equal and opposite momenta have a head-on collision and come to rest. Is momentum conserved? Is kinetic energy conserved? Why are your answers the same or different?

When two clumps of clay come to rest after a collision, momentum is conserved. Kinetic energy is turned to heat. The answers are different because momentum is a vector and kinetic energy is a scalar quantity.