Chapter 7 Physics

Rank the scale readings from highest to lowest. (Ignore friction.)

A, B=C

What famous equation by 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?

momentum = mass * velocity So if velocity is doubled, the momentum is also doubled kinetic energy = 1/2 mass * velocity^2 So if velocity is doubled, the kinetic energy is quadrupled.

Discuss why one should even bother to use a machine if it cannot multiply work input to achieve greater work output. What, then, is the use of a machine?

A machine can multiply force or multiply distance, both of which can be of value

Consider the identical balls released from rest on tracks A or B, as shown. When they reach the right ends of the tracks, which will have the greater speed? Why is this questions easier to answer than the similiar one in chapter 3?

Both balls convert the same PE to KE, so they will have the same speed.

If a golf ball and a ping pong ball both move with the same kinetic energy, can you say which has the greater speed? Explain in terms of the definition of KE. Similiarly, in a gaseous mixture of heavy molecules and light molecules with the same average KE, can you say which have the greater speed?

If KEs are the same but masses differ, then the ball with smaller mass has the greater speed.

Consider the swinging balls apparatus. If two balls are lifted and released, momentum is conserved as two balls pop out the other side with the same speed as the released balls at impact. But momentum would also conserved if one ball popped out at twice the speed. Discuss why this never happens.

But now look at this situation in accordance with the conservation of energy (½ m v2) If only 1 ball pops out with twice the velocity Energy before = ½ m v2 + ½ m v2 = m v2 Energy after = ½ (m) (2 v)2= ½ (m) (4 v2) = 2 m v2 These energies are not equal and, therefore, the law of conservation of energy is not obeyed! But, since 2 balls actually popped out Energy before = ½ m v2 + ½ m v2 = m v2 Energy after = ½ m v2 + ½ m v2 = m v2 These energies are equal and, therefore, both laws of conservation are obeyed

Can something have energy without having momentum? Explain. Can something have momentum without having energy? Discuss and defend your answer.

If an object has KE, then it must have momentum because it is moving. But it can have potential energy without being in motion, and therefore without having momentum. And every object has "energy of being". So whether an object moves or not, it has some form of energy. If it has KE, then with respect to the frame of reference in which its KE is measured, it also has momentum.

When an electric company can't meet its customers demand for electricity on a hot summer day, should the problem be called an "energy crisis" or a "power crisis"? Discuss.

Power crisis...the loads (air conditioners) are causing the problem by drawing too much power (Power = Current X Voltage...PIE) at the same time! Energy is the capacity to do work. All of the united states power plants are not operating at full capacity during the heat spell. The power transmission (wires and substations) system localized to the area just can't handle the instantaneous power demand... So since there is still excess capacity (energy) in the total system...then it is a temporary power crisis.

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 veloctiy, is relative.

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

The energy goes mostly into frictional heating of the air.

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?

The momentum of the car is equal in magnitude but opposite in direction in the two cases, not the same since momentum is a vector quantity.

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?

When the direction of the force is perpendicular to the direction of motion, as is the force of gravity on both the bowling ball on the alley and the satelitte in circular orbit, there is no force component in the direction of motion and no work is done by the force.

Consider a bob attached by a string, a simple pendulum, that swings to and fro. (a) Why doesn't the tension force in the string do work on the pendulum? (b) Explain, however, why the force due to gravity on the pendulum at nearly every point does do work on the pendulum. c) What is the single position of the pendulum where "no work by gravity" occurs?

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In the pulley system shown, block A has a mass 10 kg and is suspended precariously at rest. Assume that the pulleys and string are massless and there is no friction. No friction means that the tension in one part of the supporting string is the same as at any other part. Discuss why the mass of block B is 20 kg.

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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?

A Superball will bounce higher than its original height if thrown downward, but if simply dropped, no way. Such would violate the conservation of energy.

A ball is released from rest at the left of the metal track shown here. Assume it has only enough friction to roll, but not to lessen its speed. Rank these quantites from greatest to least at each point: a) Momentum, b)KE, c)PE

A) C, B = D, A B) C,B = D,A C) A,B = D,C

A moving hammer hits a nail and drives it into a wall. If the hammer hits the nail with twice the speed, how much deeper will the nail be driven? If the hammer hits with three times the speed?

According to the work-energy theoerm, twice the speed corresponds to 4 times the energy, and therefore 4 times the driving distance. At 3 times the speed, driving distance is 9 times as much

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 (which generate heat)

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

Energy is transformed into nonuseful forms in an inefficient machine and is lost only in the loose sense of the word. In the strict sense, it can be accounted for and is therefore not lost.

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

Gravitational potential energy comes from having mass and being above the ground. The space station, very obviously, has both. Kinetic energy is the energy of motion. Since the space station is in orbit, it is obviously moving around the earth. So, it has kinetic energy.

When a driver applies the brakes to keep a car going downhill at constant speed and constant kinetic energy, the potential energy of the car decreases. Where does this energy go? In contrast, discuss where most of it goes with a hybrid vehicle.

In a conventional car, braking converts KE to heat. In a hybrid car, braking charges up the batteries. In this way, breaking energy can soon be transformed to KE.

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? What are your answers the same or different?

Net momentum before the lumps collide is zero and is zero after collision. Momentum is indeed conserved. Kinetic energy after is zero but was greater than zero before collison. The lumps are warmer after colliding because the initial kinetic energy of the lumps transforms into thermal energy. Momentum has only one form. There is no way to "transform" momentum from one form to another, so it is conserved. But energy comes in various forms and can easily be transformed. No single form of energy such as KE need be conserved.

Discuss whether or not, once used, energy can be regenerated. Is your reasoning consistent with the common term renewable energy?

Once used, energy cannot be regenerated, for it dissipates into less useful forms in the enviornment-inconsistent with the term "renewable energy" Renewable energy refers to energy derived from renewable resources-trees, for example.

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 a half its maximum value, how much PE does it have relative to its PE at the center of the swing?

The KE of a pendulum bob is maximum where it moves fastest, at the lowest point; PE is maximum at the uppermost points. When the pendulum bob swings by the point that marks half its maximum height, it has half its maximum KE, and its PE is halfway between its minimum and maximum values. If we define PE=o at the bottom of the swing, the place where KE is half its maximum value is also the place where PE is half its maximum value and KE=PE at this point.

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 Kinetic energy is a maximum as soon as the ball leaves the hand. Potential energy is a maximum when the ball has reached its zenith.

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 design isn't good. The summit of each hill on the roller coaster is the same height, so the PE of the car at the top of each hill will be the same. If no energy were spent in overcoming friction, the car would get to the second summit with as much energy as it starts with. But in practice there is considerable friction, and the car would not roll to its inital height and have the same energy. So the maximum height of succeeding summits should be lower to compensate for friction.

A crate is pulled across a horizontal floor by a rope. At the same time, the crate pulls back on the rope, in accord with Newton's third law. Does the work done on the crate by the rope then equal zero? Explain.

The fact that the crate pulls back on the rope in action-reaction fashion is irrelevant. The work done on the crate by the rope is the horizontal component of rope force that acts on the crate multiplied by the distance the crate is moved by that force--period. How much of this work produces KE or thermal energy depends on the amount of friction acting.

This may seem like an easy question for a physics type to answer: with what force does a rock that weighs 10N strike the ground if it is dropped from a rest position 10 m high? In fact, the question cannot be answered unless you know more. Discuss why this is so.

The work that the rock does on the group is equal to its PE before being dropped, mgh=100 joules. The force of impact, however, depends on the distance that the rock penetrates into the ground. If we do not know this distance we cannot caluclate the force.

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

They're correct because for changing KE requires work, which means more fuel consumption and decrease air quality.

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? (Do you see why long-range cannons have such long barrels?)

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. (Note that the force acting on the bullet is not constant, but decreases with increasing distance inside the barrel)

In the absence of air resistance, a ball thrown vertically upward with a certain initial KE will return to its original level with the same KE. When air resistance is a factor affecting the ball, will it return to its orginial level with the same, less, or more KE? Does your answer contradict the law of energy conservation?

When air resistance is a factor, the ball will return with less speed. It therefore will have less KE. You can see this directly from the fact that the ball loses mechanical energy to the air molecules its encounters, so when it returns to its starting point and to its orginial PE, it will have less KE. This does not contradict energy conservation, for energy is transformed, not destroyed.

Suppose an object is set sliding, with a speed less than escape velocity, on an infinite frictionless plane in contact with the surface of Earth, as shown. Describe its motion. (Will it slide forever at a constant velocity? Will it slide to a stop? In what way will its energy changes be similar to that of a pendulum?)

While you don't have any surface friction, there is still the fluid friction of drag (you didn't specify a vacuum so I must assume there is an atmosphere). Drag is a function based on the drag coefficient and velocity of the object. Since the drag coefficient is constant, and velocity will always be possitive, the object will continue to deccelerate or slow down indefinitely. No matter how slow the object gets, it will never stop entirely because drag decreases with speed. The force of drag is calculated to this formula F(d) = -1/2*p(v^2)C, where p is density of the fluid, v is velocity of the object and C is the drag coefficient. So, drag increases and decreases exponentially as velocity increases and decreases, with a limit of zero. The velocity will infinitely get closer to zero, but never reach it. This is similar to a frictionless pendulum in the regards that while the amplitude of the pendulum swings is constantly decreasing due to drag, it will never stop entirely.

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?

Work done by each is the same because they reach the same height. The one who climbs in 30 seconds uses more power because work is done in a shorter time.

Why do you do not work on a 25kg backpack when you walk a horizontal distance of 100 m?

You do no work because you havne't exerted more than a negligible force on the backpack in the direction of motion. Also, the energy of the backpack hasn't changed. No change in energy means no work done.

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

Zero KE means zero speed, so momentum is also zero.