If you hang a block of mass m from a spring with constant k and then pull it downwards by a distance H and let it bounce up and down, the mechanical energy will be converted back and forth between three different kinds of energy. At the midpoint of the motion, how will the mechanical energy of the system be distributed? a)It will be all kinetic energy b)It will be all gravitational potential energy c)It will be all spring potential energy d)It will be a mixture of all three

Correct Answer – D At the top of the motion, the energy will be all gravitational potential energy. At the bottom of the motion it will be all spring potential energy. In the middle, the spring is stretched, and the block is higher than it is at the bottom, and it is moving, so all three kinds of energy are represented in the total. prengy.htm

You attach an object to the end of the spring and then let it slide back and forth on the end of the spring for a while. You notice that the amount by which the string is stretched on each successive bounce decreases steadily. In energy terms this means that the amount of potential energy stored in the spring at the endpoint of each bounce is decreasing. What does this tell you about the kinetic energy of the mass when it is moving at its fastest at the midpoint of the motion on each bounce? a)It is also decreasing with each bounce, because the total mechanical energy is decreasing b)It must be increasing with each bounce, so that the total mechanical energy remains constant

Correct Answer – A Friction reduces the total amount of mechanical energy in the system. When the object passes through the point at which the string is neither stretched or compressed, the potential energy is zero, so all of the available mechanical energy has been converted to kinetic energy. If the total mechanical energy decreases with time than the kinetic energy at this point must also decrease with time, and therefore the highest speed of the block must decrease with time. Let’s look at an animation of this situation hyslets/DampedSpring.html

Suppose you hang a small weight on the end of a long string and let it swing back and forth like a pendulum. Let’s say you always make the maximum angle it swings through be only 5 degrees. In that case, will the ball move faster at its fastest point if you use a longer string than if you use a shorter swing? A)It will move faster at its fastest point if you use the longer string B)It will move faster at its fastest point if you use the shorter string

Correct Answer – A If you use the longer string, than the height difference between the top of the swing and the bottom will be greater. This means the potential energy at the top is greater, so the kinetic energy at the bottom must be greater too. Animation –

As Halley’s comet goes around the Sun it goes from a very great distance away from the Sun (so distance it cannot be seen from Earth) to a very close pass (about half the distance from the Earth to the Sun) every 76 years. When it is at the farthest point is it moving faster or more slowly than it is at the closest approach to the Sun? a)It moves faster when farther away because it has stored up more energy then b)It moves slower when farther away because its potential energy is greater then c)It moves faster when farther away because it potential energy is smaller then d)It moves slower when farther away because it has lost a lot of energy in moving away from the Sun.

Correct Answer – B When the comet is farther from the Sun it has greater potential energy, just as an object on the Earth gains potential energy has it gets farther from the center of the Earth. If the mechanical energy is constant (which it is, note that there is no air resistance or other significant dragging effects to take mechanical energy away from the comet as it moves through space), then higher potential energy must mean lower kinetic energy.

r E This graph shows a plot of energy (E) versus distance from the Sun r. The curve depicts the “effective potential energy” of planets or comets orbiting the Sun. Which of the two objects A and B would be Earth, the other being Halley’s comet? A is Earth B is Earth A B

Correct Answer – B is Earth This graph is a (relatively sophisticated) form of the potential energy curve discussed in the book. If a planet or comet starts at a certain height on one part of the curve, then conservation of mechanical energy means that it will rise to the same height on the other side of the curve as it moves. How can we tell the difference between Earth and the comet? We know that the comet changes r, its distance from the Sun, a lot during its motion, which is possible for object A. Object B, on the other hand, is at the bottom of the potential curve, and cannot rise far up the sides, so it can never change its distance from the Sun much. It is in a nearly circular orbit, like a planet.

Looking at the previous graph again, it looks as if the you have enough energy you can get far away from the Sun, but you can’t actually fly or fall into the Sun. Why would it be difficult for a planet or comet to fall into the Sun? r E A A)Because the potential energy pushes you back B)Because when you are close to the Sun you get a gravitational kick C)Because your kinetic energy is at its highest when you are closest to the Sun

Correct Answer – C Why don’t planets and comets fall into the Sun? Because their total mechanical energy is so great that when they reach the lowest part of their orbit their speed is very high and they can swing back out and away from the Sun.

In the 1930s physicists studied the nuclear interaction known as beta decay, in which a neutron turns into a proton and emits an electron while doing so. When they added up all of the energy before and after each interaction it appeared as if some energy had gone missing? Which of the following conclusions sounds most reasonable to you? a)Energy conservation is violated in nuclear interactions b)There must be a new force involved which is storing the missing energy as potential energy c)There must be another undetected particle emitted along with the electron, whose kinetic energy makes up the missing energy d)There is a previously unsuspected new form of energy which is absorbing the missing energy

Correct Answer – C Physicists tried all of these solutions, but the correct one turned out to be that there was a very hard to detect particle, which came to be called a neutrino, which was emitted during these reactions. As the neutrino flew off it carried some kinetic energy with it.

You are on a Ferris wheel at the fairground and your speed, as you go around, is constant. When you are at the top of the Ferris wheel, is your mechanical energy greater, less than, or equal to when you are at the bottom? A) Greater at the top than at the bottom B) Equal C) Less at the top than at the bottom

Correct Answer – A Note that the question said your speed was constant as you go around. If your speed is the same at the top and at the bottom, then your mechanical energy must be greater at the top, because you clearly have more potential energy at the top. A Ferris-Wheel does not work like a swing by storing potential energy at the top and letting you go fast at the bottom? Where does the energy come from? If you are along on the Ferris wheel then the motor has to work hard to lift you to the top. If every car is filled, the motor can idle once it gets things going, because as you rise, gaining potential energy, other passengers are falling, losing potential energy. You are exchanging mechanical energy with your fellow passengers.