Physics Chapter 7 Questions

Cars used to be built as rigid as possible to withstand collisions. Today, though, cars are designed to have "crumple zones" that collapse upon impact. What is the advantage of this new design?

"Crumple zones" are similar to air bags in that they increase the time of interaction during a collision, and therefore lower the average force required for the change in momentum that the car undergoes in the collision.

When a person jumps from a tree to the ground, what happens to the momentum of the person upon striking the ground?

Consider this problem as a very light object hitting and sticking to a very heavy object. The large object - small object combination (Earth + jumper) would have some momentum after the collision, but due to the very large mass of the Earth, the velocity of the combination is so small that it is not measurable. Thus the jumper lands on the Earth, and nothing more happens.

We claim that momentum is conserved, yet most moving objects eventually slow down and stop. Explain.

For momentum to be conserved, the system under analysis must be "closed" - not have any forces on it from outside the system. A coasting car has air friction and road friction on it, for example, which are "outside" forces and thus reduce the momentum of the car. If the ground and the air were considered part of the system, and their velocities analyzed, then the momentum of the entire system would be conserved, but not necessarily the momentum of any single component, like the car.

Why can a batter hit a pitched baseball further than a ball tossed in the air by the batter?

From Eq. 7-7 for a 1-D elastic collision, A B B A v v v v . Let "A" represent the bat, and let "B" represent the ball. The positive direction will be the (assumed horizontal) direction that the bat is moving when the ball is hit. We assume the batter can swing the bat with equal strength in either case, so that A v is the same in both pitching situations. Because the bat is so much heavier than the ball, we assume that A A v v - the speed of the bat doesn't change significantly during the collision. Then the velocity of the baseball after being hit is 2 B A A B A B v v v v v v . If 0 B v , the ball tossed up into the air by the batter, then 2 B A v v - the ball moves away with twice the speed of the bat. But if 0 B v , the pitched ball situation, we see that the magnitude of 2 B A v v , and so the ball moves away with greater speed. If, for example, the pitching speed of the ball was about twice the speed at which the batter could swing the bat, then we would have 4 B A v v . Thus the ball has greater speed after being struck, and thus it is easier to hit a home run. This is similar to the "gravitational slingshot" effect discussed in problem 85.

It is said that in ancient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

If the rich man would have faced away from the shore and thrown the bag of coins directly away from the shore, he would have acquired a velocity towards the shore by conservation of momentum. Since the ice is frictionless, he would slide all the way to the shore.

According to Eq. 7-5, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

The air bag greatly increases the amount of time over which the stopping force acts on the driver. If a hard object like a steering wheel or windshield is what stops the driver, then a large force is exerted over a very short time. If a soft object like an air bag stops the driver, then a much smaller force is exerted over a much longer time. For instance, if the air bag is able to increase the time of stopping by a factor of 10, then the average force on the person will be decreased by a factor of 10. This greatly reduces the possibility of serious injury or death.

How can a rocket change direction when it is far out in space and is essentially in a vacuum?

The air bag greatly increases the amount of time over which the stopping force acts on the driver. If a hard object like a steering wheel or windshield is what stops the driver, then a large force is exerted over a very short time. If a soft object like an air bag stops the driver, then a much smaller force is exerted over a much longer time. For instance, if the air bag is able to increase the time of stopping by a factor of 10, then the average force on the person will be decreased by a factor of 10. This greatly reduces the possibility of serious injury or death.

Is it possible for an object to receive a larger impulse from a small force than from a large force? Explain.

The impulse is the product of the force and the time duration that the force is applied. So the impulse from a small force applied over a long time can be larger than the impulse applied by a large force over a small time.

At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

The turbine blades should be designed so that the water rebounds. If the water rebounds, that means that a larger momentum change for the water has occurred than if it just came to a stop. And if there is a larger momentum change for the water, there will also be a larger momentum change for the blades, making them spin faster.

When you release an inflated but untied balloon, why does it fly across the room?

When you release an inflated but untied balloon at rest, the gas inside the balloon (at high pressure) rushes out the open end of the balloon. That escaping gas and the balloon form a closed system, and so the momentum of the system is conserved. The balloon and remaining gas acquires a momentum equal and opposite to the momentum of the escaping gas, and so move in the opposite direction to the escaping gas.