We claim that momentum is conserved, yet most moving objects slow down and stop. Explain.
For momentum to be conserved, the system under analysis must be closed and defined. No forces can act from outside the system. A coasting car has air friction and road friction on it, which are outside forces. But if they were considered part of the system, and their velocities analyzed, the momentum of the entire system would be conserved but not necessarily of any single component.
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 one. The large object-small object combo would have some momentum after the collision but due to the very large mass of Earth, the velocity of the combo is not measurable. Jumper lands on Earth, and nothing more.
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 rushes out the open end. That escaping has and the balloon form a closed system and so the momentum of the system is conserved. The balloon and remaining has acquires a momentum equal and opposite to the momentum of the escaping was and so move in the opposite direction of the escaping gas.
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 ice is frictionless, he would slide all the way to the shore.
How can a rocket change direction when it is far out in space and is essentially a vacuum?
When a rocket expels gas in a given direction, it puts a force on that gas. The momentum of the gas rocket system stays constant, so if the gas is pushed to the left, the rocket will be pushed to the right due to Newton's third law. So the rocket must carry some kind of material to be ejected to change direction.
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.
The airbag greatly increases the amount o time over which the stopping force acts on the driver. If a hard object like a steering wheel stops the impact, the impact is short and strong. If an airbag stops the driver, then a much smaller force is exerted over a much longer time. It can increase the time of stopping by a factor of 10.
Cars used to be built as rigid as possible to withstand collisions. Today cards are designed to have crumple zones that collapse on 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.
Why can a batter hit a pitched baseball further than a ball tossed in the air by a batter?
From equation 7-7 in a 1D elastic collision, va-vb=va'-va'. 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 hit. We can assume that batter can swing the bat with equal strength in either case, so vA is the same in both pitching situations. Since the speed of both need to be conserved, the one with the greater speed coming in will have the greater speed going out.
Is is possible for an object to receive a larger impulse from a small force than from a large force?
Impulse is force*change in time which is equal to the change in momentum, or impulse. If a small force is applied over a longer amount of time than a large force for a very small amount of time, then yes, the impulse can be larger from a small force.
A light object and a heavy object have the same kinetic energy. Which has the greater momentum?
p=mv=square root of m^2*v^2=square of 2mKE
If 2 objects have the same kinetic energy, then the one with more mass has the greater momentum.
Describe a collision in which all the kinetic energy is lost.
2 objects, each with the same magnitude of momentum, moving in opposite directions. They have a total momentum of 0. If they collide and they have a totally inelastic collision, in which they stick together, then their final common speed must be zero so the momentum is conserved. Since they are not moving after the collision, they have no kinetic energy. So all of their kinetic energy has been lost.
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?
Water rebounds. If it rebounds, that means that a larger momentum change for the water has occurred than if it just came to a stop. 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.
A squash ball hits a wall at a 45 degree angle as shown in 7-30. What is the direction of then change of momentum of the ball and of the force on the wall?
Downward component of momentum is unchanged. The horizontal component of momentum changes from rightward to leftward. Thus the change in momentum is to the left in the picture. Since the force on the wall is opposite that on the ball, the force on the wall is to the right.
A superball is dropped from a height h onto a hard steel plate (fixed to the Earth) from which it rebounds at very nearly its original speed. Is the momentum of the ball conserved at any part of the process? If we consider the ball and the Earth as our system?
Not conserved during any part of the process because there is an external force acting on the ball at all times-gravity. And there is an upward force on the ball during the collision. So considering the ball is a system, there are always external forces acting on it.
With the ball-Earth system, momentum is conserved during the entire process. Same of piece of putty that falls and sticks to the plate for Earth-ball system.
Why do you tend to lean backward when carrying a heavy load in your arms?
In order to maintain balance, your CM must be located directly above your feet. If you have a heavy load in your arms, yourCM will be out in from of your body and not above your feet. So you lean backwards to get your CM directly above your feet. Otherwise you would fall over forwards.
Why is the CM of a 1 m length of pipe at its mid point, whereas this is not true for your arm or leg?
Pipe is uniform and has the same density throughout. Arm and leg are not uniform. CM is closer to body than geometric center.
Show on a diagram how your CM shifts when you change from lying to sitting.
Flat-your CM is inside the volume of your body. When you sit up on the floor with legs extended, your CM is outside of the volume of your bod (in front of you)
If only an external force can change the momentum of the CM of an object, how can the internal force of an engine accelerate a car?
The engine does not directly acclererate the car. The engine puts a force on the driving wheels, making them rorate. The wheels push backwards on the road as they spin. Due to Newton's third law, the car accelerates. So it is actually the external road surface that accelerates the car.
A rocket following a parabolic path through the air suddenly explodes into many pieces. What can you say about the motion of these pieces?
They will follow a parabolic path. Center of mass will follow the original path.
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