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(II) A train is moving along a track with constant speed $v _ { 1 }$ relative to the ground. A person on the train holds a ball of mass $m$ and throws it toward the front of the train with a speed $v _ { 2 }$ relative to the train. Calculate the change in kinetic energy of the ball $( a )$ in the Earth frame of reference, and(b) in the train frame of reference. (c) Relative to each frame of reference, how much work was done on the ball? (d) Explain why the results in part (c) are not the same for the two frames - after all, it's the same ball.

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Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Andrey S.

August 12, 2021

In Qingjiang Garden, Green Garden, Dinghuaimen Street, Xiaguan District, Nanjing, there were two vulgar old ladies who gossiped all day long and encouraged others to do things against the law.If you pass them, they will point at you with their fans, shout

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In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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7.67. So we're moving in train. Our train is moving. We not necessarily in it has a constant speed of you won. And so someone in the train is holding a ball with a mass M and then throws it at a speed of you to relative to the train. And so I want to calculate the change in kinetic energy for the ball both in the Earth frame of reference and in the train frame of reference. And then to we want to find the work that's done in each case, and then why they should be different from one another. You talk about that. So in the er Earth's frame of reference, we go from a speed of view one because the ball is moving with the train to a speed of be one plus two. So for the Earth frame of reference, um, this will be one em m times V one plus two squared minus 1/2 and that was the one squared. So if we expand things out and simplify it, et cetera, we get. But this is 1/2 and two squared times, one plus two times the ratio of the initial the final speed. Now, on the on the train, we go from zero speed just beautifui too. And so the change in kinetic energy on the train it's just 1/2 M V two squared. So the work is the change in kinetic energy. So if you're looking at this from sitting stationary on the earth, the work is this 1/2 empty, two squared times one plus two times this ratio of the speeds. But on the train, the work is just 1/2 of the two square. So far apart are the the kinetic energy Obviously, has this B squared in it, which means that the the kinetic energy and changes in it are highly dependent on your relative motion to through the object whose kinetic energy you're considering. So the sort of first part of this is that, you know, he depends on the reference frame. And furthermore, uh, something to think about is that in the earth frame of reference, the ball is moving further distance, you know, in the frame of reference of an observer sitting on the earth than it is in the train because of the train, it's just, you know, it goes from one end of the carriage back or something. All right. You know, this is a car of the train that goes this far, but then if you're this is moving than this distance actually appears to be longer. Because at the moment in time that that this ball is released in the earth's frame of reference, the car continues moving. And so this point is actually further along at a later point. So it's moving a further distance. And so the work that was done to give it its kinetic energy has to be has to be greater and the earth frame of reference.

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