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Old Feb 25th 2009, 04:26 AM   #1
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mass on spring accelerating 2nd mass

(1) A body starting with an initial velocity compresses a spring until it comes to rest.
(2) A body starting with an initial velocity compresses a spring attached to another fixed body known distance so that the body has a final velocity. The second body is then released and allowed to be accelerated by the spring mass system.

The masses of the two bodies are different.
How can the resultant energies/speeds of the two bodies described in (2) be found.
What will be the difference in compression of the spring between problem (1) and problem (2).
I know the mass of each body and the spring rate. I also know the starting velocity of the first body and the distance the spring is compressed before the second body is released.
The spring is assumed to be an ideal spring and there are no external forces acting on the system.

Any help would be greatly appreciated. Thanks.
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Old Feb 25th 2009, 05:35 PM   #2
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Your description of 2) isn't quite clear because you don't say whether "the body" is the first body or the second body. I think you mean that body A hits a spring attached to body B. Body B is initially held in place so the spring compresses until body A has a given velocity. Then body B is released.

Try conservation of energy. Before body A hits the spring, it has a certain kinetic energy. It loses kinetic energy when it compresses the spring. You can find how much it loses if you know its "final" velocity before body B is released. You can also find how much energy it loses to compressing the spring if you know how far it compresses the spring. Hooks law says F = kx. The energy lost is the work done by the spring while it is compressed. Work is the integral of the force F as a function of the distance x.

I don't know what the problem asks for after body B is released. When it is released, I think the spring exerts an equal and opposite force on both bodies according to hooks law. While the spring is compressed, you have the interesting situation of bodies acted upon by a non-constant force so they have non-constant accelerations. After the spring uncompresses (I assume it is not attached to both bodies, so we don't get into some kind of oscillating situation) see what conservation of energy and conservation of momentum tell you about the velocities of the masses. (This problem can be viewed as the before and after of a collision.)
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