U Physics 12E 7.71 Conservation of Energy: An experimental apparatus with mass

In summary, the question is asking for the force constant and initial compression distance of a spring in order to launch an animal without damaging it. This is achieved by using Conservation of Energy and Newton's Second Law, merging them using the compression distance x, and relating it to height h from gravitational potential energy and acceleration a from Newton's Second Law. The objective is to limit the forces so the animal is not harmed, which is achieved by pulling out x from the equation kx^2=ma and then plugging it into the equation for elastic potential energy. Once the final equation is obtained, a suitable k and x can be chosen to meet the objective.
  • #1
The question is shown below the --- or this question and answerbook is from U Physics 12E #7.71. I uploaded a JPG that can be seen at http://i43.tinypic.com/35j9jja.jpg

I don't understand this problem. I see that to solve this Conservation of Energy and N2L are merged using x, and that h from Ugrav, and a from F=ma are thus related, but why ? I understand the algebra, but how does this merger model the problem ?

An experimental apparatus with mass m is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance x. The apparatus is then released and reaches its maximum height at a distance h above the point where it is released. The apparatus is not attached to the spring, and at its maximum height it is no longer in contact with the spring. The maximum magnitude of acceleration the apparatus can have without being damaged is a, where a > g.
(a) What should the force constant of the spring be?
(b) What distance x must the spring be compressed initially?
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  • #2
o.k. i get it now. we are propagating a to limit the forces so the block/animal launched doesn't break/die. so that's why we pull out x from kx^2=ma then plug x into Uel=Ug. the objective again it to limit. then after we get the final equation, we can pick a k and an x-compression that will work.

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