A rifle fires a 2.10 x 10 -2 kg pellet straight upward, because the pellet rests

Question

A rifle fires a 2.10 x 10-2 kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 x 10-2 m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance and any other friction force, determine the spring constant.

Please be sure the answer is correct this means a lot to my grade this semester and I just can not seem to get it.

Explanation / Answer

let spring constant be K.when the spring is compressed along with the pellet there is a potential enhergy associated with the spring given by PE=1/2Kx^2 where x is compression./

using values we get PE=4.14 X 10^-3K

now when the pellet is fired the spring force gives it a kinetic energy which is ultimately converted intoo gravitational potential energy GE of the pellet ..........GE is given by GE=MgH where M is pellet masss and H is height to which it rises..

equating GE and pe WE GET

MgH=PE

or 2.1 X 10^-2 X 9.81 X 6.1= 4.14 X 10^-3K

solving we get K=303.5N/m

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