Inelastic Collision with Pendulum and Ball; finding force and work

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Homework Statement


I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic collision). One question that confuses me:

> How much work did you do in joules in compressing the spring of the spring gun for the long-range case? Which law of conservation is your answer based upon?

Some additional information: the long-range case is where we fired the ball at it's maximum speed (which I've calculated to be 4.79 m/s^2.

Homework Equations


E = K + U = 0
initial momentum = final momentum
m(v_initial) = (m + M)(v_final)
K = (1/2)(m + M)v^2
U = (1/2)kx^2 [for the spring]

The Attempt at a Solution



I'm guessing the law of conservation to use here is for that of energy, in which K + U = 0, where K is kinetic and U is final energy. The system has all potential energy (no kinetic) when the spring is compressed, which is known as (1/2)kx^2, but I don't know k...

If any other information is needed, let me know. Thanks for the help!
 
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