We did a lab in which we put a mass inside a little PVC pipe at 90 degree angle

Question

We did a lab in which we put a mass inside a little PVC pipe at 90 degree angle straight up. Inside the PVC pipe, there is a spring (this is what we put the mass on top off) and then pushed down so the spring would compress and we locked it. When we were ready for it to launch, we unlocked it, and the spring uncompressed, shooting the mass into the air.

As we added weights onto the mass, the max. height it reached got lower. I am supposed to explain this with a Free Body Diagram and kinematic equations. Which kinematic equations should I use?

Explanation / Answer

let us take a mass m and spring constant k. Assume that you are compressing the same(almost) distance every time, that is the compression length is same.

So when it is compressed, the energy stored in the spring-mass system is (1/2)*k*(x^2)

when the spring is released this entire energy is transferred to the mass in form of kinetic energy given by K=(1/2)*m*(v^2). now as the mass goes in to the air this kinetic energy transfers as potential energy and at the highes point there is no kinetic energy. So by using conservation of energy, potential energy at max height(measured from the relaxed state of spring) P=mgh.

So equating all the energies (1/2)*k*(x^2) = (1/2)*m*(v^2) = mgh

so equating 1st and 3rd, h = (1/2)*k*(x^2)/m*g

this is inversely proportional to m. as m increases h decreases.

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