Ap physics 1 algebra based

Question

A student uses a spring gun (with a spring constant of 150 N/m) to launch a marble vertically into the air. The mass of the marble is 0.01 kg and the spring is compressed 0.025 m. How high will the marble go?

Answer 1

The energy you start with E_spr = 1/2 kx² where x is the compression and k the spring constant

The energy you end with is all gravitational potential energy E_P = mgh (you don't care that the energy was in the form of kinetic energy between the initial and final states as total energy is conserved (no dissipative force)

h = kx²/(2mg) All t he units are in SI, so you can plug in.

I tacked the following on to show that there may be more to this problem...

Unfortunately, many books and standardized tests get this analysis wrong (the one I just gave you is only valid if the compression is much smaller than the height calculated. This is usually valid, but not completely. If you were actually launching something, you would care about the height above the point where the spring is uncompressed. Because potential energy is linear, the height above the unstretched spring is h-x. This can be incorporated in the energy balance as having negative potential to start with from the height of the mass of the compressed spring