Given a ball with an unknown mass, a spring with spring constant 950 N/m and a m

Question

Given a ball with an unknown mass, a spring with spring constant 950 N/m and a meter stick. You develop an experiment by using various compressions of the spring to launch the ball vertically. You use the meter stick to measure the ball's maximum height above the launch point for every compression. Your data is below. Use an appropriate graph of the data to determine the ball's mass. Also, Assume the spring is ideal and obeys Hooke’s law

data

Compression(m) Height (m)

0 0

.02 32

.03 65

.04 115

.05 189

Explanation / Answer

All the spring Potential energy stored is converted to gravitational potential energy

So, 0.5*kx^2 = mgh

So, m = kx^2/2gh

= 950*0.03^2/(2*9.8*32)

= 1.36*10^-3 kg = 1.36 g <-------answer

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