Question

An object of unknown mass M is moving at 5m/s when it collides with a spring that brings it to a stop in 3 seconds. As it does so the force of the spring as a function of tie is recorded in the graph below. What is the mass?

the graph below is force (y or the vertical axis) vs seconds (x the horizontal axis) and there is a line drawn from 7 Newtons and zero seconds down to 3 seconds and zero Newtons

Answer 1

`M = 2.1 kg`

Explanation:

Assuming the line is straight, we can assume the average force is -3.5 N. I give it a negative sign because the force is in the direction opposite the initial velocity. Applying an average force of -3.5 N for 3 s is an impulse of

`"Impulse" = F_(ave) * t = (-3.5 N) * 3 s = -10.5 N*s`

The unit N is equivalent to kg*m/s^2 (verify by looking at Newton's 2nd Law -> F=ma). Therefore we can convert the units as follows

`-10.5 N*s = -10.5 kg*m/s^2*s = -10.5 kg*m/s`

That is the units of momentum. In fact, it can be said that impulse is also "change in momentum". The object started with momentum of

`p = 0 - M*5 m/s = -5*M m/s`

So we have 2 expressions for the impulse.

`-10.5 kg*m/s = -5*M m/s`

Solving for M,

`M = (-10.5 kg*cancel(m/s))/(-5*cancel(m/s)) = 2.1 kg`

I hope this helps,
Steve