Question

A spring with a constant of `12 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `8 kg` and speed of `4 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

I got `3.3m`

Explanation:

We can use conservation of mechanical energy (no friction) equating the sum of (elastic) potential energy `U` and kinetic energy `K`:

before (spring relaxed=zero pot energy and object moving with velocity `v`)
and
after (spring compressed of length `h` giving max pot energy and object stopped `v=0`):

`K_b+U_b=K_a+U_a`

`cancel(1/2)mv^2+0=0+cancel(1/2)kh^2`

rearranging:

`h=vsqrt(m/k)=4sqrt(8/12)=3.26~~3.3m`