A spring with a constant of $8$ $kgs^-2$ is lying on the ground with one end attached to a wall. An object with a mass of $7$ $kg$ and speed of $6$ $ms^-1$ collides with and compresses the spring until it stops moving. How much will the spring compress?

Question

1529 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-25T10:18:36

The initial kinetic energy is $E_k=1/2mv^2=1/2*7*6^2=126$ $J$ .

This will be converted to spring potential energy, which will have the same value, $126$ $J$ . The equation is $E_(sp)=1/2kx^2$ .

Rearranging to make the compression distance, $x$ , the subject: $x=sqrt((2E_(sp))/k)=sqrt((2*126)/8)=5.6$ $m$ .

A spring with a constant of 88 kgs^-2kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 77 kgkg and speed of 66 ms^-1ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?