Question

A spring with a constant of `9 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `3 kg` and speed of `9 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`Delta x=3sqrt3 " "m`

Explanation:

`E_k=1/2*m*v^2`
`"The kinetic energy of object moving a speed of v and mass of m"`
`E_k=1/2*3*9^2`
`E_p=1/2 k*Delta x^2" The Potential energy of spring compressed"`
`E_k=E_p" Energy is not lost"`
`cancel(1/2)*3*cancel(9^2)=cancel(1/2)*cancel(9)*Delta x^2`
`3*9=Delta x^2`
`sqrt(3*9)=sqrt (Delta x^2)`
`Delta x=3sqrt3 " "m`