Question

A spring with a constant of `6 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `1 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

`x=sqrt 6/3 m`

Explanation:

`"The Kinetic Energy of Object is :"E_k=1/2*m*v^2`
`E_k=1/2*1*4^2=1/2*16J`
`"The kinetic energy of object turns a potential energy on spring , if spring compresses"`
`E_p=1/2*k*Delta x^2`
`E_k=E_p`
`cancel(1/2)*16=cancel(1/2)*6*Delta x^2`
`Delta x^2=16/6`
`x=sqrt(16/6)`
`x=4*1/sqrt 6`
`x=4*sqrt 6/6`
`x=(2*sqrt 6)/3 m`