Question

A spring with a constant of `5 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `9 kg` and speed of `7 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`Delta x=21*sqrt(5)/5m`

Explanation:

`E_k=1/2*m*v^2" the kinetic energy of an object with 9 kg mass"`
`E_k=1/2*9*7^2`
`E_k=1/2*9*49`
`E_p=1/2*k*Delta x^2`
`"the potential energy of a spring compressed with Delta x"`
`E_k=E_p`
`cancel(1/2)*9*49=cancel(1/2)*5*Delta x^2`
`Delta x^2=(9*49)/5`
`Delta x=sqrt ((9*49)/5)`
`Delta x=3*7*sqrt (1/5)`
`Delta x=21*sqrt(5)/5m`