Question

A spring with a constant of `2 (kg)/(s^2)` is lying on the ground with one end attached to a wall. An object with a mass of `4 kg` and speed of `3 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`Delta x=sqrt 18 m`

Explanation:

`"The kinetic energy of an object with ,mass of m and velocity of v is given as:"`
`E_k=1/2*m*v^2`
`E_k=1/2*4*3^2`
`E_k=18 J" Object has a kinetic energy of 18 J"`
`"The kinetic energy of object changes to potential energy on spring, if object stops:"`
`"The potential energy of compressed spring is given by:"`
`E_p=1/2*k*Delta x^2`
`E_p=1/2*2*Delta x^2`
`E_p=Delta x^2`
`E_p=E_k " Energy not lost"`
`18=Delta x^2`
`Delta x=sqrt 18 m`