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 `6 kg` and speed of `2 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

Spring will compress by `"2.19 m"`

Explanation:

Kinetic energy of object = Energy stored in spring

`1/2mv^2 = 1/2kx^2`

From above equation

`x = vsqrt(m/k) = "2 m/s" × sqrt("6 kg"/("5 kg/s"^2)) = "2.19 m"`

Answer 2

The compression is `=2.19m`

Explanation:

Mass of the object is `m=6kg`

Speed of the object is `v=2ms^-1`

The kinetic energy of the object is

`KE=1/2mv^2=1/2*6*(2)^2=12J`

This energy will be stored in the spring

`E=1/2kx^2`

The spring constant is `k=5kgs^-2`

Let the compression of the spring be `=xm`

Therefore,

`12=1/2*5*x^2`

`x^2=(24)/5=4.8m^2`

The compression of the spring is

`x=sqrt4.8=2.19m`