Question

A spring with a constant of `3 (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 `8 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`11.3cm(1dp)`

Explanation:

We need the following formulae

Elastic potential energy for springs

`EPE=1/2kx^2`

where`k= "the spring constant; "`

`x="the compression/extension of the spring"`

Kinetic energy

`KE=1/2mv^2`

`m="the mass of the object;"`

`v="the speed of the object"`

we have an object of mass`" "6kg" "`moving with speed `8ms^(-1)`

it will have kinetic energy of

`KE=1/2mv^2=1/2xx6xx8^2`

`KE=192J`

on collision with the spring all this will be given to the spring in terms of EPE

`KE=EPE`

`192=1/2xx3xxx^2`

`x^2=(2xx192)/3=128`

`:.x=sqrt(128)=11.3cm(1dp)`