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?

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Answer 1 · 2017-08-25T08:14:27

$11.3cm(1dp)$

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

$KE=EPE$

$192=1/2xx3xxx^2$

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

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

A spring with a constant of 3 (kg)/s^23 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 6 kg6 kg and speed of 8 m/s8 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?