A spring with a constant of #12 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #7 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Apr 11, 2016

By conservation of mechanical energy when the spring is compressed fully after collision
PE gained by the spring = Initial KE of the colliding object
#=>cancel (1/2)kx^2=cancel(1/2)mv^2#
where
m = mass=7kg
v=velocity of the object=#3m/s#
k = force constant=#12(kg)/s^2#
x= compression of spring=?
#=>x^2=mv^2/k#
#=>x=sqrt(m/kv^2)=sqrt(m/k)xxv=sqrt((7kg)/(12kg)/s^2)xx3m/s=2.3m#