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 #1 kg# and speed of #5 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Mar 24, 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=1kg
v=velocity of the object=#5m/s#
k = force constant=#2(kg)/s^2#
x= compression of spring=?
#=>x^2=mv^2#
#=>x=sqrt(m/kv^2)=sqrt(m/k)xxv=sqrt((1kg)/(2kg)/s^2)xx5m/s=3.53m#