A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Mar 22, 2016

Answer:

#=0.87m#

Explanation:

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=3kg
v=velocity of the object=#1m/s#
k = force constant=#4(kg)/s^2#
x= compression of spring=?
#=>x^2=mv^2/k#
#=>x=sqrt(m/kv^2)=sqrt(m/k)xxv=sqrt((3kg)/(4kg)/s^2)xx1m/s=0.87m#