A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #5 kg# and speed of #9 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer

Answer:

#~~8.2m#

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=5kg
v=velocity of the object=#9m/s#
k = force constant=#6(kg)/s^2#
x= compression of spring=?
#=>x^2=mv^2/k#
#=>x=sqrt(m/kv^2)=sqrt(m/k)xxv=sqrt((5kg)/(6(kg)/s^2))xx9m/s~~8.2m#