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 #8 kg# and speed of #4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Nov 8, 2017

Answer:

I got #3.3m#

Explanation:

We can use conservation of mechanical energy (no friction) equating the sum of (elastic) potential energy #U# and kinetic energy #K#:

before (spring relaxed=zero pot energy and object moving with velocity #v#)
and
after (spring compressed of length #h# giving max pot energy and object stopped #v=0#):

#K_b+U_b=K_a+U_a#

#cancel(1/2)mv^2+0=0+cancel(1/2)kh^2#

rearranging:

#h=vsqrt(m/k)=4sqrt(8/12)=3.26~~3.3m#