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

1 Answer
Feb 14, 2016

Answer:

The kinetic energy, #E_k=1/2mv^2#, of the moving mass will be converted to spring potential energy in the spring, #E_p=1/2kx^2#. The compression in the spring will be #1.5# #m#.

Explanation:

The kinetic energy of the moving mass is:

#E_k=1/2mv^2=1/2*1*3^2=4.5# #J#

As it collides with the spring, this kinetic energy will be converted into spring potential energy:

#E_p=1/2kx^2#

Rearranging:

#x=sqrt((2E_p)/k)=sqrt((2*4.5)/4) = sqrt(9/4) = 3/2 = 1.5# #m#