A spring with a constant of #12# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #5# #kg# and speed of #3# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

Question

Isabella Alvarez · Accepted Answer

The kinetic energy of the moving mass, #E_k=1/2mv^2=1/2*5*3^2=22.5# #J#, will be converted to spring potential energy, #E_p=1/2kx^2#. Rearranging this yields a compression of #x=sqrt((2E_p)/k)=1.94# #m#.

I believe everything is up above. ;-)

Nicholas Agrusa · Answer

undefined The compression of the spring can be calculated using the formula:

$$ \text{Compression} = \frac{\text{mass} \times \text{velocity}^2}{2 \times \text{spring constant}} $$

$$ \text{Compression} = \frac{5 \, \text{kg} \times (3 \, \text{m/s})^2}{2 \times 12 \, \text{kg/s}^2} $$

$$ \text{Compression} = 0.9375 \, \text{meters} $$