Question

A 1.6kg box that is sliding on a frictionless surface with a speed of 11m/s approaches a horizontal spring. The spring has a spring constant of 2000 N/m.

a. How far will the spring be compressed in stopping the box?

b. How far will the spring be compressed when the box's speed is reduced to half of its initial speed?

Answer 1

a. It compresses until
(1/2)MVo^2 = (1/2)kX^2
k is the spring constant.
Solve for X

b. X is proportional to Vo. Half the Vo results in half the deflection.