A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected by the spring?

Question

Quizplus · Accepted Answer

Since mechanical energy is conserved, the potential energy stored in the spring at the maximum compression is equal to the initial kinetic energy of the block: 
(1/2)k(l^2) = (1/2)mv^2 
Thus, v = √(k/m) * l 
When the spring ejects the block, the potential energy stored in the spring is transferred back into kinetic energy of the block: 
(1/2)k(l^2) = (1/2)mv_final^2 
Solving for v_final, we get: 
v_final = √(k/m) * l 
which is equal to the initial velocity v. Therefore, the answer is C) v.

A Block of Mass M Slides Without Friction on a Table