A block of mass m is pushed against a spring of spring constant k. The spring is compressed by a distance d, the block is then released. It is launched by the spring along a horizontal frictionless surface with a final speed v. A second block, this one having mass 4m is pushed against the same spring by distance 6d and released. What is the final speed of the block in this case?
A) v
B) 2v
C) 3v
D) 4v
E) 5v

Question

Quizplus · Accepted Answer

The potential energy stored in the spring is given by (1/2)kd^2. For the first block, this energy is converted into kinetic energy, (1/2)mv^2, giving v = sqrt(k/m) * d. For the second block, the spring is compressed by 6d, so the potential energy is (1/2)k(6d)^2 = 18kd^2. This energy is converted into kinetic energy of the second block, (1/2)(4m)v'^2. Solving for v', we get v' = sqrt(k/(4m)) * 6d = 3v.

A Block of Mass M Is Pushed Against a Spring