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?

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