Magnitude of Displacement for a Spring?

Question

Suppose the spring has a spring constant of 492 N/m and the box has a mass of 2.0 kg. The speed of the box just before it makes contact with the spring in 0.36 m/s.

What is the magnitude of the spring's displacement when the spring is fully compressed?

Answer 1

The kinetic energy (KE) of the box will be converted to the potential energy (PE) of the spring upon full compression. This follows from the conservation of energy law. Thus, KE = 1/2 mv^2 = ks^2 = PE; where m = 2 kg, v = .36 mps, k = 492, and, ta da, s is the compression you're looking for.

Thus, s^2 = mv^2/2k and you can do the math.

PE for the spring comes from WE = fs = kss = ks^2; where f = ks is the force exerted by the spring as it compresses s distance. And WE = fs is the work function that converts the KE into PE.