5. (2p.) A “stiff” spring has a force law given by F = - kx4. The work required

Question

5. (2p.) A “stiff” spring has a force law given by F = - kx4. The work required to stretch the spring from the relaxed state x = 0 to the stretched length x = L is W0. In terms of W0, how much work is required to extend the spring from the stretched length 2L to the length 3L?

3. (2p.) A 4.26 kg block starts up a 30o incline at 7.8 m/s. How far will it slide if it loses 35% ofmechanical energy due to friction?

4. (2p.) A still ball of mass 0.514kg is fastened to a cord 68.7cm long and is released when thecord is horizontal. At the bottom of its path, the ball strikes a 2.63kg steel block at rest on ahorizontal frictionless surface. On collision, one-half the kinetic energy is converted tointernal energy. Find the final speeds.

Explanation / Answer

5: F = – kx4
W = F.dx
W= – kx4.dx
= – kx5/5
Wo = -kL5/5
And, similarly: W in stretching from 0 to 2L= -32kl5/5 = 32 * Wo
So,
Work in stretching from l to 2l = 31Wo

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