Five different experiments are carried out. In each experiment, a block is attac

Question

Five different experiments are carried out. In each experiment, a block is attached to a horizontal spring. The block is pulled back a certain distance and released. The block oscillates back and forth on a frictionless surface. Rank the maximum force on the block for each of the following situations. (Rank the smallest force as 1).

-A block of mass M is attached to a spring with a spring constant (1/2)k, pulled back a distance (1/2)d, and released.

-A block of mass M is attached to a spring with a spring constant k, pulled back a distance 2d, and released.

-A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released.

-A block of mass (1/2)M is attached to a spring with a spring constant k, pulled back a distance d, and released.

-A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance d, and released.

Explanation / Answer

The max force on block will be when spring is stretched max, i.e. the distance it is pulled.

1) distance pulled x = d/2, spring constant K = k/2 Hence max force on block F1 = kx = k/2*d/2 = kd/4

2) x = 2d, K = k, max force F2 = kx = k*2d = 2kd

3) x = d, K = k, F3 = kx = kd

4) x = d, K = k, F4 = kd

5) x = d, K = 2k, F5 = 2kd

Hence F1 < F3 = F4 < F5 = F2

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