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Two blocks of masses m1 and m2 are connected by a spring of spring constant k and placed on a plank lying on a frictionless horizontal surface. The coefficient of friction between m1 and the plank is mu1, and between m2 and the plank is mu2. The plank is given a sudden horizontal acceleration of magnitude a. Which of the following statements is correct regarding the motion of the blocks immediately after the plank starts moving?

1. The spring force on both blocks is zero immediately after the plank starts accelerating
2. Block m1 slides on the plank only if a > mu1 * g
3. Block m2 slides on the plank only if a > mu2 * g
4. Both blocks slide on the plank simultaneously if a > mu1 * g and a > mu2 * g

Correct answer: Block m1 slides on the plank only if a > mu1 * g

Solution

The blocks are initially at rest on the plank. When the plank accelerates at a, the friction force is the only horizontal force on each block. Block m1 will remain stationary relative to the plank (no sliding) if friction can provide acceleration a, i.e., mu1 * m1 * g >= m1 * a, meaning a <= mu1 * g. It slides if a > mu1 * g. Similarly for m2 with mu2. The spring force is zero only at the very instant before relative motion begins; the condition for sliding depends independently on each block's friction coefficient.

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