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Two blocks of masses m1 and m2 rest on a horizontal surface and are connected by a spring of constant K. The entire surface is given a sudden acceleration a toward the right. The coefficient of friction between m1 and the surface is mu1 and between m2 and the surface is mu2. Which of the following conclusions about the spring is correct?

1. The spring may elongate if mu2 is greater than mu1
2. The spring may be compressed if mu1 equals mu2
3. The spring may elongate if mu1 is less than mu2
4. There will be no elongation or compression in the spring if mu1 equals mu2

Correct answer: The spring may elongate if mu1 is less than mu2

Solution

When mu1 < mu2, block m1 receives less maximum frictional force relative to the force needed for acceleration, so it tends to lag behind m2; the spring stretches to supply the extra force to m1, resulting in elongation.

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