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102. Problem 16.25P (HRW) Two blocks (m=1.0 kg and M=10 kg) and a spring (k=200 N/m) are arranged on a horizontal, frictionless surface as shown in the figure. The coefficient of static friction between the two blocks is 0.40. We have to find the maximum possible amplitude of simple harmonic motion if no slippage is to occur between the blocks.
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Solution: Click For PDF Version Data of the problem are:
Maximum acceleration,
Maximum amplitude for motion determines the maximum spring force exerted on the system of two blocks. We therefore have the equation
This gives
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, with
which the upper block of mass m=1.0 kg can move without slipping on the
block of mass M=10 kg is determined by the maximum force of static
friction between the two blocks. Coefficient of static friction between the two
blocks is
.
Therefore,
