A small block is pressed against a vertical wall of a cart. Coefficient of static friction between block and wall is μ. The cart has horizontal acceleration a = 2g/μ. The actual static friction on the block is:
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Question

A small block is pressed against a vertical wall of a cart. Coefficient of static friction between block and wall is μ. The cart has horizontal acceleration a = 2g/μ. The actual static friction on the block is:

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G1 Physics · Accepted Answer

The horizontal normal reaction is N = ma = m(2g/μ). Hence maximum available static friction is μN = 2mg. But static friction only adjusts to the value required. Vertical equilibrium requires f = mg upward. Therefore actual static friction is mg, not μN.