A block of mass m is placed on a surface whose vertical cross-section is y = x³/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:
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Question

A block of mass m is placed on a surface whose vertical cross-section is y = x³/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

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G1 Physics · Accepted Answer

For equilibrium on the local tangent, tanθ ≤ μ. Here dy/dx = x²/2, so x²/2 ≤ 1/2, giving xₘₐₓ = 1 m. The corresponding height is y = 1³/6 = 1/6 m.