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

Engineering

Physics

Static and Kinetic Friction

Question

A block of mass m is placed on a surface with a vertical cross-section given by y = $\frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping

$\frac{1}{3} m$

$\frac{1}{2} m$

$\frac{1}{6} m$

$\frac{2}{3} m$

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µ = tan $θ$ = 0.5 = $\frac{dy}{dx} = \frac{x^{2}}{2}$

x² = 1

x = 1 ⇒ $y = \frac{1}{6} m$