On a frictionless horizontal surface there is a wooden block A with a mass M. On top of A there is a lead block B also with a mass of M. The coefficients of static and kinetic friction between A and B are 0.5 and 0.25 respectively. A horizontal force of magnitude F is applied to B. If is increased continuously starting from F = 0, then it is observed that the acceleration of block A, aA, reaches a maximum value amax when F = Fmax. The graphs below show how the acceleration of the two blocks depends on the values of F, for F between 0 and 2Fmax. Choose the correct graph.

Engineering

Physics

Friction

Question

On a frictionless horizontal surface there is a wooden block A with a mass M. On top of A there is a lead block B also with a mass of M. The coefficients of static and kinetic friction between A and B are 0.5 and 0.25 respectively. A horizontal force of magnitude F is applied to B. If is increased continuously starting from F = 0, then it is observed that the acceleration of block A, a_A, reaches a maximum value a_max when F = F_max.

The graphs below show how the acceleration of the two blocks depends on the values of F, for F between 0 and 2F_max. Choose the correct graph.

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F_{A max} = µ_sMg = Ma_max
once sliding occurs
F_A = µ_kMg = Ma after
a after = µ_kg
after that force on B
F = – µ_kMg = Ma_B
a_B = $\frac{F}{M}$ – µ_kg
just before
F – µ_sMg = Ma_max
a_max = $\frac{F}{M}$ – m_sg

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