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A block of mass “m” sits on a (bigger) block of mass “4m” that is on...

A block of mass “m” sits on a (bigger) block of mass “4m” that is on a frictionless table. The coefficients of friction between the two blocks are μs (static) and μk (kinetic). Assume that a horizontal force “F” is applied to the block on top (i.e. the smaller block with mass “m”). The force “F” is variable. The figure below is representative of this scenario. (You may use m = 10 kg, μs = 0.8, μk = 0.6, and g = 9.8 m/s2 to obtain a numerical answer.

(i) Draw free-body diagrams for each block. Your free-body diagram must clearly show and label all forces acting on the block.

(ii) Find an expression for the maximum force “F = Fmax” that can be applied such that the two blocks do not slide relative to each other.

(iii) Find the accelerations of the two blocks when the applied force F is Fmax/3.

(iv) Find the accelerations of the two blocks when the applied force F is 3Fmax.

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