Two boxes are stacked together on a slope. The smaller box of mass... Two boxes

Question

Two boxes are stacked together on a slope. The smaller box of mass...

Two boxes are stacked together on a slope. The smaller box of mass M_2 = 2.6kg is on top, while the larger box of mass M_1 = 4.1kg is on the bottom in contact with the slope surface. There is a coefficient of static friction mu_s between the boxes, and the interface between the larger box and the slope has coefficient of kinetic friction mu_s-k. A force parallel to the slope is applied to the bottom box to push it up at constant speed. If the pushing force has magnitude 34.0N, and the slope angle is theta = 15.2 degree, what is the value of the coefficient of kinetic friction between the box and slope?

Explanation / Answer

Given

   M1= 4.1 kg, M2 = 2.6 kg

   force F = 34 N, angle theta= 15.2 0

Fnet = 0



m2*g*sintheta - us*m2*g*costheta = 0


m2*g*sintheta = us*m2*g*costheta



for m1


Fnet = 0



F - uk*m1*g*costheta + us*m2*g*costheta - m1*g*sintheta = 0


34 - (uk*4.1*9.8*cos15.2) + (2.6*9.8*sin15.2) - (4.1*9.8*sin15.2) = 0




uk = 0.77

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