The same constant force P is applied to three identical boxes at rest on the flo

Question

The same constant force P is applied to three identical boxes at rest on the floor the forces are in different directions, as shown in the diagram below. As the boxes remain at rest, on which of the three boxes is the frictional force the largest? I he smallest? Or is the frictional force on each box the same? Explain using appropriate free-body diagrams and Newton's second law. Note that this question asks about the actual friction force and not the maximum possible friction force. If P is steadily increased, will A or B start to move first? B or C? A or C? If it is not possible to answer a given question, so state.

Explanation / Answer

Given

the force applied on the box is same but at different directions

   for box A the frictional force is F = mue_s*N

where mue_s is coefficient of static friction which is same for all the boxes hereand

   N is normalforce acting on the box, so if the normal force is large then the frictional force is also large

for box A the normal forc is N = mg

for box B
   Normal force is N = mg+mg sin theta = mg(1+sin theta)

for box C

   normal force i N = mg -mg sin theta = mg(1-sintheta)

so the frictional force will be maximum for the box B and minimum for the box C

if P force is steadily increased then box A will move first among A,B
among

   B,C ; C will move first

among A,C; C will move first

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