The drawing shows three blocks, each with the same mass, stacked one upon the other. The bottom block rests on a frictionless horizontal surface and is being pulled by a force   that is parallel to this surface. The surfaces where the blocks touch each other have identical coefficients of static friction. Which one of the following correctly describes the magnitude of the net force of static friction fs that acts on each block?

fs,A = fs,C = fs,B/2
fs,A = fs,B = fs,C
fs,C = 0 and fs,A = fs,B/2
fs,A = fs,B = fs,C/2
fs,A = 0 and fs,B = fs,C/2
This answer states that the net frictional force acting on block C is zero, which implies that the surfaces where blocks B and C are in contact are frictionless. However, these surfaces have a coefficient of static friction, so a frictional force must act on block C.
B is incorrect: This answer states that the net frictional forces acting on blocks A and C have the same magnitude. However, a greater frictional force acts on block C than on block A, because the normal force pressing blocks B and C together is greater than the normal force pressing blocks A and B together.
A is incorrect: This answer states that the net frictional forces acting on blocks A and C have the same magnitude. However, a greater frictional force acts on block C than on block A, because the normal force pressing blocks B and C together is greater than the normal force pressing blocks A and B together.
E is incorrect: This answer states that the net frictional force acting on block A is zero, which implies that the surfaces where blocks A and B are in contact are frictionless. However, these surfaces have a coefficient of static friction, so a frictional force must act on block A.
C is incorrect: This answer states that the net frictional force acting on block C is zero, which implies that the surfaces where blocks B and C are in contact are frictionless. However, these surfaces have a coefficient of static friction, so a frictional force must act on block C.
D is correct: The static frictional force that blocks A and B exert on each other has a magnitude f. The force that B exerts on A is directed to the right (the positive direction), while the force that A exerts on B is directed to the left. Blocks B and C also exert static frictional forces on each other, but these forces have a magnitude 2f, because the normal force pressing B and C together is twice the normal force pressing A and B together. The force that C exerts on B is directed to the right, while the force that B exerts on C is directed to the left. In summary, then, block A experiences a single frictional force +f, which is the net frictional force; block B experiences two frictional forces, f and +2f, the net frictional force being f +2f = +f; block C experiences a single frictional force +2f, which is the net frictional force. It follows that fs,A = fs,B = fs,C/2.
Three identical blocks are being pulled or pushed across a horizontal surface by a force  , as shown in the drawings. The force   in each case has the same magnitude. Rank the kinetic frictional forces that act on the blocks in ascending order (smallest first).

B, A, C
A, C, B
C, B, A
C, A, B
B, C, A
E is incorrect: This answer states that the kinetic frictional force is smaller in C than in A. The magnitude of the frictional force is proportional to the magnitude of the normal force. However, the normal force in C is greater than the block’s weight due to the vertical component of  , whereas the normal force in A is equal to the block’s weight. Therefore, the frictional force in C is greater, not smaller, than in A.
B is incorrect: This answer states that the kinetic frictional force is smaller in C than in B. The magnitude of the frictional force is proportional to the magnitude of the normal force. However, the normal force in C is greater than the block’s weight due to the vertical component of  , whereas the normal force in B is less than the block’s weight due to the vertical component of  . Therefore, the frictional force in C is greater, not smaller, than in B.
C is correct: The magnitude of the kinetic frictional force is proportional to the magnitude of the normal force. The normal force is smallest in B, because the vertical component of   compensates for part of the block’s weight. In contrast, the normal force is greatest in C, because the vertical component of   adds to the weight of the block.

A heavy block is suspended from a ceiling using pulleys in three different ways, as shown in the drawings. Rank the tension in the rope that passes over the pulleys in ascending order (smallest first).

B is correct: More pulleys, less tension on rope.  In B the tension T is the smallest, because three rope segments support the weight W of the block, with the result that 3T = W, or T = W/3. In A the tension is the greatest, because only one rope segment supports the weight of the block, with the result that T = W.

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