Question

The diagram below shows three identical blocks with weights placed on top of them. Each weight shown has the same mass. As indicated in the diagram, the blocks and weights are arranged in three different ways on the same surface, and a horizontal force is applied to each arrangement to produce slow movement.

Image

For which arrangement is the horizontal force the greatest?

A.
Arrangement X

B.
Arrangement Y

C.
Arrangement Z

D.
The force required is the same for all three arrangements.

Answer 1

D. The force is the same for all three.

Reason: for slow (steady) motion the horizontal force must balance the total kinetic friction. Each block's friction = μ_k times its normal force, so the total friction = μ_k times the sum of all normal forces. The sum of the normals equals the total weight of the three blocks plus the three identical weights, which is the same in every arrangement. Thus the required horizontal force is the same in X, Y and Z.