A heavy wooden block is dragged by a force along a rough steel plate, as shown below for two cases. The magnitude of the applied force is the same for both cases. The normal force in (ii), as compared with the normal force in (i) is:
A) the same
B) greater
C) less
D) less for some angles of the incline and greater for others
E) less or greater, depending on the magnitude of the applied force

Question

A heavy wooden block is dragged by a force  along a rough steel plate, as shown below for two cases. The magnitude of the applied force  is the same for both cases. The normal force in (ii), as compared with the normal force in (i) is: 
A) the same 
B) greater 
C) less 
D) less for some angles of the incline and greater for others 
E) less or greater, depending on the magnitude of the applied force

Quizplus · Accepted Answer

In both cases, the weight of the block is perpendicular to the surface and exerts a normal force N on the block. The force parallel to the surface (the force of friction) is given by f = µN, where µ is the coefficient of friction. Since the force applied is the same in both cases, the only difference is the angle of the incline. As the incline becomes steeper, the gravitational force component parallel to the surface increases, which increases the force of friction. However, the normal force decreases, since it is given by the perpendicular component of the weight. This means that the net force parallel to the surface (and hence the acceleration of the block) remains the same in both cases, but the normal force is less in case (ii) than in case (i). Therefore, the answer is (C) less.

A Heavy Wooden Block Is Dragged by a Force