A push of magnitude P acts on a box of weight W as shown in the figure.The push is directed at an angle θ below the horizontal,and the box remains a rest.The box rests on a horizontal surface that has some friction with the box.The friction force on the box due to the floor is equal to
A)P sin θ.
B)P cos θ.
C)0.
D)P cos θ + W.
E)P + W.

Question

A push of magnitude P acts on a box of weight W as shown in the figure.The push is directed at an angle θ below the horizontal,and the box remains a rest.The box rests on a horizontal surface that has some friction with the box.The friction force on the box due to the floor is equal to 
A)P sin θ. 
B)P cos θ. 
C)0. 
D)P cos θ + W. 
E)P + W.

Quizplus · Accepted Answer

Since the box is at rest, the net force acting on it must be zero. The forces acting on the box are the push force P and the weight W, which are not in the same direction. The force of friction Ff acting on the box opposes the direction of motion, which is zero. Therefore, the force of friction Ff must be equal and opposite to the horizontal component of the push force, which is P cos θ. Thus, Ff = P cos θ.

A Push of Magnitude P Acts on a Box of Weight