A person is pushing on a box exerting a force of magnitude P, as shown in the figure.Earth exerts a force W on the box.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 force that the surface exerts on the box perpendicular to the surface is equal to
A)W.
B)W + P.
C)W + P cos θ.
D)W + P sin θ.
E)W - P sin θ.

Question

A person is pushing on a box exerting a force of magnitude P, as shown in the figure.Earth exerts a force W on the box.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 force that the surface exerts on the box perpendicular to the surface is equal to 
A)W. 
B)W + P. 
C)W + P cos θ. 
D)W + P sin θ. 
E)W - P sin θ.

Quizplus · Accepted Answer

Since the box is at rest, the net force acting on it must be zero. This means that the force due to friction must be equal in magnitude and opposite in direction to the force due to the push.

The force due to friction is perpendicular to the surface of the box and has magnitude μN, where μ is the coefficient of friction and N is the normal force exerted by the surface on the box.

The normal force N is equal in magnitude to the weight of the box (W), since the box is not accelerating vertically.

Therefore, the force due to friction is μW.

The force due to the push is P sinθ, since only the component of the force perpendicular to the surface contributes to the net force.

Since the net force is zero, we have:

P sinθ = μW

Solving for the normal force, we get:

N = W = (P sinθ)/μ

The force that the surface exerts on the box perpendicular to the surface is the normal force, which is equal to W.

Therefore, the answer is choice (D), W + P sinθ.

A Person Is Pushing on a Box Exerting a Force