A 50.0-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.400. What is the force of friction on the box?
A) 31.9 N
B) 196 N
C) 217 N
D) 246 N
E) 616 N

Question

Quizplus · Accepted Answer

First, we need to break the given force into its horizontal and vertical components.

Horizontal force = 250 N * cos(30) = 216.5 N
Vertical force = 250 N * sin(30) = 125 N

The maximum force of static friction can be calculated by multiplying the coefficient of static friction (0.400) by the normal force (mg) on the box.

Maximum force of static friction = 0.400 * 50.0 kg * 9.81 m/s^2 = 196 N

Since the horizontal force applied (216.5 N) is greater than the maximum force of static friction (196 N), the box will begin to move. Therefore, the force of friction will be equal to the force of static friction, which is 196 N.

Therefore, the answer is C.

A 500-Kg Box Is Resting on a Horizontal Floor