A box with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it with a force of 10 N and it does not move. To start it moving, a second person pulls vertically upward on the box. If the coefficient of static friction is 0.4, what is the smallest vertical force for which the box moves?
A) 4 N
B) 10 N
C) 14 N
D) 25 N
E) 35 N

Question

A box with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it with a force of 10 N and it does not move. To start it moving, a second person pulls vertically upward on the box. If the coefficient of static friction is 0.4, what is the smallest vertical force for which the box moves? 
A) 4 N 
B) 10 N 
C) 14 N 
D) 25 N 
E) 35 N

Quizplus · Accepted Answer

To start the box moving, the force applied by the second person (vertical force) must overcome the force of static friction between the box and the surface. The maximum force of static friction can be found by multiplying the coefficient of static friction by the normal force (the force exerted by the surface on the box, which is equal to the weight of the box):

maximum force of static friction = coefficient of static friction x normal force
= 0.4 x 50 N
= 20 N

Since the horizontal force applied by the first person is 10 N, the net force on the box is:

net force = horizontal force - maximum force of static friction
= 10 N - 20 N
= -10 N

Since the net force is negative, the box does not move horizontally. Therefore, the force applied by the second person must be greater than the maximum force of static friction in order to start the box moving.

The smallest vertical force for which the box moves can be found by setting the net force equal to zero (since the box is just starting to move, the net force is zero):

net force = vertical force - weight - maximum force of static friction
= vertical force - 50 N - 20 N
= 0 N

Solving for the vertical force gives:

vertical force = weight + maximum force of static friction
= 50 N + 20 N
= 70 N

Therefore, the smallest vertical force for which the box moves is 70 N. The closest answer option is D, 25 N, but this is not the correct choice.

A Box with a Weight of 50 N Rests on a Horizontal