Question

The manager of a department store is pushing horizontally with a force of magnitude 200N on a box of shirts. The box is sliding across the horizontal floor with a forward acceleration. Nothing else touches the box. What must be true about the magnitude of the force of kineticfriction acting on the box (choose one)?

Answer 1

Found the missing options on internet:
a) it is less than 200 N; b) it is greater than 200 N; c) it is equal to 200 N; d) none of these statements are necessarily true

Solution:
The correct answer is a) it is less than 200 N.

In fact, the box is sliding with forward acceleration different from zero. This means that the net force acting on the box is different from zero, because Newton's second law states that:
$\sum F = ma$
the resultant of the forces acting on an object is equal to its mass times its acceleration.

In this case, we have 2 forces acting on the box:
- the force of 200 N of the man pushing the box
- the frictional force, acting against the direction of motion
The net acceleration is forward, this means that the net force acting on the box must be directed forward, therefore the magnitude of the frictional force must be smaller than the force of 200 N that pushes the box.