Question

You are helping a friend move. consider two boxes which have masses in factors of m; one of mass 6m and the other of mass 9m. the coefficient of static friction between the two boxes is very large. the coefficient of static friction between the boxes and the floor is 0.9 and the coefficient of kinetic friction is 0.1. you stack the two boxes on top of each other to slide them across the floor at a certain constant velocity. you switch which one is on the bottom and slide them with the same constant velocity. in the configuration where there is the most force between the boxes, what is the ratio of the force between the boxes to the force you must apply?

Answer 1

The ratio of the force between the boxes to the force you must apply can be determined by considering the forces acting on the top box. When the top box is sliding, the force of static friction between the boxes is equal to the force you must apply to keep the boxes moving at a constant velocity.

Step-by-step explanation:

The ratio of the force between the boxes to the force you must apply can be determined by considering the forces acting on the top box. When the top box is sliding, the force of static friction between the boxes is equal to the force you must apply to keep the boxes moving at a constant velocity. The force of static friction is given by:

fs = μsN = μs(mg) = 0.9(15m)(9.8m/s²) = 132.3m²N

The force between the boxes can be determined by considering the normal force and the gravitational force acting on the top box:

fbox = mg = 15m(9.8m/s²) = 147m²N

Therefore, the ratio of the force between the boxes to the force you must apply is:

Ratio = fs / fbox = 132.3m²N / 147m²N = 0.9