Question

Consider a box lying on a table. If another box is stacked on top of it, how will the gravitational force (weight) of the top box affect the frictional force between the bottom box and the table if someone pushes slowly on the lower box?

The frictional force will increase.
It is impossible to determine how the frictional force will change.
The frictional force will decrease.
The frictional force will remain the same.

Answer 1

The frictional force will increase.

Step-by-step explanation:

There are two types of frictions: static friction and kinetic friction. When the two surfaces are moving relative to one another, the friction between the two surfaces would be kinetic friction. Otherwise, the friction between the two would be static friction.

The magnitude of static friction vary within a certain range. The exact magnitude of static friction depends on the magnitude of the external force that tries to move the two surfaces against one another.

Unlike static friction, the magnitude of kinetic friction is equal to the product of:

• the magnitude of the normal force between the two surfaces, and
• the coefficient of kinetic friction between the two surfaces.

The coefficient of kinetic friction is a fixed value between two particular surfaces. As a result, the magnitude of kinetic friction between the two surfaces would be proportional to the magnitude of the normal force.

Apply the following steps to determine how the additional box affects the friction between the lower box and the table:

• Derive how the additional box affects the normal force between the lower box and the table.
• Determine the type of friction between the lower box and the table: kinetic friction or static friction.
• Derive whether and how the change in normal force affects the magnitude of friction.

Assuming that the table is level, the normal force between the lower box and the table would be initially equal to the weight of the lower box. After adding the additional box, that box would exert a downward force on the lower box. As a result, normal force between the lower box and the table would increase.

The statement that the person is pushing the lower box "slowly" suggests that the lower box is moving. Hence, the type of the friction between the lower box and the table would be kinetic friction.

Between two lower box and the table, the magnitude of kinetic friction is proportional to the normal force. The additional box increases the normal force between the two surfaces. As a result, the magnitude of kinetic friction between the two surfaces would also increase.