The figure shows two boxes, with m₁ m₂, that are on a level frictionless surface. We can apply a horizontal force $\overrightarrow { \mathbf { F } }$ either toward the right on m₁ or toward the left on m₂. The magnitude of the force that the boxes exert on each other is A) zero newtons in either case. B) larger if $\overrightarrow { \mathbf { F } }$ is applied toward the right. C) larger if $\overrightarrow { \mathbf { F } }$ is applied toward the left. D) the same in either case.

Question

The figure shows two boxes, with m₁ > m₂, that are on a level frictionless surface. We can apply a horizontal force $\overrightarrow { \mathbf { F } }$ either toward the right on m₁ or toward the left on m₂. The magnitude of the force that the boxes exert on each other is A) zero newtons in either case. B) larger if $\overrightarrow { \mathbf { F } }$ is applied toward the right. C) larger if $\overrightarrow { \mathbf { F } }$ is applied toward the left. D) the same in either case.

Quizplus · Accepted Answer

Since m₁ > m₂, the box on the left has more mass than the box on the right. If we apply a force toward the left on the box with less mass (m₂), it will move to the left with an acceleration a. The force that the box with more mass (m₁) exerts on the other box will be equal and opposite to the force that we apply on m₂ according to Newton's Third Law. Thus, the force that the box with more mass exerts on the other box will be equal to F, the force that we apply on the box with less mass. The force of friction between the boxes will also be equal to F since the surface is frictionless. Therefore, the net force on the box with more mass will be F towards the right. Thus, according to Newton's Second Law, the acceleration of the box with more mass will be a' = F/m₁ = F/(m₂ + m₁). Since a' < a, the box with more mass will move to the right with a smaller acceleration. Therefore, the force that the boxes exert on each other will be larger if we apply the force toward the left on the box with less mass.

The Figure Shows Two Boxes, with M1 > M2, That F→\overrightarrow { \mathbf { F } }F

The Figure Shows Two Boxes, with M₁ > M₂, That $\overrightarrow { \mathbf { F } }$