# Question below, how does the way someone pushes two boxes affect the action reaction forces on each box?

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Two trunks sit side by side on the floor. The large trunk (52kg) is to the left of the smaller trunk (34kg). A person pushes on the larger trunk horizontally toward the right. The coefficient of static friction between the trunks and the floor is 0.35.

Does the force that the larger trunk exerts on the smaller trunk change if the person pushed in the opposite direction (on the smaller trunk)?

Two trunks sit side by side on the floor. The large trunk (52kg) is to the left of the smaller trunk (34kg). A person pushes on the larger trunk horizontally toward the right. The coefficient of static friction between the trunks and the floor is 0.35.

Does the force that the larger trunk exerts on the smaller trunk change if the person pushed in the opposite direction (on the smaller trunk)?

The force does depend on which way one pushes the trunks. See below for details.

If you push on the larger trunk, the force applied by the larger trunk on the smaller crate is based on the value of the static coefficient and the normal force acting on the smaller trunk (which is equal to the weight of the smaller trunk).

(Don't be confused here - the force being applied by the person pushing both trunks is dependent on the weight of both trunks, and would not change if we changed directions. But the force being exerted by the large trunk on the smaller one depends only on the weight of the smaller one. It is as though the person and the larger trunk become one object that is causing the force one the smaller trunk.)

Now, if we reverse direction, and push on the smaller trunk instead, the amount of force between the trunks is based on the value of the static coefficient and the normal force acting on the larger trunk, as it is now the one that we are attempting to move. So, the force is larger than before.

We might be inclined to think that this larger force is the actually the small trunk pushing on the big trunk, but by Newton's third law, this must be equal to the force of the big trunk on the small trunk. I mention this only in the hope of making it clear that the force of the larger trunk on the smaller, or of the smaller trunk on the larger are the type of "equal and opposite" forces as described in Newton's third law.

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When someone pushes two boxes, the action reaction forces on each box depend on the direction and magnitude of the push. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. If the person pushes one box with more force than the other, the reaction force exerted by each box on the person will be different. If the person pushes both boxes with equal force in opposite directions, the reaction forces on each box will be equal and opposite, causing them to move in opposite directions. If the person pushes both boxes with different forces in the same direction, the reaction forces on each box will be in the opposite direction of the push.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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