# Action and Reaction Forces: Law, Examples & Quiz

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### Elena Cox

Action force is force acting in one direction. Reaction force is force acting in the opposite direction. Learn more about Newton's third law as it explains action and reaction forces through several examples and test your knowledge with quiz questions.

We also recommend watching Identifying Action and Reaction Force Pairs and Rising Action in a Story: Definition, Examples & Quiz

## Definition

Forces always act in pairs. The two forces act in opposite directions. When you push on an object, the object pushes back with an equal force. Think of a pile of books on a table. The weight of the books exerts a downward force on the table. This is the action force. The table exerts an equal upward force on the books. This is the reaction force. Note that the two forces act on different objects. The action force acts on the table. The reaction force acts on the books.

## Force Pairs

The example with the boy playing with a dog's toy illustrates the idea of forces in interaction pairs. There is a force from the boy on the dog's toy, and there is a force from the dog's toy on the boy. Forces always come in pairs similar to this example. Consider the boy (A) as one system and the toy (B) as another. What forces act on each of the two systems. Looking at the force diagrams, you can see that each system exerts a force on the other. The two forces F(A on B) and F(B on A), are the forces of interaction between the two. Notice the symmetry in the subscripts: A on B and B on A.

The forces F(A on B)and F(B on A) are an interaction pair, which is a set of two forces that are in opposite directions, have equal magnitudes, and act on different objects. Sometimes, an interaction pair is called an action-reaction pair. This might suggest that one causes the other; however, this is not true. For example, the force of the boy pulling on the toy doesn't cause the toy to pull on the boy. The two forces either exist together or not at all.

There can never be a single force acting alone, without its action-reaction partner. Forces only come in action-reaction pairs. Think carefully about propelling a skateboard with your foot. Your foot presses backward against the ground. The force acts on the ground. However, you move, so a force must act on you, too. Why do you move? What force acts on you? You move because the action force of your foot against the ground creates a reaction force of the ground against your foot. You 'feel' the ground because you sense the reaction force pressing on your foot. The reaction force is what makes you move because it acts on you.

## Newton's Third Law

Newton's third law of motion explains action and reaction forces. The third law states that for every action force, there is an equal and opposite reaction force. Imagine hitting a baseball. The bat exerts a force on the ball. This is the action force. The ball exerts and equal and opposite force on the bat. This is the reaction force. In the illustration with the boy and the dog's toy, the force exerted by the boy on the toy is equal in magnitude and opposite in direction to the force exerted by the toy on the boy. Such an interaction pair is another example of Newton's third law, which states that all forces come in pairs. The two forces in a pair act on different objects and are equal in strength and opposite in direction.

The force of A on B is equal in magnitude and opposite in direction of the force of B on A:

F(A on B) = - F(B on A)

Newton realized that if one object pulls on another, the second object also pulls back on the first object. If one object pushes on another, the second pushes back on the first object. In other words, for every action by a force there is a reaction by another force.

## Draw Diagrams

When sorting out action and reaction forces, it is helpful to draw diagrams. Draw each object apart from the other. Represent each force as an arrow in the appropriate direction. Here are some guidelines to help you sort out action and reaction forces:

Consider the situation of holding a book in your hand. You can draw one diagram for you and one for the book. Are there any interaction pairs? When identifying interaction pairs, keep in mind that they always occur in two different diagrams and they always will have the symmetry of subscripts noted earlier. In this case, the interaction pair is F(book)on hand and F(hand) on book.

## Examples

We've gone through one example already; we said that when a bat exerts a force on the baseball, the ball also exerts an equal and opposite reaction force on the bat. What are some other examples? Let's look at the rocket engines. Newton's third law explains how rocket engines work. Hot gases are forced out of the back of the rocket. This is the action force. The gases exert an equal and opposite force on the rocket. This is the reaction force. The reaction pushes the rocket upward.

Notice what happens when the diver jumps on a diving board. The board springs back and forces the diver into the air. The action force exerted on the board by the diver causes a reaction force by the board on the diver. The force of the diver on the board is equal and opposite to the force exerted by the diving board. Think about the way the force of the diving board affects the diver's performance. The greater the force exerted upon the diving board, the higher the dive will be.

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