Action and Reaction Forces: Newton's Third Law of Motion

Lesson Plan - Get It!

Audio:

Force Interactions and Force Diagrams

You may already know that the force of gravity pulls you to the center of the earth and keeps you from flying out into outer space. What you might find surprising is that you are also pulling on the earth.

• How does that happen?
• How great is the force?

To understand, you must first realize that force results from the interaction of two bodies. Newton discovered that whenever an object interacts with another object, they will exert force on each other. If the earth pulls you with a force of 300 N for example, you are also pulling the earth in the opposite direction with 300 N of force.

This fundamental principle is Newton's third law of motion, or the law of action-reaction, which formally states:

"For every action, there is an equal but opposite force of reaction."

When you place a ball on a tabletop, the ball's weight is the action force that pushes the table downward. The table, on the other hand, will exert a reaction force on the ball that will push it upward.

Let's identify and illustrate the pair of forces described above.

In physics and engineering, the representation of forces acting on an object is shown in a free-body diagram or a force diagram. This is used to determine the effect of forces on the object's motion and resulting reactions.

In a force diagram, forces are represented by arrows. The length of the arrows determines its strength while the arrowhead shows the direction in which the force is acting.

These forces can be applied either horizontally along the x-axis or vertically along the y-axis.

Look at these force diagrams for a box:

The length of each arrow is the same, which means that each force acting on the box is the same amount. However, the arrows are pointing in opposite directions; which shows that the forces opposite as well.

Diagram 1 has two forces along the horizontal, or the x-axis, that are the same strength but opposite in direction.

Diagram 2 has two forces along the vertical, or y-axis, which are also the same strength and opposite in direction.

• How will you describe the motion of the box in each diagram?

If you completed the first Related Lesson in this series, you will recall that the sum of all the forces, or the net force, acting on the box is zero if the forces are the same in strength but acting in opposite directions. This condition satisfies Newton's first law of motion that when an object's net force is zero, it will remain at rest or move at a constant speed in a specific direction.

(If you have not completed the earlier Related Lessons yet, check them out in the right-hand sidebar!)

Love a Pair!

• What are some of the examples of force pairs that you see around you?

Almost anything that you touch or have interaction with involves a force. A slight tap on the screen of your mobile device, for instance, involves action and reaction forces.

• Would you believe that even your ability to walk is made possible by Newton's third law of motion?

Explore the force pairs that exist within each of the following examples:

Swimming

In swimming, the arms of the swimmer will sweep the water to the back with a certain amount of force (action force). In return, the water pushes the swimmer forward (reaction force).

The strength of the force of the hand bringing the water backward will be the same amount of force propelling or moving the swimmer forward.

Watch Newton's 3rd Law - Why does a swimmer push the water backward?, from It's AumSum Time:

An Inflated Balloon

Similar to a real rocket ship, releasing the air from an inflated balloon demonstrates Newton's third law of motion.

When the balloon is filled with air, the air pushes the inside walls of the balloon (action force). The inside walls of the balloon push the air back in the opposite direction (reaction force).

Watch Balloon Rocket! Newton's Third Law of Motion., from Scientist Susan:

Do the Math!

Remember that when the object is at rest or moving at a constant velocity, the net force acting on it is zero. Newton's third law of motion supports this statement.

Mathematically, we can express the net force acting on the object as the sum of the individual forces. Suppose we have the same ball on a tabletop where the ball exerts a force (F₁) on the table, and the table exerts a force (F₂) on the ball. We can find the net force (F_net) with this equation:

F_net = (-F₁) + F₂

Note that we use -F₁ for the force of the ball on the table because we choose a downward force to be negative.

Suppose F₁ is 10 N and F₂ is also 10 N. You substitute these values into the equation:

F_net = (-10 N) + 10 N

F_net = 0 N

A zero net force for the ball on the tabletop means that it is at rest.

Time to review what you have learned with Wisc-Online's final video, Newton's Third Law of Motion:

Now that you understand the basic principles and assumptions behind Newton's third law of motion, you are ready to explore more examples of its applications in the Got It? section!