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# Newton's Third Law

## For every action, there is an equal and opposite reaction.

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Newton's Third Law (Accelerated)

### Newton’s Third Law of Motion

Where do forces come from?  Observations suggest that a force applied to an object is always applied by another object.  A hammer strikes a nail, a car pulls a trailer, and a person pushes a grocery cart.  Newton realized that forces are not so one sided.  When the hammer exerts a force on the nail, the nail also exerts a force on the hammer – after all, the hammer comes to rest after the interaction.  This led to Newton’s Third Law of Motion, which states that whenever one object exerts a force on a second object, the second object also exerts a force on the first object, equal in magnitude and opposite in direction.

This law is sometimes paraphrased as “for every action, there is an equal and opposite reaction.”  A very important point to remember is that the two forces are on different objects – never on the same object.  It is frequently the case that one of the objects moves as a result of the force applied but the motion of the other object in the opposite direction is not apparent.  Consider the situation where an ice skater is standing at the edge of the skating rink holding on to the side rail.  If the skater exerts a force on the rail, the rail is held in place with tremendous friction and therefore, will not move in any noticeable way.  The skater, on the other hand, had little friction with the ice, and therefore will be accelerated in the direction opposite of his/her original push.  This is the process people use to jump up into the air.  The person's feet exert force on the ground and the ground exerts an equal and opposite force on the person's feet.  The force on the feet is sufficient to raise the person off the ground.  The force on the ground has little effect because the earth is so large.  One of the accelerations is visible but the other is not visible.

A case where the reaction motion due to the reaction force is visible is the case of a person throwing a heavy object out of a boat.  The object is accelerated in one direction and the boat is accelerated in the opposite direction.  In this case, both the motion of the object is visible and the motion of the boat in the opposite direction is also visible.

Rockets also work in this manner.  It is a misconception that the rocket moves forward because the escaping gas pushes on the ground or the surrounding air to make the rocket go forward.  Rockets work in outer space where there is no ground or surrounding air.  The rocket exerts a force on the gases causing them to be expelled and the gases exert a force on the rocket causing it to be accelerated forward.

#### Summary

• A force applied to an object is always applied by another object.
• Newton’s Third Law of Motion says, "whenever one object exerts a force on a second object, the second object also exerts a force on the first object, equal in magnitude and opposite in direction."

#### Practice

The following video contains a discussion and an example of Newton’s Third Law of Motion.

### Key Equations

F=F\begin{align*} \vec{F} = - \vec{F'} \end{align*}

Guidance
Newton’s 3rd\begin{align*}3^{rd}\end{align*} Law states for every force there is an equal but opposite reaction force. To distinguish a third law pair from merely oppositely directed pairs is difficult, but very important. Third law pairs must obey three rules: (1) Third law force pairs must be of the same type of force. (2) Third law force pairs are exerted on two different objects. (3) Third law force pairs are equal in magnitude and oppositely directed. Example: A block sits on a table. The Earth’s gravity on the block and the force of the table on the block are equal and opposite. But these are not third law pairs, because they are both on the same object and the forces are of different types. The proper third law pairs are: (1) earth’s gravity on block/block’s gravity on earth and (2) table pushes on block/ block pushes on table.

#### Example 1

Question: Tom and Mary are standing on identical skateboards. Tom and Mary push off of each other and travel in opposite directions.

a) If Tom (M)\begin{align*}(M)\end{align*} and Mary (m)\begin{align*}(m)\end{align*} have identical masses, who travels farther?

b) If Tom has a bigger mass than Mary, who goes farther?

c) If Tom and Mary have identical masses and Tom pushes twice as hard as Mary, who goes farther?

Solution

a) Neither. Both Tom and Mary will travel the same distance. The forced applied to each person is the same (Newton's Third Law). So Ma=ma\begin{align*} \cancel{M}a=\cancel{m}{a} \end{align*} which cancels to a=a\begin{align*} a=a \end{align*} Therefore both people will travel the same distance because the acceleration controls how far someone will travel and Tom and Mary have equal acceleration.

b) Mary will go farther. Again, the same force is applied to both Mary and Tom so Ma=ma\begin{align*} Ma=ma \end{align*} Since Tom has the larger mass, his acceleration must be smaller (acceleration and mass are inversely proportional). Finally, because Mary's acceleration is greater, she will travel farther.

c) Neither. Newton's Third Law states that for every action there is an equal and opposite reaction. Therefore if Tom pushes twice as hard as Mary, Mary will essentially be pushing back with the same strength. They will therefore travel the same distance.

### Review Questions

1. You are standing on a bathroom scale. Can you reduce your weight by pulling up on your shoes? (Try it.)
2. A VW Bug hits a huge truck head-on. Each vehicle was initially going 50 MPH.
1. Which vehicle experiences the greater force?
2. Which experiences the greater acceleration? Explain briefly.
3. You and your friend are standing on identical skateboards with an industrial-strength compressed spring in between you. After the spring is released, it falls straight to the ground and the two of you fly apart.
1. If you have identical masses, who travels farther?
2. If your friend has a bigger mass who goes farther?
3. If your friend has a bigger mass who feels the larger force?
4. If you guys have identical masses, even if you push on the spring, why isn’t it possible to go further than your friend?

Discuss in class.

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