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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

Students will learn that Newton's 3rd law holds that for every force there is an equal but opposite reaction force. Important to note that the force and reaction force act on different objects.

Key Equations

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

Newton’s \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 \begin{align*}(M)\end{align*} and Mary \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?


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 \begin{align*} \cancel{M}a=\cancel{m}{a} \end{align*} which cancels to \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 \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.

Time for Practice

  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?
  4. Analyze the situation shown here with a big kid pulling a little kid in a wagon. You’ll notice that there are a lot of different forces acting on the system. Let’s think about what happens the moment the sled begins to move.
    1. First, draw the free body diagram of the big kid. Include all the forces you can think of, including friction. Then do the same for the little kid.
    2. Identify all third law pairs. Decide which forces act on the two body system and which are extraneous.
    3. Explain what conditions would make it possible for the two-body system to move forward.

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