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# Newton's Third Law

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

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Practice Newton's Third Law

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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

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.

### Time for Practice

Refer to the Newtons Law problems section of this chapter for practice.

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