5.5 Newton’s third law  (Page 2/6)

Other examples of Newton’s third law are easy to find:

• As a professor paces in front of a whiteboard, he exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes him to accelerate forward.
• A car accelerates forward because the ground pushes forward on the drive wheels, in reaction to the drive wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw the rocks backward.
• Rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber; therefore, the gas exerts a large reaction force forward on the rocket. This reaction force, which pushes a body forward in response to a backward force, is called thrust    . It is a common misconception that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can more readily expel the exhaust gases.
• Helicopters create lift by pushing air down, thereby experiencing an upward reaction force.
• Birds and airplanes also fly by exerting force on the air in a direction opposite that of whatever force they need. For example, the wings of a bird force air downward and backward to get lift and move forward.
• An octopus propels itself in the water by ejecting water through a funnel from its body, similar to a jet ski.
• When a person pulls down on a vertical rope, the rope pulls up on the person ( [link] ).

There are two important features of Newton’s third law. First, the forces exerted (the action and reaction) are always equal in magnitude but opposite in direction. Second, these forces are acting on different bodies or systems: A ’s force acts on B and B ’s force acts on A . In other words, the two forces are distinct forces that do not act on the same body. Thus, they do not cancel each other.

For the situation shown in [link] , the third law indicates that because the chair is pushing upward on the boy with force $\overrightarrow{C},$ he is pushing downward on the chair with force $\text{−}\overrightarrow{C}.$ Similarly, he is pushing downward with forces $\text{−}\overrightarrow{F}$ and $\text{−}\overrightarrow{T}$ on the floor and table, respectively. Finally, since Earth pulls downward on the boy with force $\overrightarrow{w},$ he pulls upward on Earth with force $\text{−}\overrightarrow{w}$ . If that student were to angrily pound the table in frustration, he would quickly learn the painful lesson (avoidable by studying Newton’s laws) that the table hits back just as hard.

A person who is walking or running applies Newton’s third law instinctively. For example, the runner in [link] pushes backward on the ground so that it pushes him forward.

Forces on a stationary object

The package in [link] is sitting on a scale. The forces on the package are $\overrightarrow{S},$ which is due to the scale, and $\text{−}\overrightarrow{w},$ which is due to Earth’s gravitational field. The reaction forces that the package exerts are $\text{−}\overrightarrow{S}$ on the scale and $\overrightarrow{w}$ on Earth. Because the package is not accelerating, application of the second law yields

$\overrightarrow{S}-\overrightarrow{w}=m\overrightarrow{a}=\overrightarrow{0},$

so

$\overrightarrow{S}=\overrightarrow{w}.$

Thus, the scale reading gives the magnitude of the package’s weight. However, the scale does not measure the weight of the package; it measures the force $\text{−}\overrightarrow{S}$ on its surface. If the system is accelerating, $\overrightarrow{S}$ and $\text{−}\overrightarrow{w}$ would not be equal, as explained in Applications of Newton’s Laws .

Got questions? Get instant answers now!