Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
4.4 Newton’s Third Law
Authors: William Moebs, Samuel Ling, Jeff Sanny
Adapted by: Rob Pryce, Alix Blacklin
Learning Objectives
By the end of this section, you will be able to:
- State Newton’s third law of motion
- Identify the action and reaction forces in different situations
- Apply Newton’s third law to define systems and solve problems of motion
We have thus far considered force as a push or a pull; however, if you think about it, you realize that no push or pull ever occurs by itself. When you push on a wall, the wall pushes back on you. This brings us to Newton’s third law.
Baseball relief pitcher Mariano Rivera was so highly regarded that during his retirement year, opposing teams conducted farewell presentations when he played at their stadiums. The Minnesota Twins offered a unique gift: A chair made of broken bats. Any pitch can break a bat, but with Rivera’s signature pitch—known as a cutter—the ball and the bat frequently came together at a point that shattered the hardwood. Typically, we think of a baseball or softball hitter exerting a force on the incoming ball, and baseball analysts now focus on the resulting “exit velocity” as a key statistic. But the force of the ball can do its own damage. This is exactly what happens whenever one body exerts a force on another—the first also experiences a force (equal in magnitude and opposite in direction). Numerous common experiences, such as stubbing a toe or pushing off the floor during a jump, confirm this. It is precisely stated in Newton’s third law of motion.
Newton’s Third Law of Motion
Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.
Mathematically, if a body A exerts a force [latex]\overset{\to }{F}[/latex] on body B, then B simultaneously exerts a force [latex]\text{−}\overset{\to }{F}[/latex] on A, or in vector equation form,
We can readily see Newton’s third law at work by taking a look at how people move about. Consider a swimmer pushing off the side of a pool (Figure 4.16). She pushes against the wall of the pool with her feet and accelerates in the direction opposite that of her push. The wall has exerted an equal and opposite force on the swimmer. You might think that two equal and opposite forces would cancel, but they do not because they act on different systems. In this case, there are two systems that we could investigate: the swimmer and the wall. If we select the swimmer to be the system of interest, as in the figure, then [latex]{F}_{\text{wall on feet}}[/latex] is an external force on this system and affects its motion. The swimmer moves in the direction of this force. In contrast, the force [latex]{F}_{\text{feet on wall}}[/latex] acts on the wall, not on our system of interest. Thus, [latex]{F}_{\text{feet on wall}}[/latex] does not directly affect the motion of the system and does not c