Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion
4.3 Newton’s Second 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:
- Distinguish between external and internal forces
- Describe Newton’s second law of motion
- Explain the dependence of acceleration on net force and mass
Newton’s second law is closely related to his first law. It gives the cause-and-effect relationship between force and changes in motion. Newton’s second law is quantitative and is used extensively in biomechanics to calculate what happens in situations involving a force. Before we write down Newton’s second law as a simple equation, let’s look at some of the ideas we mentioned earlier.
Force and Acceleration
First, what do we mean by a change in motion? The answer is that a change in motion is equivalent to a change in velocity. A change in velocity means, by definition, that there is acceleration. Newton’s first law says that a net external force causes a change in motion; thus, we see that a net external force causes acceleration.
We defined external force in the previous section as a force acting on an object that originates from outside the object. Let’s consider this further. An intuitive notion of external is correct—it is outside the system of interest. For example, in Figure 4.10(a), the system of interest is the car plus the person within it. The two forces exerted by the two students are external forces. In contrast, an internal force acts between elements of the system or car. For example, the force the person in the car exerts to hang on to the steering wheel is an internal force. According to Newton’s First Law, only external forces affect the motion of an object. (The internal forces cancel each other out, as explained in the next section.)
From the example above, you can see that different forces exerted on the same mass produce different accelerations. In Figure 4.10(a), the two students push a car with a driver in it. Arrows representing all external forces are shown. The object (or system of interest) is the car and its driver. The weight [latex]\overset{\to }{w}[/latex] of the system and the support of the ground [latex]\overset{\to }{N}[/latex] are also shown for completeness and are assumed to cancel (because there was no vertical motion and no imbalance of forces in the vertical direction to create a change in motion). The vector [latex]\overset{\to }{f}[/latex] represents the friction acting on the car, and it acts to the left, opposing the motion of the car. (We discuss friction in more detail in the next chapter.)
In Figure 4.10 (b), all external forces acting on the system add together to produce the net force [latex]{\overset{\to }{F}}_{\text{net}}.[/latex] The free-body diagram shows all of the forces acting on the system of interest. The dot represents the center of mass of the system. Each force vector extends from this dot. Beca