5.3 Newton's second law  (Page 2/8)

It seems reasonable that acceleration would be directly proportional to and in the same direction as the net external force acting on a system. This assumption has been verified experimentally and is illustrated in [link] . To obtain an equation for Newton’s second law, we first write the relationship of acceleration $\overrightarrow{a}$ and net external force ${\overrightarrow{F}}_{\text{net}}$ as the proportionality

where the symbol $\propto$ means “proportional to.” (Recall from Forces that the net external force is the vector sum of all external forces and is sometimes indicated as ${\displaystyle \sum \overrightarrow{F}}.$ ) This proportionality shows what we have said in words—acceleration is directly proportional to net external force. Once the system of interest is chosen, identify the external forces and ignore the internal ones. It is a tremendous simplification to disregard the numerous internal forces acting between objects within the system, such as muscular forces within the students’ bodies, let alone the myriad forces between the atoms in the objects. Still, this simplification helps us solve some complex problems.

It also seems reasonable that acceleration should be inversely proportional to the mass of the system. In other words, the larger the mass (the inertia), the smaller the acceleration produced by a given force. As illustrated in [link] , the same net external force applied to a basketball produces a much smaller acceleration when it is applied to an SUV. The proportionality is written as

where m is the mass of the system and a is the magnitude of the acceleration. Experiments have shown that acceleration is exactly inversely proportional to mass, just as it is directly proportional to net external force.

It has been found that the acceleration of an object depends only on the net external force and the mass of the object. Combining the two proportionalities just given yields Newton’s second law .

The law is a cause-and-effect relationship among three quantities that is not simply based on their definitions. The validity of the second law is based on experimental verification. The free-body diagram, which you will learn to draw in Drawing Free-Body Diagrams , is the basis for writing Newton’s second law.