0.3 3.4 newton’s second law of motion  (Page 2/13)

To obtain an equation for Newton’s second law, we first write the relationship of acceleration and net external force as the proportionality

where the symbol $\propto$ means “proportional to,” and ${\mathbf{\text{F}}}_{\text{net}}$ is the net external force    . (The net external force is the vector sum of all external forces and can be determined graphically, using the head-to-tail method, or analytically, using components. The techniques are the same as for the addition of other vectors, and are covered in Two-Dimensional Kinematics .) This proportionality states what we have said in words— acceleration is directly proportional to the net external force . Once the system of interest is chosen, it is important to identify the external forces and ignore the internal ones. It is a tremendous simplification not to have to consider the numerous internal forces acting between objects within the system, such as muscular forces within the child’s body, let alone the myriad of forces between atoms in the objects, but by doing so, we can easily solve some very complex problems with only minimal error due to our simplification

Now, 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. And indeed, as illustrated in [link] , the same net external force applied to a car produces a much smaller acceleration than when applied to a basketball. The proportionality is written as

where $m$ is the mass of the system. Experiments have shown that acceleration is exactly inversely proportional to mass, just as it is exactly linearly proportional to the 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 of motion.

Units of force

${\mathbf{\text{F}}}_{\text{net}}=m\mathbf{\text{a}}$ is used to define the units of force in terms of the three basic units for mass, length, and time. The SI unit of force is called the newton (abbreviated N) and is the force needed to accelerate a 1-kg system at the rate of $1{\text{m/s}}^2$ . That is, since ${\mathbf{\text{F}}}_{\text{net}}=m\mathbf{\text{a}}$ ,