Chapter 7, Problem 1ASA

Write Newton’s second law in mathematical form, and describe how the acceleration of an object or system varies with a net force and mass of the system.

To determine

The mathematical form of Newton’s second law and the variation of acceleration of an object with net force and mass of the system.

Answer to Problem 1ASA

The mathematical form of Newton’s second law is ${\overrightarrow{\text{F}}}_{\text{net}}=m\overrightarrow{\text{a}}$ and the acceleration increases with increase in net force and decreases with decrease in net force. If the net force is fixed, the lighter masses will have larger acceleration and the heavy systems will have small acceleration.

Explanation of Solution

The mathematical form of Newton’s second law is given by the relation,

  ${\overrightarrow{\text{F}}}_{\text{net}}=m\overrightarrow{\text{a}}$

Where, ${\overrightarrow{\text{F}}}_{\text{net}}$ is the net force on the system, $m$ is the mass of the system, and $\overrightarrow{\text{a}}$ is the acceleration of the system.

The above equation can be solved for acceleration as,

  $\overrightarrow{\text{a}}=\frac{{\overrightarrow{\text{F}}}_{\text{net}}}{m}$

It is clear that the acceleration of the system is directly proportional to the net force and inversely proportional to the mass of the system. Thus, as the net force increases, the acceleration of the system increases. If the net force is less, the acceleration will be less for a fixed mass. If the net force is fixed, then the system with larger mass will have less acceleration. Lighter masses will have larger acceleration if the net force is kept constant.