Chapter 3.2, Problem 18R

To determine

To explain: The reason for an object with a smaller mass to have a larger acceleration compare larger mass whereas both mass have same force.

Explanation of Solution

Introduction:

Newton’s second law of motion, the rate of change of linear momentum of a body is equal to the external force of the body.

  ${\overrightarrow{F}}_{ext}=\frac{d\overrightarrow{p}}{dt}\mathrm{...}\left(1\right)$

Or,

  $\begin{array}{l}{\overrightarrow{F}}_{ext}=\frac{d\left(m\overrightarrow{v}\right)}{dt}\\ {\overrightarrow{F}}_{ext}=m\frac{d\left(\overrightarrow{v}\right)}{dt}\\ {\overrightarrow{F}}_{ext}=m\overrightarrow{a}\mathrm{...}\left(2\right)\end{array}$

Where,

  ${\overrightarrow{F}}_{ext}=$ External force

  $\overrightarrow{p}=$ Linear momentum

  $m=$ Mass

  $\overrightarrow{a}=$ Acceleration

From equation (2),

  $\begin{array}{l}{\overrightarrow{F}}_{ext}=m\overrightarrow{a}\\ \overrightarrow{a}=\frac{{\overrightarrow{F}}_{ext}}{m}\mathrm{...}\left(3\right)\end{array}$

From equation (3), the acceleration is equal to the ratio of external force and mass. The external force for both masses is same so the acceleration is depend only the mass and it is reciprocal of mass. The reciprocal of smaller mass is greater than the larger mass so the acceleration of smaller mass is greater than the larger mass.

Conclusion:

Hence, the acceleration of smaller mass is larger than the larger mass because the acceleration is depends on the mass and exerted force.