Chapter 1, Problem 60A

(a)

To determine

Graph between mass and acceleration

Explanation of Solution

Introduction:

Acceleration depends upon the force applied and the mass of the object. For a constant force the acceleration and mass are inversely proportional.

The mass is taken on the x -axis and the acceleration is taken on the y -axis.

(b)

To determine

Conclusion from graph.

Explanation of Solution

Introduction:

Acceleration depends upon the force applied and the mass of the object. For a constant force the acceleration and mass are inversely proportional.

As the relation between the mass and the acceleration for a constant force is inverse, the slope of the graph is negative.

Conclusion:

The slope between mass and acceleration is negative.

(c)

To determine

The equation relating acceleration to mass, given by the data.

Explanation of Solution

Introduction:

Acceleration depends upon the force applied and the mass of the object. For a constant force the acceleration and mass are inversely proportional.

The relation between the mass and the acceleration for a constant force is inverse, the slope of the graph is negative.

  $a\propto \frac{1}{m}$

  $a=\frac{c}{m}$

Where, a is the acceleration, m is the mass and c is a constant.

Conclusion:

  $a=\frac{c}{m}$ is the equation relating acceleration to mass.

(d)

To determine

Units of the constant.

Answer to Problem 60A

Units of constant are Newton and $\text{kg}\cdot {\text{m/s}}^{\text{2}}$ .

Explanation of Solution

Given:

  $a=\frac{c}{m}$

Where a is the acceleration, m is the mass and c is a constant.

Formula used:

  $c=a\times m$

Where a is the acceleration, m is the mass and c is a constant.

Calculation:

  $c=a\times m$

Substituting the units in the equation.

  $c={\text{m/s}}^{\text{2}}\cdot \text{kg}$

  $c=\text{kg}\cdot {\text{m/s}}^{\text{2}}$

These are also the units force.

Conclusion:

Units of constant care Newton or $\text{kg}\cdot {\text{m/s}}^{\text{-2}}$ .