Chapter 1, Problem 7STP

(a)

To determine

To Rewrite: The force equation for acceleration.

Explanation of Solution

Given:

Equation for force:

  $F=ma$

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

Calculation:

Divide both sides of the given equation by mass (m):

  $\begin{array}{l}F=ma\\ \frac{F}{m}=\frac{ma}{m}\\ \Rightarrow a=\frac{F}{m}\end{array}$

Conclusion:

Thus, acceleration a in terms of F and m can be written as: $a=\frac{F}{m}$ .

(b)

To determine

To Write: The conversion factor for grams to kilograms.

Explanation of Solution

Introduction:

SI unit of mass is kilograms. Grams is a smaller unit of mass.

There are 1000 g in 1 kg

  $\begin{array}{l}1000\text{g}=1\text{kg}\\ \Rightarrow \text{1g}={10}^{-3}\text{kg}\end{array}$

So, to convert grams to kilograms, one must multiply by ${10}^{-3}$ .

Conclusion:

Thus, 1000 grams are equivalent to 1 kilogram.

(c)

To determine

To Find: The acceleration of the given mass.

Answer to Problem 7STP

  $7.7{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Force, $F=2.7\text{N}$

Mass, $m=350\text{g}$

Formula Used:

  $\begin{array}{l}F=ma\\ \frac{F}{m}=\frac{ma}{m}\\ \Rightarrow a=\frac{F}{m}\end{array}$

Conversion factor:

  $\text{1g}={10}^{-3}\text{kg}$

Calculations:

Convert mass from g to kg:

  $\begin{array}{l}m=350\text{g}\times {\text{10}}^{-3}\text{kg/g}\\ m=\text{0}\text{.350}\text{kg}\end{array}$

Acceleration can be calculated as follows:

  $\begin{array}{l}a=\frac{2.7\text{}\text{N}}{0.350\text{kg}}\\ a=7.7{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Thus, the acceleration of the given mass is $7.7{\text{m/s}}^{\text{2}}$ .