Chapter 1, Problem 42A

(a)

To determine

To Find: The force due to gravity on the given mass.

Answer to Problem 42A

  $\text{ 4}\text{.1}\times {\text{10}}^2\text{N}$

Explanation of Solution

Given:

Mass, $m=41.63\text{kg}$

Acceleration due to gravity, $g=9.8\text{N/kg}$

Formula Used:

Force due to gravity can be obtained by:

  $F=mg$

Where, m is the mass and g is the acceleration due to gravity.

Calculations:

Substitute the values and solve:

  $\begin{array}{c}F=mg\\ =\left(41.63\text{kg}\right)\left(9.8\text{N/kg}\right)\\ =407.974\text{N}\\ \approx \text{ 4}\text{.1}\times {\text{10}}^2\text{N}\end{array}$

The result has been rounded off to two significant factors because the least number of significant digits in the numbers is 2.

Conclusion:

Thus, the force due to gravity on the given mass is $\text{ 4}\text{.1}\times {\text{10}}^2\text{N}$ .

(b)

To determine

To Find: The mass of the object.

Answer to Problem 42A

  $\text{6}\text{.4}\times {10}^1\text{kg}$

Explanation of Solution

Given:

Force of gravity on the object, $F=632\text{}\text{N}$

Acceleration due to gravity, $g=9.8\text{N/kg}$

Formula Used:

Force due to gravity can be obtained by:

  $F=mg$

Where, m is the mass and g is the acceleration due to gravity.

Calculations:

Substitute the values and solve:

  $\begin{array}{c}F=mg\\ m=\frac{F}{g}\\ =\frac{632\text{}\text{N}}{9.8\text{N/kg}}\\ =64.48\text{kg}\\ \approx \text{6}\text{.4}\times {10}^1\text{kg}\end{array}$

The result has been rounded off to two significant factors because the least number of significant digits in the numbers is 2.

Conclusion:

Thus, the mass of the object is $\text{6}\text{.4}\times {10}^1\text{kg}$ .