Chapter 6, Problem 5PC

How many joules of potential energy does a 1.5kg book gain when it is elevated 2 m ? When it is elevated 4 m ? (Let g = 10 N/kg .)

To determine

The potential energy when it is elevated 2 m and 4 m .

Answer to Problem 5PC

The potential energy when it is elevated 2 m is 30 J and for 4 m is 60 J .

Explanation of Solution

Given info: Mass of the book is 1.5kg and the elevation of the book is 2 m and 4m .

Write the expression for the potential energy.

$$

PE = mgh

Here,

m is the mass of the book

g is the acceleration due to gravity

h is the elevation from the ground

Calculate potential energy for the elevation of .

Substitute 1.5kg for m , 2 m for h and 10 N/kg for g in the above equation to get PE .

$\begin{array}{c}PE=1.5\text{kg}\times 10\text{N}/\text{kg}\times 2\text{m}\\ PE=30\text{N}\cdot \text{m}\times \frac{1\text{J}}{1\text{N}\cdot \text{m}}\\ PE=30\text{J}\end{array}$

Calculate potential energy for the elevation of 4 m .

Substitute 1.5kg for m , 4 m for h and 10 N/kg for g in the above equation to get PE .

$\begin{array}{c}PE=1.5\text{kg}\times 4\text{m}\times 10\text{N}/\text{kg}\\ PE=60\text{N}\cdot \text{m}\times \frac{1\text{J}}{1\text{N}\cdot \text{m}}\\ PE=60\text{J}\end{array}$

Conclusion:

Therefore, the potential energy when it is elevated 2 m is 30 J and for 4 m is 60 J .