# Potential energy formula

The potential energy formula, PE = m g h, establishes a relationship between the potential energy (PE) of an object, its mass (m), gravitational acceleration (g), and height (h). By utilizing this formula, one can calculate the amount of potential energy stored in an object based on its mass, gravitational acceleration, and height.

Contents

## Practice problems

### Problem #1

Calculate the potential energy of a 1.5 kg book that is about to fall from the top of a 2.65 m bookshelf. Assume a gravitational acceleration value of g = 9.8 m/s2.

Solution

Given data:

• Potential energy of a book, PE = ?
• Mass of a book, m = 1.5 kg
• Height from which a book is about to fall, h = 2.65 m
• Gravitational acceleration, g = 9.81 m/s2

Applying the formula:

• PE = m g h
• PE = 1.5 × 9.81 × 2.65
• PE = 38.99 J

Therefore, a book has the potential energy of 38.99 J, before it falls from the top of a bookshelf.

### Problem #2

A stone with a mass of 4 kg is resting at the edge of a hill that has a height of 50 m. Calculate the potential energy of the stone right before it falls off the hill. Use a gravitational acceleration value of g = 9.8 m/s2.

Solution

Given data:

• Mass of a stone, m = 4 kg
• Height from which a stone is about to fall, h = 50 m
• Potential energy of a stone, PE = ?
• Gravitational acceleration, g = 9.81 m/s2

Applying the formula:

• PE = m g h
• PE = 4 × 9.81 × 50
• PE = 1962 J

Therefore, a stone has the potential energy of 1962 J, right before it falls off the hill.

### Problem #3

Determine the potential energy of a 500 g fruit hanging from a tree branch that is about to fall from a height of 2 m. Consider a gravitational acceleration value of g = 9.8 m/s2.

Solution

Given data:

• Potential energy of a fruit, PE = ?
• Mass of a fruit, m = 500 g = 0.5 kg
• Height from which a fruit is about to fall, h = 2 m
• Gravitational acceleration, g = 9.81 m/s2

Applying the formula:

• PE = m g h
• PE = 0.5 × 9.81 × 2
• PE = 9.81 J

Therefore, a fruit hanging from a tree branch has the potential energy of 9.81 J.

### Problem #4

A monkey weighing 10 kg is sitting on the edge of a wall and is about to jump from a height of 4 m. Calculate the potential energy of the monkey. Take the gravitational acceleration value as g = 9.8 m/s2.

Solution

Given data:

• Mass of a monkey, m = 10 kg
• Height from which a monkey is about to jump, h = 4 m
• Potential energy of a monkey, PE = ?
• Gravitational acceleration, g = 9.81 m/s2

Applying the formula:

• PE = m g h
• PE = 10 × 9.81 × 4
• PE = 392.4 J

Therefore, a monkey sitting on the edge of a wall has the potential energy of 392.4 J.