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# Potential Energy Problems With Solutions

## Introduction

In this post, I will guide you on how to solve potential energy problems with solutions. I will also explain a few important points to help you understand how to calculate potential energy.

Definition of potential energy: Potential energy is a type of energy of the body by virtue of its position. We can also define potential energy as the energy at rest by virtue of its position above the earth’s surface.

The symbol for potential energy is P.E

The unit for potential energy P.E is in Joules

The formula for calculating potential energy is P.E = mgh

## Potential Energy Problems With Solutions

Here are solved problems on potential energy:

### Example 1

A fruit from a tree of mass 5 kilograms is 5 meters above the ground. Calculate the potential energy of the fruit above the ground. (gravitational acceleration, g = 10 ms-2)

Data

Mass of the fruit, m = 5 kg

Distance above the ground = height, h = 5 m

Gravitational acceleration, g = 10 ms-2

Unknown value to find

Potential energy, P.E =?

Formula

Potential energy, P.E = mgh

Solution

P.E = mgh = 5 x 5 x 10 = 250 J

Therefore, the potential energy is 250 Joules.

### Example 2

Calculate the potential energy of the Kainji dam if the height is 200 meters and the mass and the mass of the water is 5 kilograms. Take gravitational acceleration as 10 meters per second square.

Data

Height of the dam, h = 200 m

Mass of the water, m = 5 kg

Gravitational acceleration, g = 10 ms-2

Unknown value to find

Potential energy, P.E =?

The Formula to apply

Potential energy, P.E = mgh

Solution

We can now insert our data into the formula to solve the problem

Potential energy, P.E = mgh = 200 x 5 x 10 = 10,000 J = 10kJ

Therefore, the potential energy of the Kainji dam is 10 kilojoules.

### Example 3

A stone of mass 750 grams is thrown vertically upward with a velocity of 10 meters per second. Find the potential energy at the greatest height if its height above the ground is 5 meters

Data

Mass of the stone, m = 750 g = 0.75 kg

The velocity of the stone, v = 10 m/s

Height above the ground, h = 5 meters

Gravitational acceleration, g = 10 ms-2

The formula to solve the problem is

Potential energy, P.E = mgh

Solution

P.E = mgh = 0.75 x 10 x 5 = 37.5 J

Therefore, the potential energy P.E is 37.5 Joules

### Example 4

A bag of mass 20 kilograms is lifted to a height of 3 meters. Find the potential energy of the bag.

Data

Height of the bag, h = 3 m

Mass of the bag, m = 20 kg

Gravitational acceleration, g = 10 ms-2

Unknown value to find

Potential energy, P.E =?

The Formula to apply

Potential energy, P.E = mgh

Solution

We can now insert our data into the formula to solve the problem

Potential energy, P.E = mgh = 3 x 20 x 10 = = 600 J

Therefore, the potential energy of the bag is 600 Joules.

### Example 5

A ball with a mass of 0.5 kilograms is thrown vertically up a clip with a height of 50 meters. Determine the potential energy of the ball at the top of its trajectory.

Data

Height of the bag, h = 50 m

Mass of the bag, m = 0.5 kg

Gravitational acceleration, g = 10 ms-2

Unknown value to find

Potential energy, P.E =?

The Formula to apply

Potential energy, P.E = mgh

Solution

We can now insert our data into the formula to solve the problem

Potential energy, P.E = mgh = 50 x 0.5 x 10 = = 250 J

Therefore, the potential energy of the bag is 250 Joules.

You may also like to read:

How to Calculate Kinetic Energy

How to Calculate Work Done in Physics

Sources:

Wikipedia