Potential Energy Revision Notes for Grade 10 NSC Matric Physical Sciences

Potential Energy

What is potential energy?

Potential energy is the energy that an object possesses because of its position or state. This means an object can have stored energy simply by being in a particular location or condition, even when it's not moving.

There are several types of potential energy, including gravitational potential energy, elastic potential energy, and chemical potential energy. In this section, we focus specifically on gravitational potential energy.

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Understanding potential energy is crucial because it helps explain how energy is stored in objects based on their position. This stored energy can later be converted into other forms of energy, such as kinetic energy when objects move.

Gravitational potential energy

Gravitational potential energy is the energy an object has due to its position in a gravitational field relative to some reference point. On Earth, this means the energy an object has because of its height above the ground.

The higher an object is positioned above the ground, the more gravitational potential energy it possesses. This energy can be converted to other forms of energy, such as kinetic energy, when the object moves.

The formula for gravitational potential energy

Gravitational potential energy can be calculated using the formula:

$E_P = mgh$

Where:

$E_P$ = gravitational potential energy (measured in joules, J)
$m$ = mass of the object (measured in kilograms, kg)
$g$ = gravitational acceleration (9.8 m⋅s⁻² on Earth)
$h$ = perpendicular height from the reference point (measured in metres, m)

The reference point is usually chosen as ground level, where the height ( $h$ ) equals zero.

Understanding the relationship between height and potential energy

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Objects have maximum potential energy when they are at their maximum height above the reference point. As objects move closer to the reference point (usually the ground), their potential energy decreases.

When an object reaches the ground level ( $h = 0$ ), its gravitational potential energy becomes zero, assuming we use the ground as our reference point.

Worked example 1: Basic gravitational potential energy calculation

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Worked Example: Basic Potential Energy Calculation

Question: A brick with a mass of 1 kg is lifted to the top of a 4 m high roof. It slips off the roof and falls to the ground. Calculate the gravitational potential energy of the brick at the top of the roof and on the ground once it has fallen.

Solution:

Step 1: Analyse the given information

Mass of the brick: $m = 1$ kg
Height when lifted: $h = 4$ m
All quantities are in SI units

Step 2: Identify what we need to find

Gravitational potential energy at the top of the roof
Gravitational potential energy when the brick reaches the ground

Step 3: Calculate the potential energy at the top of the roof

$E_P = mgh$ $E_P = (1 \text{ kg})(9.8 \text{ m⋅s⁻²})(4 \text{ m})$ $E_P = 39.2 \text{ J}$

Step 4: Calculate the potential energy on the ground

When the brick is on the ground, $h = 0$ m:

$E_P = mgh$ $E_P = (1 \text{ kg})(9.8 \text{ m⋅s⁻²})(0 \text{ m})$ $E_P = 0 \text{ J}$

Worked example 2: Multiple position calculations

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Worked Example: Multiple Position Calculations

Question: A netball player, who is 1.7 m tall, holds a 0.5 kg netball 0.5 m above her head and shoots for the goal net which is 2.5 m above the ground. What is the gravitational potential energy of the ball:

when she is about to shoot it into the net?
when it gets right into the net?
when it lands on the ground after the goal is scored?

Solution:

Step 1: Analyse the given information

Player height: 1.7 m
Ball mass: 0.5 kg
Ball held 0.5 m above player's head
Net height: 2.5 m above ground

Step 2: Calculate the ball's height when shooting

Height when shooting = player height + height above head $h = 1.7 \text{ m} + 0.5 \text{ m} = 2.2 \text{ m}$

Step 3: Calculate potential energy when shooting

$E_P = mgh$ $E_P = (0.5 \text{ kg})(9.8 \text{ m⋅s⁻²})(2.2 \text{ m})$ $E_P = 10.78 \text{ J}$

Step 4: Calculate potential energy at the net

At the net, $h = 2.5$ m:

$E_P = mgh$ $E_P = (0.5 \text{ kg})(9.8 \text{ m⋅s⁻²})(2.5 \text{ m})$ $E_P = 12.25 \text{ J}$

Step 5: Calculate potential energy on the ground

When the ball lands on the ground, $h = 0$ m:

$E_P = mgh$ $E_P = (0.5 \text{ kg})(9.8 \text{ m⋅s⁻²})(0 \text{ m})$ $E_P = 0 \text{ J}$

Key principles to remember

Understanding these fundamental principles will help you master gravitational potential energy concepts:

Gravitational potential energy is directly proportional to height - the higher the object, the greater its potential energy
The choice of reference point affects the calculated value, but the ground is typically used as the reference ( $h = 0$ )
Gravitational acceleration on Earth is constant at 9.8 m⋅s⁻²
Potential energy can be converted to other forms of energy when objects change position
Objects at the same height have the same potential energy per unit mass

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Key Points to Remember:

Gravitational potential energy is the energy an object has due to its position in a gravitational field
Use the formula $E_P = mgh$ where $E_P$ is in joules, $m$ is in kg, $g$ is 9.8 m⋅s⁻², and $h$ is in metres
Higher positions mean greater potential energy - maximum height gives maximum potential energy
Ground level (reference point) typically has zero potential energy
Always identify your reference point when calculating potential energy values

Potential Energy (Grade 10 NSC Matric Physical Sciences): Revision Notes