Potential energy

Learn it by playing

Answer these questions to earn energy, then fish and explore. No account needed.

For teachers: ready-to-use lesson slides, revision notes, diagrams for Potential energy (NGSS Middle School Science, Physics) — use them in your lesson, or run the topic as an interactive class activity your students play as a live game.

Lesson notes

What is Potential Energy?

**Potential energy** is stored energy due to an object's **position** or **configuration** relative to other objects.
It is the energy that is 'waiting' to be released, like a ball held above the ground or a stretched spring.
The SI unit for potential energy is the **joule (J)**.
Potential energy is associated with **conservative forces** (e.g., gravity, spring force) where work done depends only on start and end positions, not the path taken.

Gravitational Potential Energy

**Gravitational potential energy** is energy stored due to an object's height above a reference point (e.g., the ground).
It depends on the object's **mass (m)**, the **acceleration due to gravity (g ≈ 9.8 m/s²)**, and the **height (h)** above the reference.
The formula is: **PE_grav = m × g × h**.
Lifting an object increases its gravitational potential energy; dropping it converts that energy into kinetic energy.

Elastic Potential Energy

**Elastic potential energy** is stored when an elastic object (like a spring or rubber band) is stretched or compressed.
The energy is stored in the **deformation** of the material and is released when the object returns to its original shape.
For a spring, the energy depends on how far it is stretched or compressed (displacement x) and its **spring constant (k)** (stiffness).
The formula is: **PE_elastic = ½ × k × x²**.

Other Forms of Potential Energy

**Chemical potential energy** is stored in the bonds between atoms and molecules (e.g., in food, batteries, fossil fuels).
**Electric potential energy** is stored due to the position of charged particles in an electric field.
**Nuclear potential energy** is stored in the nucleus of an atom and is released in nuclear reactions.
**Thermal energy** includes both kinetic energy of particle motion and potential energy from particle configurations.

How Potential Energy Changes

Work done **against** a conservative force (e.g., lifting a weight) **increases** potential energy.
Work done **by** a conservative force (e.g., a falling weight) **decreases** potential energy.
The change in potential energy (ΔU) equals the negative of the work done by the conservative force: **W = –ΔU**.
Potential energy is always measured relative to a **reference position** (e.g., ground level for gravity).

Everyday Examples

A book on a high shelf has gravitational potential energy; if it falls, that energy becomes kinetic.
A drawn bow stores elastic potential energy; releasing the bowstring turns it into kinetic energy of the arrow.
A roller coaster at the top of a hill has maximum gravitational potential energy, which converts to kinetic energy as it descends.
Batteries store chemical potential energy, which is converted to electrical energy when used.

Particle arrangement in solids, liquids, and gases. Potential energy is stored in the bonds between particles; changing state involves changes in potential energy.

Slides

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

Practice questions

Free preview — 8 of 40 questions. Sign up to see them all.

1.What is potential energy?
Easy
- AEnergy stored due to an object's position or configuration
- BEnergy of motion
- CEnergy transferred by heat
- DEnergy stored in chemical bonds only
2.Which of the following is the SI unit of potential energy?
Easy
- AJoule
- BNewton
- CWatt
- DPascal
3.A ball of mass 0.5 kg is lifted to a height of 2 m above the ground. What is its gravitational potential energy? (Take g = 10 m/s²)
Medium
- A10 J
- B5 J
- C1 J
- D20 J
4.A spring is compressed 0.1 m from its natural length. If the spring constant is 200 N/m, what is the elastic potential energy stored?
Medium
- A1 J
- B2 J
- C10 J
- D0.5 J
5.Which of the following is an example of gravitational potential energy?
Easy
- AA book on a high shelf
- BA moving car
- CA stretched rubber band
- DA battery
6.Which type of potential energy is stored in a compressed spring?
Medium
- AElastic potential energy
- BGravitational potential energy
- CChemical potential energy
- DNuclear potential energy
7.Two objects of masses m and 2m are at heights h and 2h respectively. What is the ratio of their gravitational potential energies?
Hard
- A1:4
- B1:2
- C1:1
- D2:1
8.When a ball is thrown upward, what happens to its gravitational potential energy as it rises?
Medium
- AIt increases
- BIt decreases
- CIt remains constant
- DIt becomes zero

Revision notes

## Potential Energy - Quick Revision ### Definition Potential energy is the energy stored in an object or system due to its position relative to other objects or the arrangement of its parts. It is equal to the work done against a restoring force (like gravity or a spring). The SI unit is the joule (J). ### Key Types - **Gravitational potential energy**: Stored due to height above a reference point. For an object of mass m at height h: \( U_g = mgh \) (g ≈ 9.8 m/s² on Earth) - **Elastic potential energy**: Stored in a deformed spring or elastic material. - **Chemical potential energy**: Stored in bonds between atoms/molecules (e.g., fossil fuels). - **Electric potential energy**: Stored due to position in an electric field. ### How It Works - Potential energy is associated with **conservative forces** (gravity, spring force). Work done by a conservative force depends only on start and end positions, not the path. - Work done against a force field **increases** potential energy; work done by the force field **decreases** it. - Formula: \( W = -\Delta U \) (negative sign means work done by the force reduces potential energy). ### Examples - Lifting a book: You do work against gravity → gravitational PE increases. - Stretching a rubber band: Work done against elastic force → elastic PE increases. - Dropping a ball: Gravitational PE converts to kinetic energy as it falls. ### Key Points - Potential energy is **stored energy** that can be converted to other forms (e.g., kinetic). - It is always measured relative to a reference position (e.g., ground level for gravity). - Common symbols: PE, U, V, Ep. ### History - Term coined by William Rankine in 1853. - Also called 'energy of configuration' (Rankine) vs. 'kinetic energy' (Thomson).

Potential energy: The energy stored in an object or system due to its position relative to other objects or the arrangement of its parts.
Gravitational potential energy: Potential energy due to an object's height above a reference point, calculated as U_g = mgh.
Elastic potential energy: Potential energy stored in a deformed elastic object, such as a stretched spring.
Conservative force: A force for which the work done depends only on the initial and final positions, not the path taken (e.g., gravity, spring force).
Joule: The SI unit of energy, symbol J.

Flashcards

What is potential energy?

Potential energy is the energy stored in an object or system due to its position relative to other objects or the configuration of its particles.

What are common types of potential energy?

Common types include gravitational potential energy, elastic potential energy, and electric potential energy.

What is the SI unit for energy?

The SI unit for energy is the joule (symbol J).

Who coined the term 'potential energy'?

The term was coined by Scottish engineer and physicist William Rankine in 1853.

What is gravitational potential energy?

Gravitational potential energy is the energy stored due to an object's position in a gravitational field, given by U = mgh for an object of mass m at height h.

What is elastic potential energy?

Elastic potential energy is the energy stored in a deformed elastic object, such as a stretched or compressed spring.

How is potential energy related to work?

Work done against a conservative force increases potential energy; work done by the force decreases potential energy. Mathematically, W = -ΔU.

What are conservative forces?

Conservative forces are forces for which the total work done depends only on the initial and final positions, not on the path taken. Examples include gravity and elastic forces.

What is the formula for gravitational potential energy near Earth's surface?

U = mgh, where m is mass, g is acceleration due to gravity (about 9.8 m/s²), and h is height above a reference point.

How does stretching a spring affect its potential energy?

Stretching a spring increases its elastic potential energy because work is done against the restoring force of the spring.

What happens to gravitational potential energy when an object is lifted?

Lifting an object increases its gravitational potential energy because work is done against gravity.

What happens to potential energy when an object falls?

As an object falls, its gravitational potential energy decreases and is converted into kinetic energy.

Define conservative force field.

A conservative force field is a region where the force at each point is such that the work done moving between two points is path independent, and the force can be derived from a potential energy function.

What is the relationship between potential energy and force in a conservative field?

The force is the negative gradient of the potential energy: F = -∇U.

Why is potential energy considered 'stored energy'?

Potential energy is stored because it can be released and converted into other forms of energy, such as kinetic energy, when the object moves under the influence of a conservative force.

What is the reference position for potential energy?

Potential energy is defined relative to a reference position, often chosen as zero at a convenient point (e.g., ground level for gravity).

Give an example of potential energy in everyday life.

A book on a high shelf has gravitational potential energy; a drawn bow has elastic potential energy.

How does the mass of an object affect its gravitational potential energy?

Gravitational potential energy is directly proportional to mass (U = mgh), so a heavier object has more potential energy at the same height.

How does height affect gravitational potential energy?

Gravitational potential energy increases with height (U = mgh), so an object at a greater height has more potential energy.

What is the potential energy of an object at ground level if ground is the reference?

If ground level is chosen as the reference (h=0), then the gravitational potential energy is zero.

Can potential energy be negative?

Yes, potential energy can be negative if the reference point is chosen such that the object's position is below it.

What is the difference between potential energy and kinetic energy?

Potential energy is stored energy due to position or configuration, while kinetic energy is energy of motion.

How is potential energy related to the work done by an external force?

The work done by an external force against a conservative force is stored as potential energy.

Unlock all 40 questions, flashcards & more

Create a free account to see every question, the slides, flashcards and revision notes for this topic.

Past papers

Past-paper practice for this topic is coming soon.

Coming soon