1.5Chapter 1: Energy

Gravitational potential energy and kinetic energy — Alhussan Physics - Stage 7 Revision Notes & Topical Questions

5 min read 7 parts Lesson 5 of 8 2 quizzes

📚 Alhussan Physics - Stage 7 Hub / Topical Revision

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1.5 Gravitational potential energy and kinetic energy — Alhussan International Academy — Physics (Stages 7–9) notes: Describe the factors that affect gravitational potential energy and kinetic energy and the energy changes between them, including dissipation.GPE = the energy some…

Rearranging
Stationary
Ball thrown upwards
Entering water
Bouncing ball
Pulling back

Part 1 of 5Gravitational potential energy (GPE)

GPE

GPE the energy something has because of its position, another term for energy in a gravity store or energy stored gravitationally.

Height

GPE depends on distance from the centre of the Earth, so moving up two floors gains twice as much GPE as moving up one floor.

Mass

Mass it also depends on mass, so a mother with twice the mass of her son gains twice as much GPE going up one floor.

Formula

GPE = mass × gravitational field strength × height, E = m × g × h.
On Earth g = 10 N/kg, and height must be in metres and mass in kilograms.
A 2 kg book on a shelf 1.5 m high has 30 J of GPE.

Rearranging

Rearranging h = GPE ÷ (m × g) and m = GPE ÷ (g × h).

Graph

Graph a graph of GPE against height is a straight line through the origin, with gradient m × g.

Part 2 of 5Kinetic energy (KE)

KE the energy something has when it is moving, another term for energy in a kinetic store or energy stored kinetically.

Mass

Mass if a lion and an antelope move at the same speed, the lion has more kinetic energy because it has more mass.

Speed

Speed two lions of the same mass running at different speeds have different kinetic energy, and the faster lion has more.
Doubling the speed makes the kinetic energy four times as large.

Formula

KE = ½ × m × v².
What the symbols mean: E_k = kinetic energy (J) · m = mass (kg) · v = speed (m s⁻¹)

Stationary

Stationary a stationary object has zero KE.

Part 3 of 5Up and down

Ball thrown upwards

Ball thrown upwards it slows down, stops for an instant, then speeds up as it falls.
On the way up, energy moves from the kinetic store to the gravitational store.
The increase in GPE equals the decrease in kinetic energy.
On the way down, energy is transferred from the gravitational store to the kinetic store.

Dissipation

Dissipation a very small amount of energy is transferred to the surroundings because of air resistance.

Diver

Diver at the top of the board GPE is greatest and KE is zero, halfway they have equal amounts,
- and just above the water GPE is smallest and KE is greatest.

Position	GPE	KE
Top	Maximum	Zero
Halfway	Half	Half
Just above the ground or water	Minimum	Maximum

Entering water

KE is transferred to the kinetic energy of the water, thermal energy and sound.

Bouncing ball

Bouncing ball it converts between KE and GPE but loses a little energy to thermal and sound on each bounce, so each bounce is lower.

Part 4 of 5Back and forth: the pendulum

Pendulum

Pendulum a ball on a string that swings backwards and forwards.

Pulling back

Pulling back when you pull the pendulum back you also pull it up, so its GPE increases.

Letting go

Letting go it falls and energy is transferred to a kinetic store.

Swinging up

Swinging up energy is transferred back to a gravity store.
At the highest point of the swing there is no kinetic energy and GPE is a maximum.
At the lowest point KE is a maximum and GPE is a minimum.

Swing

Swing a child on a swing behaves like a pendulum.
If the father stops pushing, she does not swing so high, because friction warms parts of the swing and air resistance heats the air.
Kinetic energy is transferred to the thermal store of the surroundings, which is dissipation.

Part 5 of 5Rollercoasters

Design

Design engineers think carefully about kinetic energy and GPE to know how much energy is needed for passengers to reach the top of the hills.

Lifting

Lifting the ride lifts people up high so they can move fast on the way down.

Calculation

Calculation a 500 kg car lifted 20 m gains 100 000 J of GPE.
Ignoring friction, all of this becomes KE at the bottom of the first drop, where the car reaches its top speed.

Dissipation

Dissipation friction and air resistance mean the car has less KE than expected, so later hills must be lower than the first.

Ordering GPE

Ordering GPE compare mass × height, using consistent units.

Key terms

Term	Meaning
Gravitational potential energy	the energy stored because of position in a gravitational field.
Kinetic energy	the energy of a moving object.
Gravitational field strength	the force per kilogram of mass, 10 N/kg on Earth.
Joule	the unit of energy.
Pendulum	a mass hanging from a pivot that swings freely.
Air resistance	a force from air that opposes motion and heats the air.