Kinetic elastic and gravitational potential energy - Teacher Slides.pptx

AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Kinetic, elastic and gravitational potential energy

Energy

Lesson 2 of 7

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Warm-up

Energy

Lesson 2 of 7

Answer each one, then check.

1

Write the unit for mass.

2

Convert 6.0 cm to metres.

3

Work out 4².

4

What does g stand for in E_p = mgh?

5

What is the unit of speed?

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Warm-up - Answers

Energy

Lesson 2 of 7

1

Write the unit for mass.

Kilograms (kg)

2

Convert 6.0 cm to metres.

0.060 m

3

Work out 4².

16

4

What does g stand for in E_p = mgh?

Gravitational field strength

5

What is the unit of speed?

Metres per second (m/s)

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Learning Objectives

Energy

Lesson 2 of 7

1

Recall and apply the equation for kinetic energy.

2

Recall and apply the equation for elastic potential energy.

3

Apply the equation for gravitational potential energy.

4

Use energy conservation to find speeds and heights.

5

Convert units and give answers to an appropriate number of significant figures.

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Energy

Lesson 2 of 7

THREE ENERGY EQUATIONS

E_k = ½mv² E_e = ½ke² E_p = mgh

Learn the first two. E_p = mgh is on the equation sheet, and the value of g (9.8 N/kg) is always given in the question.

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Three Stores, Three Equations

Energy

Lesson 2 of 7

Check the units before you substitute.

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Quantities and Units

Energy

Lesson 2 of 7

Always use these units.

Quantity

Symbol

Unit

Kinetic energy

E_k

joules (J)

Elastic potential energy

E_e

joules (J)

Gravitational potential energy

E_p

joules (J)

Mass

m

kilograms (kg)

Speed

v

metres per second (m/s)

Spring constant

k

newtons per metre (N/m)

Extension

e

metres (m)

Gravitational field strength

g

newtons per kilogram (N/kg)

Height

h

metres (m)

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Kinetic Energy

Energy

Lesson 2 of 7

A car of mass 1200 kg travels at 15 m/s. Calculate its kinetic energy.

1

Write the equation

E_k = ½mv²

2

Substitute

E_k = 0.5 × 1200 × 15²

3

Square first

15² = 225

4

Answer

E_k = 135 000 J

ANSWER

Kinetic energy = 135 000 J (or 135 kJ).

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Elastic Potential Energy

Energy

Lesson 2 of 7

A spring has a spring constant of 40 N/m. It is stretched by 25 cm. Calculate the elastic potential energy stored.

1

Convert the extension

25 cm = 0.25 m

2

Substitute

E_e = 0.5 × 40 × 0.25²

3

Answer

E_e = 1.25 J

ANSWER

1.25 J

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Gravitational Potential Energy

Energy

Lesson 2 of 7

A 2.0 kg book is lifted 3.0 m onto a shelf. g = 9.8 N/kg. Calculate the gain in gravitational potential energy.

1

Write the equation

E_p = mgh

2

Substitute

E_p = 2.0 × 9.8 × 3.0

3

Answer

E_p = 58.8 J

ANSWER

58.8 J (about 59 J)

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Using Energy Conservation

Energy

Lesson 2 of 7

A roller coaster car starts from rest at a height of 20 m. Ignoring friction, find its speed at the bottom. g = 9.8 N/kg.

1

Gravitational potential lost equals kinetic gained

mgh = ½mv²

2

The mass cancels

v² = 2gh = 2 × 9.8 × 20 = 392

3

Square root

v = 19.8 m/s

ANSWER

19.8 m/s

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Common Mistakes

Energy

Lesson 2 of 7

Marks are often lost here.

Squaring

Square only the speed or extension, not the whole of ½mv.

Units

Convert cm to m and g to kg before substituting.

Halving

Do not forget the 0.5 in the kinetic and elastic equations.

Significant figures

Give the answer to the same number of s.f. as the least accurate data, usually 2 or 3.

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Key Terms

Energy

Lesson 2 of 7

Kinetic energy

Energy stored in the movement of an object.

Elastic potential energy

Energy stored in a stretched or compressed object.

Gravitational potential energy

Energy stored in an object raised above the ground.

Spring constant

How stiff a spring is; force needed per metre of extension.

Extension

The increase in length of a spring.

Gravitational field strength

The force on each kilogram; 9.8 N/kg on Earth.

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Energy

Lesson 2 of 7

YOUR TASK

Energy Race

12 minutes

Calculate each. (a) A 0.50 kg ball moving at 8.0 m/s. (b) A spring with k = 100 N/m stretched by 0.10 m. (c) A 60 kg climber 15 m up a cliff (g = 9.8 N/kg).

1

Write the equation.

2

Substitute and calculate.

3

Add the unit.

WHAT A GOOD ANSWER SHOWS

(a) 16 J (b) 0.50 J (c) 8820 J (about 8800 J).

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Can I...?

Energy

Lesson 2 of 7

Recall the kinetic energy equation.

Recall the elastic potential energy equation.

Use the gravitational potential energy equation.

Convert cm to m.

Square the correct quantity.

Use conservation of energy to find a speed.

Give units and sensible significant figures.

Rearrange an equation.

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Summary & Exam Focus

E_k = ½mv².

E_e = ½ke², with e in metres.

E_p = mgh, with g given.

Energy lost from one store is gained by another if no energy is dissipated.

EXAM FOCUS

A 0.40 kg ball moves at 12 m/s. Calculate its kinetic energy. (2 marks)

Write the equation, substitute, then give the unit.

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Exam Practice: Kinetic, elastic and gravitational potential energy

Energy

Lesson 2 of 7

Answer all questions. Use the mark allocation as a guide to how much to write. · 17 minutes

Question 1 · 2 marks · Calculate

A ball of mass 0.40 kg moves at 12 m/s. Calculate the kinetic energy of the ball. Use the equation: kinetic energy = 0.5 × mass × (speed)²

Question 2 · 3 marks · Calculate

A person of mass 55 kg climbs a ladder to a height of 4.0 m. Calculate the increase in gravitational potential energy. Gravitational field…

Question 3 · 3 marks · Calculate

A spring has a spring constant of 25 N/m. It is stretched by 6.0 cm. Calculate the elastic potential energy stored in the spring. Assume…

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Exam Practice: Kinetic, elastic and gravitational potential energy (cont.)

Energy

Lesson 2 of 7

Question 4 · 4 marks · Calculate

The diagram shows a roller coaster car of mass 400 kg. It is released from rest at A. Gravitational field strength = 9.8 N/kg. (a)…

Question 5 · 4 marks · Calculate

A ball of mass 0.050 kg is thrown vertically upwards at 20 m/s. Assume there is no air resistance. Calculate the maximum height reached by…

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Question 1 · 2 marks · Calculate

Energy

Lesson 2 of 7

“

A ball of mass 0.40 kg moves at 12 m/s. Calculate the kinetic energy of the ball. Use the equation: kinetic energy = 0.5 × mass × (speed)²

HOW TO ANSWER IT

Command word: Calculate. Worth 2 marks, so plan before writing.

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Question 1 · mark scheme

Energy

Lesson 2 of 7

2 marks available. Award a mark for each point made.

Correct substitution

1 mark

28.8 J

1 mark

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Question 2 · 3 marks · Calculate

Energy

Lesson 2 of 7

“

A person of mass 55 kg climbs a ladder to a height of 4.0 m. Calculate the increase in gravitational potential energy. Gravitational field strength = 9.8 N/kg. Give your answer to 2 significant figures.

HOW TO ANSWER IT

Command word: Calculate. Worth 3 marks, so plan before writing.

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Question 2 · mark scheme

Energy

Lesson 2 of 7

3 marks available. Award a mark for each point made.

Correct substitution

1 mark

2156 J

1 mark

2200 J

1 mark

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Question 3 · 3 marks · Calculate

Energy

Lesson 2 of 7

“

A spring has a spring constant of 25 N/m. It is stretched by 6.0 cm. Calculate the elastic potential energy stored in the spring. Assume the limit of proportionality has not been exceeded.

HOW TO ANSWER IT

Command word: Calculate. Worth 3 marks, so plan before writing.

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Question 3 · mark scheme

Energy

Lesson 2 of 7

3 marks available. Award a mark for each point made.

Converts 6.0 cm to 0.060 m

1 mark

Correct substitution

1 mark

0.045 J

1 mark

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Question 4 · 4 marks · Calculate

Energy

Lesson 2 of 7

The diagram shows a roller coaster car of mass 400 kg. It is released from rest at A. Gravitational field strength = 9.8 N/kg. (a) Calculate the gravitational potential energy stored when the car is at A. (b) Assume no energy is dissipated. Calculate the speed of the car at B. (4 marks)

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Question 4 · mark scheme

Energy

Lesson 2 of 7

4 marks available. Award a mark for each point made.

98 000 J

1 mark

Kinetic energy gained = 78 400 J

1 mark

v² = 2E_k ÷ m

1 mark

19.8 m/s (accept 20 m/s)

1 mark

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Question 5 · 4 marks · Calculate

Energy

Lesson 2 of 7

“

A ball of mass 0.050 kg is thrown vertically upwards at 20 m/s. Assume there is no air resistance. Calculate the maximum height reached by the ball. Gravitational field strength = 9.8 N/kg.

HOW TO ANSWER IT

Command word: Calculate. Worth 4 marks, so plan before writing.

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Question 5 · mark scheme

Energy

Lesson 2 of 7

4 marks available. Award a mark for each point made.

Kinetic energy = 10 J

1 mark

Kinetic energy equals gravitational potential energy at the top

1 mark

h = E_p ÷ (mg)

1 mark

20 m (accept 20.4 m)

1 mark

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