Conservation of energy and calculations
Energy can be counted. Because the total before a change equals the total after, you can calculate an unknown quantity from the ones you know.
Part of your national curriculum
- Physics: energy: Understand energy as a quantity that can be quantified and calculated, and the total energy has the same value before and after a change
Lesson overview
What you'll learn in this lesson
Understand energy as a quantity that can be quantified and calculated, and the total energy has the same value before and after a change
Key learning points
- • The conservation principle
- • Calculating energy in stores
- • Using conservation to solve problems
- • Efficiency calculations
This lesson at a glance
- 30 minutes
- 21 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 21
Visual introductionPicture this
Conservation of energy and calculations
Energy can be counted. Because the total before a change equals the total after, you can calculate an unknown quantity from the ones you know.
In a nutshell
Understand energy as a quantity that can be quantified and calculated, and the total energy has the same value before and after a change
Learning cycle
Part 2 of 21
Learning cycle 1 of 2
Part 1 · The conservation principle
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 21
Learn
The conservation principle
Energy cannot be created or destroyed, only transferred between stores. When a swinging pendulum slows, its energy has not vanished: it has been transferred to the thermal store of the air and the pivot through friction, spread out too thinly to be useful.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 21
Learn
Calculating energy in stores
Kinetic energy = 0.5 × mass × speed², so a 2 kg object at 3 m/s has 9 J. Gravitational potential energy = mass × gravitational field strength × height, so lifting 2 kg by 5 m on Earth stores about 100 J. Doubling speed quadruples kinetic energy, which is why stopping distances grow so sharply.
Quick check
Part 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 21
Learning cycle 2 of 2
Part 2 · Using conservation to solve problems
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 21
Learn
Using conservation to solve problems
For a dropped object, the gravitational store lost equals the kinetic store gained if air resistance is ignored. Setting mgh = 0.5mv² lets you find the landing speed without knowing the time, and the mass cancels, which is why all objects fall at the same rate in a vacuum.
Explore the idea
Part 11 of 21
Learn
Efficiency calculations
Efficiency = useful energy out ÷ total energy in, often given as a percentage. A motor supplied with 500 J that does 350 J of useful work is 70% efficient, and the remaining 150 J has been dissipated, mostly by heating. Efficiency can never exceed 100%, so an answer above that signals an error.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
Worked example
Worked answer: a 2 kg ball is dropped from 5 m. Find its speed on landing, ignoring air resistance (4 marks)
Gravitational store lost = mgh = 2 × 10 × 5 = 100 J (1). By conservation, this all becomes kinetic energy, so 0.5mv² = 100 (1). Substituting the mass: v² = 100 ÷ (0.5 × 2) = 100 (1), so v = 10 m/s (1). The assumption that no energy is transferred to the air is what makes this calculation valid.
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 17 of 21
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 18 of 21
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ cannot be created or destroyed, only transferred between stores.
Challenge round
Part 19 of 21
Game · Recall cards
What does the law of conservation of energy state?
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Conservation of energy and calculations
4 questions, marked with the reasoning shown. No timer.
1. What does the law of conservation of energy state?
2. A falling object's gravitational potential energy mainly transfers into which store as it falls?
3. If a raised ball has 50 J of gravitational potential energy, what is the total energy just before landing (ignoring air resistance)?
4. A 2 kg object moving at 3 m/s has kinetic energy of
Lesson round-up
Part 21 of 21
Lesson round-up
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Understand energy as a quantity that can be quantified and calculated, and the total energy has the same value before and after a change