Teacher sheet · Ages 15–16 · about 45–50 minutes
Energy: calculations, conservation and efficiency
Lesson page: echoesof.science/school/energy/ages-15-16/ · Pupil worksheet: echoesof.science/school/energy/ages-15-16/print/
Learning aims
- Use E_k = ½mv² and E_p = mgh with correct units.
- Apply conservation of energy to falling objects.
- Calculate efficiency and power, including kWh.
- Measure an efficiency and evaluate its uncertainty.
Lesson plan
| Time | Activity |
|---|---|
| 5 min | Starter: why does a bouncing ball eventually stop? |
| 10 min | Read the text; work through the falling-rock example. |
| 25 min | Bouncing-ball efficiency experiment with video. |
| 5 min | Compare balls; discuss the uncertainty of video readings. |
| 5 min | Quiz, or the game as homework. |
Materials for the experiment
- Two or three different balls (tennis, bouncy, ping-pong)
- Balance
- Metre rule or tape fixed vertically to a wall
- Phone camera (slow motion if possible)
- A hard floor
Safety: Drop the balls, don't throw them. Keep the area clear and don't stand on tables or chairs to drop from higher than you can reach safely.
Common misconceptions
| Pupils may think… | Actually… |
|---|---|
| Energy is lost when a ball stops bouncing. | It is not destroyed: it is dissipated as thermal energy (and sound). |
| Efficiency can be more than 100% if a machine is very good. | Useful output can never exceed the input, because total energy is conserved. |
| A higher power means more energy. | Power is energy per second; total energy also depends on the time. |
Worksheet answers
- Bars: E_p at the top; E_k (nearly the same) just before impact; a smaller E_p at the top of the bounce; the difference is dissipated as heat and sound.
- E_p = 0.060 × 9.8 × 1.5 ≈ 0.88 J. ½mv² = mgh gives v = √(2gh) = √(2 × 9.8 × 1.5) ≈ 5.4 m/s.
- Efficiency = 0.62 ÷ 1.00 = 0.62 = 62%. The other 38% is dissipated mainly as thermal energy in the ball and floor, and as sound.
- Saving = (60 − 9) W × 1000 h = 51 000 Wh = 51 kWh.
Quiz answers
- What is the kinetic energy of a 2 kg ball moving at 3 m/s? 9 J. E_k = ½ × 2 × 3² = 9 J.[3]
- How much potential energy does a 5 kg box gain when lifted 2 m? (g = 9.8 m/s²) 98 J. E_p = m·g·h = 5 × 9.8 × 2 = 98 J.[3]
- A 10 kg rock falls 10 m from rest. Ignoring air resistance, its kinetic energy is then… 980 J. The 980 J of lost potential energy becomes kinetic energy.[3]
- A 60 W bulb produces 5 W of light. Its efficiency is about… 8%. Efficiency = 5 ÷ 60 ≈ 0.08 = 8%.[5]
- A 0.200 kW computer runs 6 hours a day for 30 days. How much energy does it use? 36 kWh. 0.200 kW × 180 h = 36 kWh.[5]
- Which has the highest typical efficiency? An electric motor. Representative values: electric motor 98%, petrol engine 30%, solar cell 10%.[4]
Going further
Plot h₂ against h₁ for each ball. Is the graph a straight line through the origin? What would a constant efficiency look like on this graph? Research why a power station's efficiency is limited.
Sources used in this lesson
- [3] Physics, 9.2 Mechanical Energy and Conservation of Energy (OpenStax, Rice University): reliability High
- [4] College Physics 2e, 7.6 Conservation of Energy (OpenStax, Rice University): reliability High
- [5] College Physics 2e, 7.7 Power (OpenStax, Rice University): reliability High
- [6] LED Lighting (U.S. Department of Energy, Energy Saver): reliability High
Full list with links and a note on each source's reliability: echoesof.science/school/energy/sources/
Privacy: the lesson pages have no ads, no tracking and no cookies. Quiz answers and game scores stay in the pupil's browser. A short video for each age is coming.