echoesof.science · Ages 15–16
Energy: calculations, conservation and efficiency
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the game and the quiz
echoesof.science/school/energy/ages-15-16/
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Kinetic energy: Ek = ½·m·v². Gravitational potential energy (near Earth's surface): Ep = m·g·h. Both are measured in joules (J).
Conservation of energy: in a closed system the total energy is constant. Energy can change form or be transferred, but it is never created or destroyed.
Example: a 10 kg rock falls from a 20 m cliff. After falling 10 m it has lost m·g·Δh = 10 × 9.8 × 10 = 980 J of potential energy, so (ignoring air resistance) it has gained 980 J of kinetic energy.
Experiment: Efficiency of a bouncing ball
- Measure the mass of each ball.
- Drop a ball from h₁ = 1.00 m (bottom of the ball) and film it next to the rule. Read the height h₂ the bottom of the ball reaches after the first bounce.
- Repeat five times and calculate the mean h₂ and its spread (half the range).
- Calculate E_p before the drop (m·g·h₁) and at the top of the bounce (m·g·h₂).
- Efficiency of the bounce = useful energy out ÷ energy in = m·g·h₂ ÷ m·g·h₁ = h₂ ÷ h₁.
- Repeat for the other balls and for two more drop heights. Does the efficiency depend on the drop height?
- Optional: from the video, find the speed just before impact and compare ½·m·v² with m·g·h₁.
| Ball | Mass (kg) | h₁ (m) | Mean h₂ (m) | Efficiency h₂/h₁ |
|---|---|---|---|---|
Questions
Draw a bar chart (or Sankey diagram) of the energy of your ball: at the top, just before impact, and at the top of the bounce.
🍎A 0.060 kg ball is dropped from 1.5 m. Calculate its potential energy and its speed just before it hits the floor (ignore air resistance).
Your ball bounced to 0.62 m after a 1.00 m drop. Calculate the efficiency of the bounce. Where did the rest of the energy go?
A 9 W LED and a 60 W incandescent bulb are each on for 1000 hours. How many kWh does the LED save?
Sources for every fact on this sheet: echoesof.science/school/energy/sources/