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Problem 1a Solution:
- Total energy from lunch: 700 Calories × 4186 J/Calorie = 2,930,200 Joules.
- Radiating rate: 100 Joules per second.
- Time to radiate all energy: 2,930,200 J ÷ 100 J/s = 29,302 seconds.
- Convert to hours: 29,302 s ÷ 3600 s/h ≈ 8.14 hours.
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Problem 1b Solution:
- Energy available for lifting: 2,930,200 Joules (ignoring radiation).
- Work to lift one piano: Force × Distance = 5000 N × 10 m = 50,000 Joules.
- Number of pianos: 2,930,200 J ÷ 50,000 J/piano ≈ 58.6 pianos.
- Since you can’t lift a fraction of a piano, the student could lift 58 pianos.
- Energy Conservation Equation: E_initial = E_final → 2,930,200 J = 58 × 50,000 J + leftover energy (≈ 30,200 J).
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Problem 2 Solution:
- Mass of bucket: 12 kg.
- Gravitational force: F = mg = 12 kg × 9.8 m/s² = 117.6 N.
- Work done: W = F × d = 117.6 N × 10 m = 1176 Joules.
- Power required: P = W / t = 1176 J ÷ 5 s = 235.2 Watts.
- Energy Conservation Equation: E_input = E_output → Work done on bucket = 1176 J (all converted to gravitational potential energy since speed is constant).
Parent Tip: Review the logic above to help your child master the concept of power in flowing energy worksheet answers.
