For each question: list what you know, decide which equation to use, then use FIFA. The solution starts by showing how to pick the equation. c water = 4200 J/kg °C.
Q1 (F) A 0.50 kg ball moves at 6.0 m/s. How much energy is in its kinetic store?
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Which equation? Know mass and speed, want kinetic energy → Eₖ = ½mv²
I: Eₖ = 0.5 × 0.50 × 6.0²
A: 9.0 J
Q2 (F) A 60 kg student climbs 4.0 m of stairs. How much gravitational potential energy does she gain?
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Which equation? Know mass and height gained → Eₚ = mgh
I: Eₚ = 60 × 9.8 × 4.0
A: 2352 J
Q3 (F) A heater transfers 45 000 J of energy in 30 s. Calculate its power.
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Which equation? Know energy and time, want power → P = E / t
I: P = 45 000 ÷ 30
A: 1500 W
Q4 (F) A motor does 6000 J of work in 20 s. Calculate its power.
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Which equation? Know work done and time, want power → P = W / t
I: P = 6000 ÷ 20
A: 300 W
Q5 (F) A lamp transfers 20 J of energy usefully for every 100 J supplied. Calculate its efficiency.
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Which equation? Know useful and total energy → efficiency = useful output ÷ total input
I: efficiency = 20 ÷ 100
A: 0.20 (20%)
Q6 (F) A spring with a spring constant of 200 N/m is stretched 0.10 m. How much energy does it store?
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Which equation? Know spring constant and extension, want energy stored → Eₑ = ½ke²
I: Eₑ = 0.5 × 200 × 0.10²
A: 1.0 J
Q7 (F/H) 0.50 kg of water is warmed by 30 °C. How much energy is needed?
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Which equation? Know mass and temperature change → ΔE = mcΔθ
I: ΔE = 0.50 × 4200 × 30
A: 63 000 J
Q8 (F/H) A motor has an input power of 800 W and a useful output power of 600 W. Calculate its efficiency as a percentage.
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Which equation? Given powers, not energies → efficiency = useful power output ÷ total power input
I: efficiency = 600 ÷ 800 = 0.75
A: 75%
Q9 (F/H) A 1000 kg car has 200 000 J of kinetic energy. Calculate its speed.
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Which equation? Know kinetic energy and mass, want speed → Eₖ = ½mv²
I: 200 000 = 0.5 × 1000 × v²
F: v² = 400, v = √400
A: 20 m/s
Q10 (H) How long does a 2.0 kW kettle take to transfer 360 kJ?
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Which equation? Know power and energy, want time → P = E / t
Convert: 2.0 kW = 2000 W; 360 kJ = 360 000 J
I: 2000 = 360 000 ÷ t
F: t = 360 000 ÷ 2000
A: 180 s
Q11 (H) A 75 kg climber gains 1.47 × 104 J of gravitational potential energy. How high has she climbed?
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Which equation? Know GPE and mass, want height → Eₚ = mgh
I: 14 700 = 75 × 9.8 × h
F: h = 14 700 ÷ 735
A: 20 m
Q12 (H) A 3.0 kg metal block releases 27 000 J as it cools by 20 °C. Calculate the specific heat capacity of the metal.
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Which equation? Temperature change and energy → ΔE = mcΔθ
I: 27 000 = 3.0 × c × 20
F: c = 27 000 ÷ 60
A: 450 J/kg °C
