Work, Energy and Power Solved Examples (Class 11 Physics)
Deepen understanding of work-energy theorem, conservation of energy, and power calculations. These problems cover conservative and non-conservative forces.
TL;DR: Deepen understanding of work-energy theorem, conservation of energy, and power calculations. These problems cover conservative and non-conservative fo…
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Deepen understanding of work-energy theorem, conservation of energy, and power calculations. These problems cover conservative and non-conservative forces.
Work, Energy and Power — Solved Numerical Examples (Step by Step)
Example 1: A 5 kg object is lifted vertically 10 m. How much work is done against gravity? (g = 10 m/s²)
Solution: Work W = mgh = 5 × 10 × 10 = 500 J
Example 2: A force of 100 N acts on a body at 60° to the horizontal, moving it 5 m horizontally. Calculate the work done.
Solution: Work W = F × d × cos(θ) = 100 × 5 × cos(60°) = 100 × 5 × 0.5 = 250 J
Example 3: A 2 kg object falls freely from a height of 20 m. Calculate its kinetic energy just before hitting the ground. (g = 10 m/s²)
Solution: By conservation of energy: KE at ground = PE at height
KE = mgh = 2 × 10 × 20 = 400 J
Example 4: A 10 kg object is dragged along a horizontal surface with a friction force of 50 N acting. If it moves 20 m, find work done by friction.
Solution: Work done by friction W_f = -F_friction × d = -50 × 20 = -1000 J
(Negative because friction opposes motion)
Example 5: A motor does 5000 J of work in 10 seconds. What is its power?
Solution: Power P = W/t = 5000 / 10 = 500 W
Example 6: A body of mass 4 kg is thrown upward with velocity 25 m/s. Using energy conservation, find the maximum height. (g = 10 m/s²)
Solution: Initial KE = (1/2)mv² = (1/2) × 4 × 25² = 2 × 625 = 1250 J
At maximum height, all KE converts to PE = mgh
1250 = 4 × 10 × h
1250 = 40h
h = 31.25 m
Tips
- Work-Energy Theorem: Net work done = Change in kinetic energy (W_net = ΔKE).
- Conservation of Energy: In absence of non-conservative forces, total mechanical energy remains constant (KE + PE = constant).
- Power is rate of doing work: P = W/t, and can also be expressed as P = F·v (force dot velocity).
Frequently Asked Questions
What is the difference between conservative and non-conservative forces?
Conservative forces (gravity, spring) depend only on position; work done is path-independent. Non-conservative forces (friction, air resistance) depend on the path; work done varies with path.
Can kinetic energy be negative?
No, kinetic energy KE = (1/2)mv² is always non-negative because both mass and velocity squared are positive.
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