Work and Energy Solved Examples (Class 9 Physics)
Understand work, energy, and power calculations in mechanics. These problems cover work done by forces, kinetic energy, potential energy, and energy conser
TL;DR: Understand work, energy, and power calculations in mechanics. These problems cover work done by forces, kinetic energy, potential energy, and energy c…
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Understand work, energy, and power calculations in mechanics. These problems cover work done by forces, kinetic energy, potential energy, and energy conser
Work and Energy — Solved Numerical Examples (Step by Step)
Example 1: A force of 50 N is applied to a block at an angle of 30° to the horizontal, moving it 4 m. Calculate the work done.
Solution: Work W = F × d × cos(θ)
W = 50 × 4 × cos(30°)
cos(30°) = √3/2 = 0.866
W = 50 × 4 × 0.866 = 173.2 J
Example 2: A 2 kg object is moving with a velocity of 5 m/s. Calculate its kinetic energy.
Solution: Kinetic energy KE = (1/2)mv²
KE = (1/2) × 2 × (5)²
KE = 1 × 25 = 25 J
Example 3: A 3 kg object is lifted vertically to a height of 10 m. Calculate the gravitational potential energy gained. (g = 10 m/s²)
Solution: Gravitational potential energy PE = mgh
PE = 3 × 10 × 10
PE = 300 J
Example 4: A ball is thrown upward with an initial velocity of 20 m/s. At what height will its kinetic energy equal its potential energy? (g = 10 m/s², mass = 1 kg)
Solution: Initial KE = (1/2) × 1 × 20² = 200 J
At height h: KE + PE = 200 (energy conservation)
Let v be velocity at height h: (1/2)mv² + mgh = 200
Also, v² = u² - 2gh = 400 - 20h
So (1/2) × (400 - 20h) + 10h = 200
200 - 10h + 10h = 200
When KE = PE: (1/2)mv² = mgh
(1/2)v² = gh
From v² = 400 - 20h: (1/2)(400 - 20h) = 10h
200 - 10h = 10h
200 = 20h
h = 10 m
Example 5: A 500 W motor lifts a 10 kg mass vertically. How long does it take to lift it by 20 m? (g = 10 m/s²)
Solution: Work to be done W = mgh = 10 × 10 × 20 = 2000 J
Power P = W/t
t = W/P = 2000 / 500 = 4 s
Example 6: A force of 20 N does 400 J of work. What is the distance moved in the direction of force?
Solution: Work W = F × d
d = W / F = 400 / 20 = 20 m
Tips
- Work is positive when force and displacement are in the same direction, negative when opposite, and zero when perpendicular.
- Always convert angles to the angle between force and displacement vectors when using W = Fd cos(θ).
- Energy conservation states that in an isolated system, total mechanical energy (KE + PE) remains constant.
Frequently Asked Questions
Can work be negative?
Yes, when the force opposes the motion (like friction acting against movement). Negative work decreases the object's energy.
What is the difference between power and energy?
Energy is the capacity to do work (measured in joules), while power is the rate of doing work (measured in watts or J/s).
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