Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
Work, Energy and Power are fundamental concepts linking force and motion to energy. Conservation of energy is one of the most important principles in all of physics. This chapter is important for both board exams and NEET/JEE.
Work
Work is done when a force causes displacement in its direction.
W = F · s = Fs cosθ
- θ = 0°: W = Fs (maximum, positive work)
- θ = 90°: W = 0 (no work done — perpendicular force)
- θ = 180°: W = −Fs (negative work — force opposes motion)
Work is a scalar quantity. SI unit: joule (J)
Kinetic and Potential Energy
| Type | Formula | Description |
|---|---|---|
| Kinetic energy | KE = ½mv² | Energy due to motion |
| Gravitational PE | PE = mgh | Energy due to position |
| Elastic PE | PE = ½kx² | Energy stored in stretched spring |
Work-Energy Theorem
W_net = ΔKE = ½mv² − ½mu²
Net work done on a body equals the change in its kinetic energy.
Conservation of Mechanical Energy
In the absence of non-conservative forces (friction, air resistance):
KE + PE = constant
At height h: ½mv² + mgh = constant
Example — Free fall: As height decreases, PE decreases and KE increases; total mechanical energy remains constant.
Power
P = W/t = Fv
SI unit: watt (W) = 1 J s⁻¹
- 1 horsepower = 746 W
- Kilowatt-hour (kWh) = unit of energy (not power)
- 1 kWh = 3.6 × 10⁶ J
Collisions
| Type | Momentum | Kinetic Energy |
|---|---|---|
| Elastic | Conserved | Conserved |
| Inelastic | Conserved | NOT conserved |
| Perfectly inelastic | Conserved | Maximum loss |
Elastic Collision in 1D (equal masses)
After collision: velocities are exchanged
Perfectly Inelastic Collision
Bodies stick together: v = (m₁u₁ + m₂u₂) / (m₁ + m₂)
Coefficient of restitution (e):
- e = 1: perfectly elastic
- e = 0: perfectly inelastic
- 0 < e < 1: partially inelastic
Important Questions
One Mark
- State the work-energy theorem.
- What is the SI unit of power?
- In which collision is kinetic energy conserved?
- Define coefficient of restitution.
- When is work done by a force zero?
Short Answer (3 marks)
- Derive the expression for kinetic energy using the work-energy theorem.
- What is elastic potential energy? Derive the expression for energy stored in a spring.
- A body of mass 2 kg moving at 5 m/s collides with a stationary body of mass 3 kg. They stick together. Find the final velocity.
Long Answer (5 marks)
- State the law of conservation of energy. Verify it for a freely falling body at three points: initial position, midway, and just before hitting ground.
- Explain elastic and inelastic collisions. Derive expressions for final velocities after a one-dimensional elastic collision between two unequal masses.
Common Mistakes
- Confusing work (scalar) with force (vector) — work has no direction.
- Ignoring the cosθ factor when force and displacement are not parallel.
- Using total KE instead of change in KE in the work-energy theorem.
Board Exam Tips
- Conservation of energy problems often involve inclined planes and springs — practise these specifically.
- Collision problems frequently appear as numericals — know both elastic and perfectly inelastic formulas.
- NEET: power and energy numericals appear almost every year; easy marks if formula is known.