Chapter 5: Work, Energy and Power
1. Work
Work is done when a force causes displacement.
W = F × s × cosθ
- θ = angle between force and displacement
- Unit of work = Joule (J)
- Work can be positive, negative or zero
2. Work Done by Variable Force
Work is calculated using integration.
W = ∫F dx
3. Kinetic Energy
KE = ½mv²
- Energy due to motion
- Always positive
4. Work-Energy Theorem
Work done = Change in kinetic energy
5. Power
Power = Work / Time
- Unit = Watt (W)
6. Potential Energy
PE = mgh
- Energy due to position
Spring Potential Energy
PE = ½kx²
7. Conservative and Non-Conservative Forces
- Conservative: Work independent of path (e.g., gravity)
- Non-conservative: Work depends on path (e.g., friction)
8. Motion in Vertical Circle
- Energy conservation applies
- Minimum speed at top required
9. Collisions
Elastic Collision
- Momentum conserved
- Kinetic energy conserved
Inelastic Collision
- Momentum conserved
- Kinetic energy not conserved
10. MCQ One-Liners
- Unit of work is Joule.
- Work = F × s × cosθ.
- Kinetic energy depends on velocity.
- KE = ½mv².
- Power unit is Watt.
- Potential energy depends on height.
- PE = mgh.
- Spring energy = ½kx².
- Work-energy theorem relates work and KE.
- Conservative force is path independent.
- Friction is non-conservative.
- Elastic collision conserves KE.
- Inelastic collision loses KE.
- Momentum always conserved.
- Power = work/time.
- Work is zero if θ = 90°.
- Negative work reduces energy.
- Gravity is conservative force.
- Spring obeys Hooke’s law.
- Energy unit is Joule.
11. Numerical Problems with Solutions
1. Work Done
F = 10 N, s = 5 m, θ = 0°
W = 10×5×cos0 = 50 J
2. Kinetic Energy
m = 2 kg, v = 4 m/s
KE = ½×2×16 = 16 J
3. Potential Energy
m = 5 kg, h = 10 m
PE = 5×10×10 = 500 J
4. Power
Work = 100 J, Time = 5 s
Power = 100/5 = 20 W
5. Spring Energy
k = 200 N/m, x = 0.1 m
PE = ½×200×0.01 = 1 J
6. Work-Energy Theorem
Work = 50 J
Change in KE = 50 J
7. Velocity from Energy
KE = 100 J, m = 2 kg
100 = ½×2×v² → v²=100 → v = 10 m/s
8. Collision Concept
Total momentum before = 20
After collision total momentum = 20 (conserved)
