Grade 12 Physical Science
Work, Energy and Power – Term 4 Final Exam Revision
Quick Study Info
Study Time
60-90 min
Difficulty
High
Exam Weight
~20-25 marks
What You’ll Master
- Calculate work done by forces at different angles
- Apply the Work-Energy Theorem to solve complex problems
- Distinguish between conservative and non-conservative forces
- Solve conservation of energy problems on inclines and vertical planes
- Calculate power in various scenarios including pumps and motors
Essential Definitions
1. Work (W)
Definition: Work done by a constant force on an object is the product of the magnitude of the force, the magnitude of the displacement, and the cosine of the angle between them.
Formula: W = F × Δx × cos θ
Unit: Joule (J) or N·m
Remember: Work is a SCALAR quantity. Angle θ is between force and displacement vectors.
Key Points:
- Positive work: Force has component in direction of motion (0° ≤ θ < 90°)
- Zero work: Force perpendicular to motion (θ = 90°)
- Negative work: Force opposes motion (90° < θ ≤ 180°)
2. Kinetic Energy (Ek)
Definition: The energy an object has due to its motion.
Formula: Ek = ½mv²
Unit: Joule (J)
Remember: Always POSITIVE (velocity is squared). If stationary, Ek = 0.
3. Gravitational Potential Energy (Ep)
Definition: Energy due to position in a gravitational field relative to a reference point.
Formula: Ep = mgh
Unit: Joule (J)
Remember: Choose reference point wisely – usually ground level or lowest point.
4. Power (P)
Definition: The rate at which work is done or energy is transferred.
Formulas:
- P = W/t (general)
- P = F·v·cos θ (for constant velocity)
Unit: Watt (W) or J/s
Remember: 1 kW = 1000 W. Power tells you how FAST work is done, not HOW MUCH.
Critical Theorems
Work-Energy Theorem
Statement: The net work done on an object equals the change in its kinetic energy.
Wnet = ΔEk = Ek,f – Ek,i
Key Insight: Works for ALL forces. Calculate net force first, then apply!
Conservation of Mechanical Energy
Statement: In a system where ONLY conservative forces work, mechanical energy remains constant.
Em,i = Em,f
Ek,i + Ep,i = Ek,f + Ep,f
When NON-conservative forces are present:
Wnc = ΔEk + ΔEp
Worked Examples
Example 1: Work Done at an Angle
- Given: F = 50 N, Δx = 8 m, θ = 30°
- W = F·Δx·cos θ
- W = (50)(8)(cos 30°)
- W = (50)(8)(0.866)
- W = 346.4 J
Answer: 346.4 J
Example 2: Conservation of Energy
- No friction → Energy conserved
- At top: Ek,i = 0, Ep,i = mgh = (2)(9.8)(5) = 98 J
- At bottom: Ep,f = 0, Ek,f = ½mvf²
- Em,i = Em,f → 98 = ½(2)vf²
- vf² = 98
- vf = 9.90 m/s
Answer: 9.90 m/s
Example 3: Work-Energy with Friction
- Friction force: fk = μk·mg = (0.3)(5)(9.8) = 14.7 N
- Work by friction: Wf = -fk·Δx = -14.7 × 10 = -147 J
- Work-Energy Theorem: Wnet = ΔEk
- -147 = ½(5)vf² – ½(5)(8)²
- -147 = 2.5vf² – 160
- vf² = 5.2
- vf = 2.28 m/s
Answer: 2.28 m/s
Common Mistakes to AVOID
Mistake 1: Using distance instead of displacement
Why wrong: Work depends on displacement (straight-line), NOT total distance traveled.
Do this: Always use net displacement vector.
Mistake 2: Forgetting the angle
Why wrong: Only force component IN DIRECTION of motion does work.
Do this: Always identify angle between F and Δx. Draw diagram!
Mistake 3: Using conservation when friction present
Why wrong: Energy only conserved with NO non-conservative forces.
Do this: If friction mentioned, use Wnc = ΔEk + ΔEp
Practice Questions
Quick Check
- A 10 N force pulls a box 5 m horizontally. Calculate work done.
- A 2 kg ball thrown vertically upward at 10 m/s. Calculate maximum kinetic energy.
- 5 kg object lifted 3 m vertically. Calculate work against gravity.
- 300 J of work in 10 seconds. What is power output?
- State TWO conservative forces.
Challenge Questions
- 1500 kg car accelerates from 10 m/s to 25 m/s over 100 m. Calculate: (a) Work done (b) Average net force
- 20 kg box slides down rough 30° incline from 8 m height. μk = 0.25. Calculate: (a) Work by friction (b) Speed at bottom
Formula Quick Reference
| Concept | Formula |
|---|---|
| Work | W = F·Δx·cos θ |
| Kinetic Energy | Ek = ½mv² |
| Potential Energy | Ep = mgh |
| Work-Energy Theorem | Wnet = ΔEk |
| Conservation | Em,i = Em,f |
| Power | P = W/t or P = F·v·cos θ |
Final Exam Preparation
High Priority Topics
- Conservation of energy with friction (most common)
- Work-energy theorem on inclines
- Power calculations for pumps
- Work done at angles
Exam Format
Typical marks: 20-25 marks in Paper 1
Time allocation: ~1.2 minutes per mark
Common question types: Multi-step problems combining forces, energy, and power
Answer Key
Click to reveal answers
Quick Check:
- 50 J
- 100 J
- 147 J
- 30 W
- Gravitational force, spring force
Challenge:
- (a) 421,875 J (b) 4,218.75 N
- (a) -679.4 J (b) 11.5 m/s
Your Next Steps
After This
Momentum, Vertical Projectiles
Review
Newton’s Laws, Forces, Free-body diagrams
Practice
DBE past papers 2019-2024
For Parents and Teachers
Support Tips:
- Expected mastery: Solve 10-mark problems independently in under 10 minutes
- Watch for: Confusion between distance/displacement, sign errors with friction, not showing working
- Practice at home: Use real examples (lifting groceries, climbing stairs), work through past papers together
- Get help if: Consistent scores below 40%, avoiding multi-step problems, cannot explain formula choices
- Exam weight: 20-25 marks in Paper 1 – HIGH priority topic!