Work, energy and power is one of those Grade 12 Physical Science topics where students know the formulas but still get the questions wrong. It forms part of the Mechanics section in Paper 1, which carries around 65 marks in total. This topic alone can account for 20 to 25 of those marks. The reason students struggle is not the maths. It is knowing when to use the work-energy theorem versus conservation of energy, and how to handle friction in calculations.
In This Post You Will Learn
✓ The difference between the work-energy theorem and conservation of mechanical energy
✓ How to calculate work done by a force, including forces at an angle
✓ When to use conservation of energy and when you cannot use it
✓ How to solve inclined plane problems involving friction and energy
✓ The meaning of power and how to calculate it in real exam questions
✓ Common mistakes that cost students marks in the NSC exam
What is Work in Physics?
In everyday language, "work" means effort. In physics, work has a very specific definition.
Work is done when a force causes an object to move in the direction of the force.
The formula is: W = F.d.cosθ
Where:
W = work done (measured in joules, J)
F = applied force (in newtons, N)
d = displacement (in metres, m)
θ = the angle between the force and the direction of motion
When is Work Positive, Negative, or Zero?
This trips up a lot of students, but it is straightforward once you understand it.
Positive work: The force and displacement are in the same direction. Example: you push a box forward and it moves forward. θ = 0°, so cos 0° = 1.
Negative work: The force and displacement are in opposite directions. Example: friction acts backward while the object moves forward. θ = 180°, so cos 180° = -1.
Zero work: The force is perpendicular to the displacement. Example: the normal force acts upward while the object moves horizontally. θ = 90°, so cos 90° = 0.
Worked Example: Calculating Work Done at an Angle
A person pulls a crate with a force of 200 N at an angle of 30° to the horizontal. The crate moves 5 m along the floor.
W = F.d.cosθ
W = 200 x 5 x cos30°
W = 200 x 5 x 0.866
W = 866 J
Only the horizontal component of the force does work because the crate moves horizontally. That is what the cosθ accounts for.
Kinetic Energy and Potential Energy in Grade 12
There are two types of mechanical energy you need to know.
Kinetic energy (Ek) is the energy an object has because it is moving.
Ek = ½mv²
Where m is mass in kg and v is speed in m/s.
Gravitational potential energy (Ep) is the energy an object has because of its height above a reference point.
Ep = mgh
Where m is mass in kg, g = 9.8 m/s², and h is the height in metres.
Example: A 2 kg ball is 10 m above the ground and moving at 4 m/s.
Ek = ½(2)(4²) = ½(2)(16) = 16 J
Ep = (2)(9.8)(10) = 196 J
Total mechanical energy = Ek + Ep = 16 + 196 = 212 J
The Work-Energy Theorem Explained
The work-energy theorem states:
The net work done on an object is equal to the change in its kinetic energy.
W_net = ΔEk = ½mv_f² - ½mv_i²
This theorem works in every situation, whether friction is present or not. It considers ALL forces acting on the object.
Worked Example: Using the Work-Energy Theorem
A 5 kg block slides along a rough horizontal surface. It starts with a speed of 8 m/s and comes to rest after 4 m. Calculate the frictional force.
Step 1: Find the change in kinetic energy.
ΔEk = ½mv_f² - ½mv_i²
ΔEk = ½(5)(0²) - ½(5)(8²)
ΔEk = 0 - 160
ΔEk = -160 J
Step 2: The net work equals the change in kinetic energy.
W_net = -160 J
Step 3: The only horizontal force is friction (normal force and weight do zero work on a horizontal surface).
W_friction = f x d x cos180°
-160 = f x 4 x (-1)
f = 40 N
The frictional force is 40 N.
For full live lessons on this topic, see our Grade 12 Physical Science tuition page.
Conservation of Mechanical Energy
This is the principle that confuses students the most, because they do not understand when they are allowed to use it.
Conservation of mechanical energy states:
In an isolated system (no external forces like friction or applied forces), the total mechanical energy remains constant.
Ek_i + Ep_i = Ek_f + Ep_f
Or equivalently: ½mv_i² + mgh_i = ½mv_f² + mgh_f
The Critical Rule for Conservation of Energy
You can ONLY use conservation of mechanical energy when there are NO non-conservative forces doing work.
Non-conservative forces include friction, air resistance, applied forces (pushing or pulling), and tension in some cases.
If friction is present, you CANNOT simply write Ek_i + Ep_i = Ek_f + Ep_f. You must account for the energy lost to friction.
In that case, use:
Ek_i + Ep_i + W_nc = Ek_f + Ep_f
Where W_nc is the work done by non-conservative forces (usually negative because friction removes energy from the system).
Worked Example: Conservation Without Friction
A 3 kg ball is dropped from a height of 20 m. Calculate its speed just before hitting the ground. Ignore air resistance.
Since there is no friction or air resistance, we can use conservation of energy.
At the top: Ek_i = 0 (starts from rest), Ep_i = mgh = 3(9.8)(20) = 588 J
At the bottom: Ep_f = 0 (ground level), Ek_f = ½mv_f²
Ek_i + Ep_i = Ek_f + Ep_f
0 + 588 = ½(3)v_f² + 0
588 = 1.5v_f²
v_f² = 392
v_f = 19.80 m/s
Worked Example: Energy Conservation With Friction on an Incline
A 4 kg block slides down a rough inclined plane that is 5 m long and makes an angle of 30° with the horizontal. The coefficient of kinetic friction is 0.2. The block starts from rest. Find the speed at the bottom.
Step 1: Find the height.
h = 5 x sin30° = 5 x 0.5 = 2.5 m
Step 2: Find the normal force.
N = mgcos30° = 4(9.8)(0.866) = 33.95 N
Step 3: Find friction.
f = μN = 0.2 x 33.95 = 6.79 N
Step 4: Find work done by friction.
W_friction = f x d x cos180° = 6.79 x 5 x (-1) = -33.95 J
Step 5: Apply the energy equation with friction.
Ek_i + Ep_i + W_nc = Ek_f + Ep_f
0 + (4)(9.8)(2.5) + (-33.95) = ½(4)v_f² + 0
98 - 33.95 = 2v_f²
64.05 = 2v_f²
v_f² = 32.025
v_f = 5.66 m/s
How to Calculate Power in Grade 12 Physics
Power is the rate at which work is done.
P = W/t
Where P is power in watts (W), W is work done in joules, and t is time in seconds.
There is a second formula that is very useful:
P = Fv
This gives you the power when you know the force applied and the velocity of the object.
Worked Example: Power of a Motor
A motor lifts a 500 kg crate through a height of 12 m in 30 seconds at constant velocity.
Work done against gravity:
W = mgh = 500 x 9.8 x 12 = 58 800 J
Power:
P = W/t = 58 800/30 = 1 960 W or 1.96 kW
Common Mistakes Students Make
- Using conservation of energy when friction is present
This is the number one mistake. Students see a ball rolling down a slope and immediately write Ek_i + Ep_i = Ek_f + Ep_f, without checking whether friction is acting. If the question says "rough surface" or gives a coefficient of friction, you must include W_nc in the equation. Read the question carefully. The word "rough" means friction is present. The word "smooth" means you can ignore it.
- Getting the sign of work wrong
Work done by friction is always negative (it removes energy from the system). Work done by an applied force in the direction of motion is positive. Students mix these up and get answers that do not make physical sense. If your final speed comes out higher than expected on a rough surface, check your signs.
- Forgetting to use the component of weight on an incline
On an inclined plane, the component of weight parallel to the surface is mgsinθ, and the normal force is mgcosθ. Students often use mg for the normal force instead of mgcosθ, which gives the wrong friction value and throws off the entire calculation.
- Confusing power with force or energy
Power is not force. Power is not energy. Power is the rate of doing work. When a question asks for power, you need both the work done and the time. Students sometimes give the work done as their final answer and lose marks.
- Not choosing a reference point for potential energy
You can choose any point as your reference level (where h = 0), but you must be consistent. If you set the bottom of the slope as h = 0, then the height at the top is positive. If you set the top as h = 0, the bottom has negative height. Pick one and stick with it for the entire question.
How This Topic Appears in the NSC Exam
Work, energy and power appears in Paper 1 of the Grade 12 Physical Science NSC exam.
It falls under the Mechanics section and typically carries between 20 and 25 marks. Combined with Newton's Laws and Momentum (the other two mechanics topics), the entire Mechanics block is worth about 65 marks out of 150, making it the biggest section in Paper 1.
This topic usually appears around Question 4 or Question 5 in Paper 1. The DBE tends to structure it as a multi-part question with a scenario involving an object on an inclined plane or a falling/rising object. Part (a) often asks you to calculate work done by a specific force. Part (b) asks you to use the work-energy theorem or conservation of energy to find a final speed. Part (c) may ask for the power of a motor or engine.
In the 2023 NSC exam, this topic appeared as a question involving a block on an inclined plane with friction, requiring students to apply the work-energy theorem. A separate sub-question tested the power formula.
The DBE frequently tests whether students know the difference between conservative and non-conservative forces. A common theory question is: "State the work-energy theorem in words" or "Define a conservative force." These are easy marks if you have memorised the exact definitions from the CAPS document.
Pattern to watch for: the DBE loves combining this topic with Newton's second law. You may need to use F_net = ma to find acceleration, then use kinematics to find displacement, and finally use W = Fd to find work done. Be ready to combine topics in a single question.
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