Work, energy and power

IB Physics SL· 45 min read

1. Work Done by a Constant Force★★☆☆☆⏱ 15 min

📘 Definition

Work

W

Work is the energy transferred when a force moves an object through a displacement. For a constant force, it equals the product of the parallel component of force and displacement.

W = F s \cos\theta

$θ$ is the angle between the force vector and the displacement vector. If $θ = 9 0^{\circ}$ , $cos θ = 0$ so work done is zero, even if a force is applied.

📐 Worked Example

A 50 N force pulls a box across a horizontal floor at 30° to the horizontal. The box moves 4 m horizontally. Calculate the work done by the applied force.

1
Identify given values: $F = 50$ N, $s = 4$ m, $θ = 3 0^{\circ}$
2
Substitute into the work formula:
3
$W = 50 \times 4 \times \cos(30^\circ)$
4
Calculate the final result:
5
$W = 200 \times \frac{\sqrt{3}}{2} \approx 173 \text{ J}$

2. Kinetic Energy and the Work-Energy Theorem★★★☆☆⏱ 15 min

📘 Definition

Kinetic Energy

E_k

Kinetic energy is the energy an object has due to its motion. It is proportional to the object's mass and the square of its speed.

Example:

A 1000 kg car moving at 10 m/s has 50,000 J of kinetic energy

E_k = \frac{1}{2} m v^2

The work-energy theorem connects net work done on an object to its change in kinetic energy:

W_{net} = \Delta E_k = E_{k,\text{final}} - E_{k,\text{initial}}

📐 Worked Example

A 0.5 kg ball moving at 4 m/s is slowed to rest by constant friction over 2 m. Calculate the magnitude of the frictional force.

1
Calculate initial kinetic energy:
2
$E_{k,i} = \frac{1}{2} m v_i^2 = 0.5 \times 0.5 \times (4)^2 = 4 \text{ J}$
3
Final kinetic energy is 0, so $Δ E_{k} = 0 - 4 = - 4$ J. The negative sign matches the negative work done by friction.
4
Apply the work-energy theorem: net work equals work done by friction
5
$-f s = \Delta E_k \implies -f (2) = -4 \implies f = 2 \text{ N}$

3. Gravitational Potential Energy★★☆☆☆⏱ 10 min

📘 Definition

Change in Gravitational Potential Energy

$Δ E_{p}$

Gravitational potential energy is energy stored due to an object's position in a gravitational field. Near Earth's surface, we only calculate changes in potential energy, not absolute values.

\Delta E_p = m g \Delta h

📐 Worked Example

A 2 kg brick is lifted from the ground to a shelf 1.5 m high. Calculate the change in gravitational potential energy. Take $g = 9.8 m s^{- 2}$ .

1
Identify values: $m = 2$ kg, $Δ h = 1.5$ m, $g = 9.8$ m s⁻²
2
Substitute into the potential energy formula:
3
$\Delta E_p = 2 \times 9.8 \times 1.5 = 29.4 \text{ J}$
4
The positive change means energy is stored as gravitational potential energy in the brick-Earth system.

4. Power and Efficiency★★★☆☆⏱ 15 min

📘 Definition

Power

P

Power is the rate at which work is done or energy is transferred. When a force is parallel to velocity, power can be written as the product of force and speed.

P = \frac{W}{\Delta t} = F v

Efficiency describes how much of the total input energy is converted to useful output energy, because all real processes waste some energy as heat.

\eta = \frac{P_{\text{useful out}}}{P_{\text{total in}}} \times 100\%

📐 Worked Example

A 1000 kg car accelerates from rest to 20 m/s in 10 s. The engine has an efficiency of 25%. Calculate the total power input from the fuel.

1
Calculate useful kinetic energy output:
2
$E_{\text{useful}} = \frac{1}{2} m v^2 = 0.5 \times 1000 \times (20)^2 = 200 000 \text{ J}$
3
Calculate useful power output:
4
$P_{\text{out}} = \frac{E_{\text{useful}}}{t} = \frac{200 000}{10} = 20 000 \text{ W} = 20 \text{ kW}$
5
Rearrange the efficiency formula to solve for total input power:
6
$P_{\text{in}} = \frac{P_{\text{out}}}{\eta} = \frac{20 000}{0.25} = 80 000 \text{ W} = 80 \text{ kW}$

5. Common Pitfalls

Wrong move:

Ignoring the angle $θ$ and just calculating $W = F s$ for angled forces

Why:

Only the component of force parallel to displacement contributes to work; perpendicular components do no work

Correct move:

Always multiply by $cos θ$ when force is at an angle to displacement, and remember work is zero when force is perpendicular

Wrong move:

Using work done by a single force instead of net work in the work-energy theorem

Why:

The work-energy theorem relates the total work from all forces acting on an object to the change in kinetic energy

Correct move:

Sum the work done by all individual forces to get net work before equating to $Δ E_{k}$

Wrong move:

Using absolute height instead of change in height for gravitational potential energy

Why:

Zero potential energy is an arbitrary reference point, only changes in height are physically meaningful

Correct move:

Always use the difference between final and initial vertical height to calculate $Δ E_{p}$

Wrong move:

Using percentage efficiency directly in calculations (e.g. 25 instead of 0.25)

Why:

Efficiency is a ratio between 0 and 1, percentage is just for reporting final results

Correct move:

Divide the percentage efficiency by 100 before substituting into the efficiency formula

6. Quick Reference Cheatsheet

Quantity	Formula	Key Notes
Work (constant F)	$W = F s cos θ$	$θ$ = angle between F and s
Kinetic Energy	$E_{k} = \frac{1}{2} m v^{2}$	Always non-negative
Work-Energy Theorem	$W_{n e t} = Δ E_{k}$	Net work = change in KE
Gravitational PE change	$Δ E_{p} = m g Δ h$	$Δ h$ = vertical change
Power	$P = \frac{W}{Δ t} = F v$	$F v$ for parallel F and v
Efficiency	$η = \frac{P _{o u t}}{P _{in}} \times 100%$	$0 < η < 100%$ for all real systems

7. Frequently Asked

Why can work be negative? What does that mean?

Negative work means the force opposes the motion of the object, reducing the object's total kinetic energy. Friction always does negative work on moving objects, for example.

Is total energy ever destroyed in IB problems?

Total energy is always conserved. Non-conservative forces like friction dissipate energy as heat, so total mechanical energy (kinetic + potential) decreases, but energy is not destroyed.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · P1
Work done by angled force
2024 · P2
Power and efficiency of car engine
2023 · P1
Work-energy theorem application

Going deeper

simulationPhET Work & Energy Skate ParkVisualize energy transformations

What's Next

Work, energy and power is a foundational concept that extends to nearly every topic in IB Physics SL. Understanding energy transformations is key for thermal physics, circular motion, and electricity, where energy transfer is a core theme. Mastery of this sub-topic will also make solving complex mechanics problems much simpler, as energy methods often avoid needing to calculate acceleration. Next, you will build on this knowledge to explore conservation of mechanical energy, then extend to momentum for systems of multiple objects.