Theme A — Space, Time and Motion
A.3.8 Energy and Power — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 39 of 63 1 quiz
Lesson summary
A.3.8 Energy and Power — IB PHYSICS SL notes: Define power as the rate of energy transfer and use P = W/t and P = Fv in calculations.Power = the rate at which energy is transferred, which is the rate of doing work.Equation — P = ΔW/Δt = ΔE/Δt.P is the power in W, W the work in J …
- SI base units
- Two motors
- Acceleration
- Derivation
- Fixed power
- Average power
Part 1 of 8Definition of power
Power
Power the rate at which energy is transferred, which is the rate of doing work.
Equation
- P = ΔW/Δt = ΔE/Δt.
- P is the power in W, W the work in J and t the time in s.
The watt
- 1 W = 1 J s−1, a transfer of 1 joule in 1 second.
SI base units
- SI base units the watt is kg m2 s−3.
Scalar
- Scalar power has no direction.
Multiples
- 1 kW = 103 W and 1 MW = 106 W.
Rating
- Rating a 60 W lamp transfers 60 J of electrical energy each second.
Part 2 of 8Why time matters
Two cars
- Two cars if both transfer the same energy to reach the same speed, the more powerful one does it sooner.
Two motors
- Two motors lifting the same weight through the same height, the one that lifts faster has more power.
Acceleration
- Acceleration power is required to produce an acceleration.
Part 3 of 8Power and velocity
Equation
- P = Fv, for a constant force moving a body at constant velocity.
Derivation
- Derivation the work done in time t is Fvt, so the power is Fv.
Direction
- Direction the force is applied in the same direction as the velocity.
Vehicles
- Vehicles at constant speed the driving force equals the resistive force, so engine power = resistive force × speed.
Drag
- Drag the force used is the one that balances the drag.
Fixed power
- Fixed power a higher speed means a lower driving force.
- This is why a vehicle accelerates more slowly at high speed and why gears exist.
Part 4 of 8Average and instantaneous power
1Average power
- Average power total energy transferred divided by total time.
2Instantaneous power
- Instantaneous power the rate at one moment, equal to F × the instantaneous speed.
3Energy–time graph
- Energy–time graph the gradient is the power.
4Power–time graph
- Power–time graph the area under the curve is the energy transferred.
5Constant acceleration from rest
- Constant acceleration from rest the power needed rises linearly with time.
6Peak and average
- Peak and average a sprinter may reach several kilowatts briefly but average far less.
Part 5 of 8Power in different contexts
| Context | Expression |
|---|---|
| Lifting | P = mgΔh/Δt = weight × vertical speed |
| Electrical | P = VI = I2R = V2/R |
| Wind turbine | P = ½ρAv3 |
| Radiation | Intensity I = P/A |
Part 6 of 8Input, output and cost
Efficiency
- Efficiency the useful output power is less than the input power, and the difference is lost as thermal power.
Input needed
- Input needed divide the output power by the efficiency.
Energy unit
- 1 kW h = 3.6 × 106 J.
Cost
- Cost energy in kW h is power in kW times time in hours; a 2.0 kW heater for 3.0 h uses 6.0 kW h.
Part 7 of 8Plausibility
Car
- Car an engine delivering 15 kW at cruising speed is realistic.
Humans
- Humans a person sustains 100 to 200 W, and over 1 kW for a second or two in a sprint or jump.
Power of ten errors
- Power of ten errors estimation catches unit-conversion mistakes.
Part 8 of 8More from the specification
More from the specification
Gravitational and Elastic Potential Energy
- Gravitational potential energy stored in an object elevated to height h is Ep = m·g·h,
- while elastic potential energy stored in a stretched or compressed spring is given by Ee = ½·k·x².
Mechanical Energy Conservation
- In an isolated mechanical system without resistive dissipation, total mechanical energy remains constant during motion.
- (sum of kinetic energy Ek = ½·m·v² and potential energy)
Energy Transformations and Power
- When an object moves along a horizontal or inclined surface, work done against friction results in wasted thermal energy dissipated to surroundings;
- power represents the rate of mechanical energy transfer (P = W/t = F·v).
Kinetic energy
- K = ½mv2, energy of motion.
Wasted energy
- Energy transferred to stores that are not useful, usually thermal in the surroundings.
Mechanical energy
- Sum of kinetic and potential energy.
Sankey diagram
- Diagram where arrow width shows energy amount.
Energy conservation
- Mgh = ½Mv2 + ½Iω2.
Resultant force
- Another name for net force.
Final speed
- Speed at the end, v
Elastic
- Returns to original shape when force is removed.
Friction
- Force parallel to the surface opposing relative motion or its tendency.
Density
- Mass per unit volume.
Component
- Part of a vector along one axis.
Position
- Location relative to a reference point.
Distance
- Total length of path travelled, a scalar.
Potential energy
- Energy stored by the configuration of a system.
Gravitational potential
- Work done per unit mass in bringing a test mass from infinity to the point.
W = Fs
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
Key terms
| Term | Meaning |
|---|---|
| Power | The rate at which work is done or energy is transferred |
| Watt (W) | The unit of power; 1 J s−1 |
| Kilowatt-hour | Unit of energy equal to 3.6 × 106 J |
| Average power | Total energy transferred divided by total time |
| Instantaneous power | Rate of energy transfer at a single moment |
| Power rating | Energy transferred per second by an appliance |
Avoid these mistakes
1
Using P = Fv when the force or velocity is not constant — use instantaneous values or P = W/t.
2
Mixing kW h with J — convert with 3.6 × 106.
3
Using the average speed when the instantaneous speed is needed — use the speed at that moment.
4
Forgetting to divide by efficiency to find the input power — input = output / efficiency.
5
Confusing power with energy — power is energy per second.
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