Section 1 of 6What Power Means
Power tells us how quickly something converts energy, not how much energy it converts in total.
Definition
- Power is the rate at which energy is transferred, or the rate at which work is done.
Equation
- P = ΔE/t = W/t, where P is power in watts, W is work in joules and t is time in seconds.
The watt
- One watt is the transfer of one joule of energy each second, so 1 W = 1 J s⁻¹.
Larger units
- Power stations use kilowatts, megawatts and gigawatts, which are 10³ W, 10⁶ W and 10⁹ W.
Comparing machines
- Two machines doing the same work are distinguished by power, because the more powerful one finishes sooner.
Section 2 of 6Power, Force and Velocity
Many mechanics questions use the second form of the equation.
1
Start with P = W/t and replace the work by force × distance, so P = Fs/t.
2
The ratio s/t is the speed in the direction of the force, so P = Fv.
3
At constant speed the driving force equals the resistive force, so power equals resistance × speed.
4
If the power output is fixed, a larger force can only be produced at a lower speed, which is why vehicles use low gears on hills.
5
The equation requires force and velocity to be in the same direction; otherwise only the component along the motion is used.
Section 3 of 6Energy Bills and Units
Energy Bills and Units
Kilowatt-hour
- A kilowatt-hour is the energy used by a 1 kW device running for one hour.
Conversion
- 1 kW h = 1000 W × 3600 s = 3.6 × 10⁶ J, which is why it is used for large domestic quantities.
Cost
- Cost equals energy in kW h multiplied by the price per kW h, so power in kW and time in hours are used.
Rated power
- The power rating on an appliance gives the energy it transfers every second at its normal operating voltage.
Section 4 of 6Applications
Lifting
- A crane lifting a load steadily must supply power equal to the load’s weight multiplied by its speed.
Vehicle motion
- At top speed the engine’s useful power is the product of drag force and speed.
Human power
- Short bursts of exercise transfer energy faster than steady activity, so a sprinter’s power is far above an average walker’s.
Section 5 of 6Worked Example
Question
- A crane lifts an 800 kg load vertically at a constant speed of 0.50 m s⁻¹.
- Calculate the useful power delivered to the load.
- (g = 9.81 N kg⁻¹)
- At constant speed the lifting force equals the weight: F = mg = 800 × 9.81 = 7848 N.
- P = Fv = 7848 × 0.50 = 3924 W.What the symbols mean: P = power (W = J s−1) · W or E = work done / energy transferred (J) · t = time (s) · F = force (N) · v = velocity (m s−1)
Answer P ≈ 3.9 × 10³ W, or 3.9 kW.
Section 6 of 6Exam Checklist & Tips
3.6.6 – Key Points for the Exam
- Power The rate of transfer of energy, measured in watts.
- Watt The power when one joule of energy is transferred each second.
- Kilowatt-hour An energy unit equal to 3.6 × 10⁶ J.
- Work done The energy transferred by a force moving an object in its direction.
Common Mistakes
- Mixing up energy (joules) with power (watts), for example calling a bulb "a 60 joule bulb".
- Forgetting to convert minutes or hours to seconds when using P = W/t.
- Using P = Fv with a force that is not along the direction of motion.
- Treating kW h as a unit of power rather than a unit of energy.