Work Done, Energy and Power
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed — only transferred between stores. In any closed system, the total energy before a process equals the total energy after. Energy that seems to ‘disappear’ has been dissipated — spread out into less useful thermal energy in the surroundings (P5.1a).
Energy can be stored in different ways: kinetic (moving objects), gravitational potential (objects at height), elastic potential (stretched or compressed objects), chemical (food, fuels, batteries), thermal (hot objects), magnetic, electrostatic and nuclear. Energy transfers between these stores via heating, radiation, electrical current or mechanical work.
Energy cannot be created or destroyed. It transfers between stores (kinetic, gravitational potential, elastic, chemical, thermal, magnetic, electrostatic, nuclear). Dissipated energy is wasted as heat.
Work Done
When a force moves an object through a distance, work is done. Work done is a measure of energy transferred. The equation is (P5.1d):
$$W = F \times d$$
where \(W\) = work done in joules (J), \(F\) = force in newtons (N), and \(d\) = distance moved in the direction of the force in metres (m). One joule of work is done when a force of 1 N moves an object 1 m.
Example: a person pushes a box with a force of 50 N across 3 m. Work done = \(50 \times 3 = 150\) J. This 150 J of energy has been transferred from the person’s chemical energy store to the kinetic energy store of the box (and some to thermal energy through friction).
When work is done against gravity (e.g. lifting an object), energy is transferred to the object’s gravitational potential energy store. The equation is:
$$GPE = m \times g \times h$$
where \(m\) = mass in kg, \(g\) = gravitational field strength (10 N/kg on Earth) and \(h\) = height gained in metres. For example, lifting a 5 kg bag to a shelf 2 m high: \(GPE = 5 \times 10 \times 2 = 100\) J.
Similarly, a moving object has kinetic energy calculated by:
$$KE = \frac{1}{2} \times m \times v^2$$
where \(v\) = speed in m/s. Notice that kinetic energy depends on \(v^2\) — doubling the speed quadruples the kinetic energy. This is why braking distance increases dramatically at higher speeds and why speed limits exist in residential areas.
Power measures how quickly energy is transferred (P2.2n). The equations are:
$$P = \frac{E}{t} \quad \text{and} \quad P = \frac{W}{t}$$
where \(P\) = power in watts (W), \(E\) = energy transferred in joules (J), \(W\) = work done in joules (J), and \(t\) = time in seconds (s). One watt equals one joule per second.
Example: a 60 W light bulb transfers 60 J of energy every second. If it is on for 5 minutes (300 s), total energy transferred = \(60 \times 300 = 18{,}000\) J = 18 kJ.
A more powerful device transfers the same amount of energy in less time. This is why a 2000 W kettle boils water faster than a 1000 W kettle — it transfers energy at twice the rate.
Work done: \(W = F \times d\) (joules). Power: \(P = E/t\) or \(P = W/t\) (watts). Power measures the rate of energy transfer — higher power means faster energy transfer.
Efficiency
No energy transfer is 100% efficient. Some energy is always dissipated as waste heat. Efficiency measures how much of the input energy is usefully transferred (P5.2d):
$$\text{Efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}$$
Efficiency can be expressed as a decimal (0 to 1) or as a percentage (multiply by 100). For example, a motor that receives 500 J of electrical energy and does 350 J of useful work has efficiency = \(\frac{350}{500} = 0.70\) = 70%. The remaining 150 J is dissipated as heat and sound.
Engineers design systems to minimise energy waste and improve efficiency:
• Lubrication — reduces friction between moving parts, decreasing the thermal energy wasted.
• Streamlining — reduces air resistance on vehicles, so less energy is wasted overcoming drag.
• Thermal insulation — slows heat transfer from buildings (loft insulation, double glazing, cavity wall insulation), keeping homes warmer with less heating.
• LED lighting — converts a higher proportion of electrical energy into light compared to incandescent bulbs, which waste most energy as heat.
Improving efficiency is important for reducing fuel consumption, lowering energy bills and decreasing carbon emissions from fossil fuels.
In calculations, you may need to combine the work, power and efficiency equations. For example, if a crane with 40% efficiency lifts a 2000 N load through 15 m in 30 seconds, the useful work done is \(2000 \times 15 = 30{,}000\) J. Since only 40% of the input energy is useful: total input energy = \(\frac{30{,}000}{0.4} = 75{,}000\) J. The power of the crane = \(\frac{75{,}000}{30} = 2{,}500\) W = 2.5 kW.
Elastic potential energy is stored when a spring or elastic material is stretched or compressed. The equation is:
$$EPE = \frac{1}{2} \times k \times e^2$$
where \(k\) = spring constant in N/m and \(e\) = extension in metres. Like kinetic energy, elastic potential energy depends on the square of the extension — doubling the stretch quadruples the energy stored. This equation applies only within the limit of proportionality, where force and extension are directly proportional (Hooke’s Law).
Efficiency = useful output ÷ total input. No device is 100% efficient. Wasted energy can be reduced through lubrication, streamlining, insulation and using more efficient technologies like LEDs.