Energy transfers, work and efficiency
Section: Work, Energy and Power | Syllabus: Cambridge AS Level Physics (9702)
What is Energy?
Energy is a quantity that must be transferred in order to do work. It is a scalar quantity (no direction). The SI unit is the joule (J).
Forms of Energy
Energy is stored in objects and systems in various forms:
| Energy Form | Description |
|---|---|
| Chemical Potential | Stored in chemical bonds (fossil fuels, food, batteries). |
| Elastic Potential | Stored in objects changed in shape reversibly (stretched springs). |
| Gravitational Potential | Stored due to position in a gravitational field. |
| Kinetic | Stored in any moving object. |
| Nuclear | Stored in the nucleus of atoms (released in fission/fusion). |
Ways of Transferring Energy
| Process | Examples |
|---|---|
| Electrically | Electric current transferring energy from a battery to a lamp. |
| By Radiation | Electromagnetic waves (light, X-rays). |
| Mechanically | By forces (pushing a car, sound waves). |
| By Heating | Thermal energy transfer due to temperature difference. |
What is Work?
Work is done when a force causes an object to move. It is the product of force and displacement in the direction of the force.
W = FsWhere F is a constant force.
Base Units of the JouleSince Work = Force × Distance (N × m) and Force = Mass × Acceleration (kg × m s^-2):
1 Joule = 1 N m = 1 kg m^2 s^-2.
Work Done by a Variable Force
If the force is not constant, we cannot simply use W=Fs. Instead, the work done is the area under the force-displacement graph.
Figure 5.1: Area under a Force-Displacement GraphShow a graph with Force (y-axis) vs Displacement (x-axis). A curved line indicates a changing force. Shade the area under the curve to represent the total work done. Highlight a small strip of width Δ s and height F to show W ≈ Σ F Δ s.
Calculating Work Done with Angles
If the force acts at an angle θ to the direction of motion, only the component of force in the direction of motion does work.
W = Fs cos θ Figure 5.2: Resolving Force ComponentsShow a model tractor being pulled by a force F at an angle θ to the horizontal. Show the horizontal component F cos θ (doing work) and the vertical component F sin θ (doing no work against horizontal motion).
Worked Example: Pulling a Box (Figure 5.3)Question: A box is pulled across level ground by a rope inclined at 20° above the horizontal. The constant force applied is 140 N. Calculate the work done in moving the box 5.0 m.
AnswerWe use the component of force in the direction of displacement (F cos θ).
W = F s cos θ
W = 140 × 5.0 × cos 20^ = 660 JConservation of Energy
Principle of Conservation of Energy The total energy of a closed system is constant. Energy cannot be created or destroyed, only transferred or converted from one form to another. Closed SystemsA "closed system" is one where no energy enters or leaves. For example, a battery and lamp can be treated as a system, but if heat escapes to the surrounding air, the air must be included in the "closed system" to balance the energy equation.
Discovery of the NeutrinoThe conservation of energy is fundamental. When scientists observed beta decay, energy seemed to disappear. Rather than abandon the principle, they predicted a new particle (the neutrino) was carrying away the missing energy. This was later confirmed.
Efficiency
Efficiency measures how much input energy is converted to useful output energy.
Efficiency = (Useful Energy Output/Total Energy Input)(Multiply by 100 for percentage)
Sankey Diagrams
Sankey diagrams visualize energy transfers. The width of the arrow represents the amount of energy.
Figure 5.9: Sankey DiagramShow an input arrow (Energy transferred by electricity, 9 J) splitting into two: a thin arrow going straight (Light, 0.8 J) and a thick arrow curving down (Thermal energy, 8.2 J). This visually demonstrates the low efficiency of a filament bulb.
Worked Example: Power Station EfficiencyScenario: A power station has Total Input 610 MJ. It produces 150 MJ useful electrical energy and 270 MJ useful thermal energy. 190 MJ is wasted.
AnswerTotal Useful Output = 150 + 270 = 420 MJ.
Efficiency = 420 / 610 = 0.69.
Percentage Efficiency = 69\%Interactive revision notes, videos and practice questions load below.