Work, energy, power and deformation
5. Work, Energy and Power
5 min read 11 parts Lesson 16 of 17 Unit quiz
Lesson summary
5. Work, Energy and Power — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Calculate work done, kinetic and gravitational potential energy, efficiency and power, and apply conservation of energy to transfers between stores.Work done — the energy transferred when a fo…
- Component rule
- Dissipation
- Using work
- Conditions
- Derivation
- Kinetic energy
Section 1 of 11Work done
- Work done
- the energy transferred when a force moves an object through a displacement in the direction of the force: W = Fs.
- The unit is the joule: 1 J = 1 N m.
- If the force is along the motion the object gains energy; if opposite, it loses energy.
- Component rule
- only the component of the force parallel to the displacement does work.
Section 2 of 11Principle of conservation of energy
- Statement
- energy cannot be created or destroyed, only transferred from one store to another, so the total in a closed system is constant.
- Examples
- a falling object in a vacuum, and a horizontal mass on a spring (elastic potential to kinetic).
- (gravitational potential to kinetic)
- a falling object in a vacuum, and a horizontal mass on a spring (elastic potential to kinetic).
Section 3 of 11Energy stores
| Store | Description |
|---|---|
| Kinetic | Moving objects |
| Gravitational potential | Objects raised in a gravitational field |
| Elastic potential | Objects stretched or compressed |
| Electrostatic | Interacting charges |
| Magnetic | Interacting magnets |
| Chemical | Energy released in chemical reactions |
| Nuclear | Energy released in nuclear reactions |
| Thermal | All objects; greater for hotter objects |
Section 4 of 11Energy transfers and dissipation
- Transfers
- mechanical (a force acting), electrical, heating (hot to cold) and radiation (electromagnetic waves).
- (charge through a p.d.)
- mechanical (a force acting), electrical, heating (hot to cold) and radiation (electromagnetic waves).
- Dissipation
- energy not transferred to a useful store is wasted to the surroundings by heating, light or sound.
- What counts as wasted depends on the system:
- Television: the useful outputs are light and sound; heating the surrounding air is wasted.
- Heater: heating the room is useful; the light emitted is wasted.
Section 5 of 11Efficiency
- Efficiency
- the ratio of useful output energy to total input energy: efficiency = × 100%.
- (useful energy output ÷ total energy input)
- The same ratio works with power: efficiency = useful power output ÷ total power input.
- High efficiency means most of the input is useful; low efficiency means most is wasted.
- Give a ratio as a decimal or fraction; multiply by 100 for a percentage.
- the ratio of useful output energy to total input energy: efficiency = × 100%.
Section 6 of 11Efficiency in multi-step problems
- Identify the energy transfer, for example kinetic energy of water to gravitational potential energy of lifted water.
- Write the useful output as efficiency × input energy.
- Substitute the energy equations and solve.
Section 7 of 11Power
- Power
- the rate of energy transfer,
- or work done per unit time: P = E/t = W/t, measured in watts (1 W = 1 J s−1).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)
- or work done per unit time: P = E/t = W/t, measured in watts (1 W = 1 J s−1).
- An appliance rating such as 60 W or 1000 W shows how much energy it transfers electrically each second.
- the rate of energy transfer,
- Using work
- P = Fs/t.
Section 8 of 11Deriving P = Fv
- Power is the rate of doing work: P = W/t.
- Work done is W = Fs.
- At constant velocity, s = vt, so W = Fvt.
- Substituting: P = Fvt/t = Fv.
- Conditions
- the equation applies when a constant force acts in the direction of a constant velocity.
- When a drag force is involved, the driving force needed equals the drag force (at constant speed), not its negative.
Section 9 of 11Gravitational potential energy
- Meaning
- the energy stored in a mass because of its position in a gravitational field.
- Derivation
- lifting a mass m through a height Δh requires a force equal to its weight mg, so work = mgΔh.
- Equation
- ΔEp = mgΔh (J), for a change in height in a uniform field.What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
- It increases when the mass is raised and decreases when it falls.
- The GPE-height graph is a straight line through the origin (ground level taken as zero).
- It is valid only near the Earth's surface; for large distances in space the field is not uniform.
- ΔEp = mgΔh (J), for a change in height in a uniform field.
Section 10 of 11Kinetic energy
- Meaning
- the energy an object has because it is moving.
- Derivation
- work done accelerating a mass from rest.
- A mass starting from rest is accelerated by a resultant force F over a displacement s; work done W = Fs.
- Newton's second law gives F = ma, and v2 = 2as (with u = 0) gives a = v2/2s.
- So W = m(v2/2s)s = ½mv2.
- Equation
- Ek = ½mv2, in joules; kinetic energy depends on the square of the speed.
- A falling object gains kinetic energy by losing gravitational potential energy.
Section 11 of 11More from the specification
- Principle of Conservation of Energy
- Energy cannot be created or destroyed, only transformed from one form to another; total energy in an isolated system remains constant.
- Work Done Moving Up an Inclined Slope
- Pulling a barrel or load up an inclined slope requires work W = F · d, equal to the increase in gravitational potential energy plus thermal energy lost to friction.
- Energy Transformation in a Roller Coaster
- In a roller coaster, gravitational potential energy (mgh) is converted into kinetic energy (½ mv²) as it descends, with total mechanical energy reduced by work done against resistive forces.
- Power and Efficiency of Electrical Supply
- Electrical motors connected to the mains supply convert electrical energy into mechanical power (P = IV = W/t),
- where efficiency is useful power output divided by total power input.
- Principle of Conservation of Energy
- Energy cannot be created or destroyed, only transformed from one form to another; total energy in an isolated system remains constant.
- Work Done Moving Up an Inclined Slope
- Pulling a barrel or load up an inclined slope requires work W = F · d, equal to the increase in gravitational potential energy plus thermal energy lost to friction.
- Energy Transformation in a Roller Coaster
- In a roller coaster, gravitational potential energy (mgh) is converted into kinetic energy (½ mv²) as it descends, with total mechanical energy reduced by work done against resistive forces.
- Power and Efficiency of Electrical Supply
- Electrical motors connected to the mains supply convert electrical energy into mechanical power (P = IV = W/t),What the symbols mean: P = power (W) · I = current (A) · V = potential difference (V)
- where efficiency is useful power output divided by total power input.
- Electrical motors connected to the mains supply convert electrical energy into mechanical power (P = IV = W/t),
- Mains supply
- Domestic a.c. supply, rated 230 V rms at 50 Hz in the UK.
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