Work, Energy & Power
Section: Motion, Forces & Energy | Syllabus: Cambridge IGCSE Physics (0625)
Energy Stores
- energy is the capacity to do work, and it exists in different stores
- energy can be stored as:
- kinetic - in moving objects
- gravitational potential - due to an object's position in a gravitational field
- chemical - in fuels, food and batteries
- elastic (strain) - in stretched or squashed objects, e.g. springs and elastic bands
- nuclear - in the nucleus of atoms
- electrostatic - between electrically charged objects, e.g. a charged balloon attracting your hair
- internal (thermal) - in hot objects, due to the motion of their particles
Energy Transfers
- energy can be transferred from one store to another during an event or process
- energy can be transferred by:
- forces - called mechanical work done, e.g. lifting a box or pushing a trolley
- electrical currents - called electrical work done, e.g. a current flowing through a lamp or motor
- heating - e.g. a hot object warming its cooler surroundings
- electromagnetic waves - e.g. light or infrared radiation carrying energy from the Sun
- sound waves - e.g. a loudspeaker transferring energy to the surrounding air
- other waves
- you should be able to describe the store-to-store changes in a process, e.g. a ball falling: gravitational potential energy → kinetic energy
As a ball falls, its gravitational potential energy store transfers to its kinetic energy store
Conservation of Energy
- the Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one store to another
- total energy input = total energy output, even though some of the output is often transferred to a less useful store, such as heat or sound
- simple flow diagrams can be used to show how energy is transferred between stores during a process
Worked Example
- Muumbe swings a pendulum bob from rest at one side.
Describe the energy transfers as it swings.Energy transfers as a pendulum bob swings from one side to the other
- at the highest point on each side: maximum gravitational potential energy, zero kinetic energy
- at the lowest point of the swing: maximum kinetic energy, zero gravitational potential energy (relative to that point)
- as the bob swings, energy is continuously transferred between the gravitational potential and kinetic stores
- a small amount of energy is transferred to heat and sound because of air resistance and friction at the support, so the bob never swings quite as high as before
Kinetic Energy
Extended Only
- kinetic energy is the energy an object has because it is moving
- Formula:
- E_k = (1/2)mv^2
- Where:
- E_k = kinetic energy (J)
- m = mass (kg)
- v = speed (m/s)
- because kinetic energy depends on v^2, doubling an object's speed quadruples its kinetic energy
Kinetic energy increases with the square of speed
Worked Example: Kinetic Energy
- Museli's bicycle and rider have a combined mass of 60 kg and are moving at 5 m/s. Calculate the kinetic energy.
Museli's bicycle and rider, mass 60 kg, moving at 5 m/s
- E_k = (1/2)mv^2 = (1/2) × 60 × 5^2 = 750 J
Change in Gravitational Potential Energy
Extended Only
- gravitational potential energy is the energy an object has because of its position in a gravitational field
- when an object's height changes, its gravitational potential energy changes
- Formula:
- Δ E_p = mgΔ h
- Where:
- Δ E_p = change in gravitational potential energy (J)
- m = mass (kg)
- g = gravitational field strength (N/kg)
- Δ h = change in height (m)
- height must always be measured vertically from the reference level, not along a slope
Gravitational potential energy changes to kinetic energy as an object falls
Worked Example: Change in Gravitational Potential Energy
- Muchindu lifts a 4 kg box from the floor onto a shelf 3 m higher. (Take g = 10 N/kg.) Calculate the change in gravitational potential energy.
Muchindu lifts a 4 kg box onto a shelf 3 m above the floor
- Δ E_p = mgΔ h = 4 × 10 × 3 = 120 J
Sankey Diagrams
Extended Only
- in more complex processes, energy is transferred through several stages at once, with some usefully transferred and some wasted, usually as heat or sound
- a Sankey diagram can be used to show these transfers:
- the width of each arrow is proportional to the amount of energy it represents
- a single input arrow can split into several output arrows, showing energy being usefully transferred and energy being wasted
- because energy is conserved, the total width of the arrows leaving a stage always equals the total width entering it
A Sankey diagram for a car engine, showing useful and wasted energy transfers
Work Done
- mechanical work done = the energy transferred when a force moves an object through a distance
- electrical work done = the energy transferred by an electric current, e.g. in a lamp or motor
- both mechanical work done and electrical work done are equal to the energy transferred
- Formula:
- W = Fd = Δ E
- Where:
- W = work done (J)
- F = force (N)
- d = distance moved in the direction of the force (m)
- Δ E = energy transferred (J)
- if there is no movement in the direction of the force, no work is done, even if a force is applied
Work done = force × distance moved in the direction of the force
Worked Example: Work Done
- Muumbe pushes a crate with a force of 60 N, moving it 5 m across a warehouse floor. Calculate the work done.
Muumbe pushes a crate 5 m across the floor with a force of 60 N
- W = Fd = 60 × 5 = 300 J
Power
- power is defined as the work done per unit time, or equivalently, the energy transferred per unit time
- Formula:
- P = (W/t) = (Δ E/t)
- Where:
- P = power (W)
- W = work done (J)
- Δ E = energy transferred (J)
- t = time taken (s)
- 1 watt = 1 joule of energy transferred per second
Worked Example: Power
- Museli's electric motor does 900 J of work in 10 s. Calculate the power of the motor.
Museli's motor does 900 J of work in 10 s
- P = (W/t) = (900/10) = 90 W
Efficiency
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