Work, energy and the conservation of energyEdexcel A-Level Physics: Revision notes
Section 1
Work done by a force
Work is done when a force moves its point of application in the direction of the force. For a force F that moves an object through a distance s in the direction of the force:
W = Fs
The unit is the joule (J). One joule is the work done when a force of 1 N moves an object through 1 m in the direction of the force. Work done is a transfer of energy, so the energy transferred equals the work done.
Section 2
Force not along the line of motion
If the force acts at an angle θ to the direction of motion, only the component along the motion does work:
W = Fs cos θ
A force at right angles to the motion does no work, for example the normal contact force on an object sliding on a level surface.
Worked example. A suitcase is pulled 20 m by a force of 60 N at 30° above the horizontal. W = 60 × 20 × cos 30° = 1040 J. At constant speed the friction force equals the horizontal component, 60 cos 30° = 52 N.
Using sin θ when θ is measured from the direction of motion. Check that θ is the angle between the force and the displacement.
Section 3
Kinetic energy
Kinetic energy is the energy an object has because it is moving:
Ek = ½mv²
It follows from W = Fs and v² = u² + 2as. For an object accelerated from rest by a resultant force F, Fs = mas = ½mv². The work done by the resultant force equals the change in kinetic energy. Because v is squared, doubling the speed quadruples the kinetic energy.
Forgetting to square the speed, or squaring the whole expression ½mv.
Section 4
Gravitational potential energy
Near the Earth's surface, where the gravitational field strength g is constant, the change in gravitational potential energy when an object of mass m is lifted through a height Δh is:
ΔEgrav = mgΔh
This equals the work done against gravity. Take g = 9.81 N kg⁻¹. Only the vertical change in height matters, not the path taken.
Section 5
Conservation of energy
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. For an object moving without resistive forces, the loss of gravitational potential energy equals the gain in kinetic energy: mgh = ½mv², so v = √(2gh), which is independent of mass.
When resistive forces act, work is done against them and energy is transferred as thermal energy to the surroundings: gravitational potential energy lost = kinetic energy gained + energy dissipated.
Worked example. A 70 kg skier descends 45 m and reaches 22 m s⁻¹. Loss of potential energy = 70 × 9.81 × 45 = 3.09 × 10⁴ J. Kinetic energy = ½ × 70 × 22² = 1.69 × 10⁴ J. Energy dissipated = 1.4 × 10⁴ J.
Write the energy equation in words first: gravitational potential energy lost = kinetic energy gained + work done against resistive forces. Then substitute.
Must know
- W = Fs, and W = Fs cos θ when the force is at angle θ to the motion
- Ek = ½mv² and ΔEgrav = mgΔh
- Energy is conserved: mgh = ½mv² without resistive forces, so v = √(2gh)
- With resistive forces, energy lost = work done against them = Fs
- A force at right angles to the motion does no work
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Work, energy and the conservation of energy
- A traveller pulls a suitcase 20 m along a level airport floor using a handle. The handle is held at 30° above the horizontal and the pulling force is a constant 60 N. The suitcase moves at a constant speed.Calculate the frictional force acting on the suitcase.2 marks
- A child releases a toy car of mass 0.30 kg from rest at the top of a straight ramp. The top of the ramp is 0.80 m above the floor. Take g = 9.81 N kg⁻¹.In practice the car reaches the bottom of the ramp at 3.2 m s⁻¹. Calculate the energy transferred to the surroundings as thermal energy.2 marks
- A skier of mass 70 kg starts from rest at the top of a straight slope and skis down to the bottom. The bottom of the slope is 45 m lower than the top and the slope is 280 m long. At the bottom the skier's speed is 22 m s⁻¹. Take g = 9.81 N kg⁻¹.Calculate the gravitational potential energy lost by the skier, the kinetic energy gained, and the energy dissipated as thermal energy.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).