Work Revision Notes

Work is defined as the energy transferred to or from an object when a force causes displacement of that object.

This energy transfer can be mechanical, such as lifting or pushing an object, or electrical, such as moving charges through a potential difference in a circuit.

Work done is equal to the amount of energy transferred and is measured in joules (J), the same unit as energy.

• Work is energy transfer by force causing displacement.
• Work done = energy transferred.
• Units of work and energy are joules (J).

When a force F is applied to an object causing it to move a distance d in the direction of the force, mechanical work is done on the object.

If the force is at an angle θ to the direction of displacement, only the component of the force in the direction of displacement does work.

The formula for mechanical work is: W = F × d × cos(θ).

• W = Fd cos(θ), where θ is angle between force and displacement.
• If force and displacement are in the same direction, cos(0°) = 1, so W = Fd.
• If force is perpendicular to displacement, cos(90°) = 0, so no work is done.

Electrical work involves energy transfer when charges move through an electrical circuit.

When a charge Q moves through a potential difference V, work done (energy transferred) is W = QV.

This work corresponds to electrical energy transferred to components such as resistors or lamps.

• W = QV for electrical work.
• Charge Q in coulombs (C), potential difference V in volts (V).
• Work done W in joules (J).

Work and energy are measured in joules (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.

The newton (N) is the unit of force, the metre (m) is the unit of displacement.

In electrical work, the coulomb (C) is the unit of charge and the volt (V) is the unit of potential difference.

• 1 J = 1 N × 1 m.
• Force in newtons (N), distance in metres (m).
• Charge in coulombs (C), potential difference in volts (V).

Work is only done when a force causes displacement of an object in the direction of the force.

If there is no displacement, no work is done, even if a force is applied.

If the displacement is perpendicular to the force, no work is done because the force does not move the object in its own direction.

• Work requires force and displacement in the same or component direction.
• No displacement means zero work.
• Perpendicular force and displacement means zero work.

Mechanical work is done when a force causes an object to move in the direction of the force. If there is no displacement, no work is done, even if a force is applied.

Work is a measure of energy transfer by mechanical means. When work is done on an object, energy is transferred to or from that object, changing its energy store.

• Work is done only when a force causes displacement.
• Work transfers energy between stores.
• No displacement means zero work done.

The mechanical work done (W) by a constant force (F) acting along the direction of displacement (d) is given by:

\[ W = F \times d \] where: F is the magnitude of the force in newtons (N), d is the displacement in metres (m), and W is the work done in joules (J).

This formula assumes the force and displacement are in the same straight line. If the force is at an angle θ to the displacement, the work done is \( W = Fd \cos \theta \).

• Work done (W) = Force (F) × Displacement (d)
• Units: N × m = joules (J)
• If force and displacement are not parallel, use \( W = Fd \cos \theta \)

The work done on an object results in a change in its energy, such as kinetic energy, potential energy, or internal energy.

This relationship is expressed as: \[ W = \Delta E \] where \( \Delta E \) is the change in energy of the object or system.

For example, lifting an object increases its gravitational potential energy; pushing a box increases its kinetic energy.

• Work done equals energy transferred: \( W = \Delta E \)
• Energy can be kinetic, potential, or other forms
• Work changes the energy stored in a system

The SI unit of work and energy is the joule (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.

Mathematically: \[ 1\,\text{J} = 1\,\text{N} \times 1\,\text{m} \]

Since work and energy share the same unit, they are directly comparable quantities.

• 1 joule = 1 newton × 1 metre
• Work and energy have the same units
• Use consistent SI units in calculations

A force of 10 N is applied to push a box along a horizontal surface for 3 m. Calculate the work done by the force.

Using the formula: \[ W = Fd \] Substitute the values: \[ W = 10\,\text{N} \times 3\,\text{m} = 30\,\text{J} \]

Therefore, the work done is 30 joules, meaning 30 joules of energy have been transferred to the box (e.g., increasing its kinetic energy).

• Formula: \( W = Fd \)
• Substitute: \( F = 10\,\text{N}, d = 3\,\text{m} \)
• Calculate: \( W = 30\,\text{J} \)
• Answer: 30 joules of work done