Understand that mechanical or electrical work done is equal to the energy transferred

1.7.2 Work

Learning Objective

Understand that mechanical or electrical work done is equal to the energy transferred.

Key Definitions

• Work (W): The transfer of energy that occurs when a force acts on an object and moves it through a distance.
• Mechanical Work: Work done by a force that moves an object.
• Electrical Work: Work done when an electric current moves charge through a potential difference.
• Energy Transfer: The process by which energy moves from one system to another, often expressed as work.

Fundamental Formulae

Mechanical work:

\$W = F \times s \times \cos\theta\$

where \$F\$ is the magnitude of the force (N), \$s\$ is the displacement (m), and \$\theta\$ is the angle between the force and displacement vectors.

Electrical work:

\$W = V \times Q\$

or, using current \$I\$ and time \$t\$:

\$W = V \times I \times t\$

where \$V\$ is the potential difference (V), \$Q\$ is the charge transferred (C), \$I\$ is the current (A), and \$t\$ is the time (s).

Relationship to Energy

Work done on a system results in an equivalent amount of energy transferred to or from that system:

\$\text{Work} = \text{Energy transferred}\$

Thus, the unit of work (joule, J) is also the unit of energy.

Units and Conversion

Worked Examples

1. Mechanical Work Example

   A student pushes a 15 kg crate across a floor with a constant horizontal force of 60 N over a distance of 5 m. Calculate the work done.

   Solution:

   \$W = F \times s \times \cos 0^\circ = 60\;\text{N} \times 5\;\text{m} \times 1 = 300\;\text{J}\$

   The work done on the crate is 300 J, which means 300 J of kinetic energy has been transferred to the crate (ignoring friction).

2. Electrical Work Example

   A 12 V lamp draws a current of 2 A for 3 minutes. Find the electrical work done by the battery.

   Solution:

   \$t = 3\;\text{min} = 180\;\text{s}\$

   \$W = V \times I \times t = 12\;\text{V} \times 2\;\text{A} \times 180\;\text{s} = 4320\;\text{J}\$

   The battery supplies 4320 J of energy to the lamp.

Common Misconceptions

• Work is done only when the force is in the direction of motion. If the force is perpendicular to the displacement, \$\cos\theta = 0\$ and no work is done.
• All energy transferred is called work; however, energy can also be transferred as heat, which is not counted as work in the mechanical sense.
• In electrical circuits, the product \$V \times I\$ gives power (watts). Work is power multiplied by time.

Link to Power

Power is the rate at which work is done or energy is transferred:

\$P = \frac{W}{t}\$

For mechanical systems \$P = F \times v\$ (when force and velocity are parallel). For electrical systems \$P = V \times I\$.

Practice Questions

1. Calculate the work done when a 10 N force pulls a sled 8 m up a slope that makes a 30° angle with the horizontal.
2. A battery supplies 9 V and powers a device drawing 0.5 A for 2 hours. How much energy is transferred in kilojoules?
3. Explain why a force applied perpendicular to the motion of an object does not transfer energy to the object.

Suggested Diagram