Force Diagrams (AQA A-Level Mathematics): Revision Notes

• A force diagram is a simplified representation of an object (or system) with all the forces acting on it illustrated as vectors.
• The object is usually represented by a simple shape, like a dot or a box, and the forces are shown as arrows pointing in the direction in which the forces act.

1. Identify the object: Determine which object you are analysing and isolate it from the surroundings.
2. Draw the object: Represent the object by a simple shape, often a point (for simplicity) or a box if more context is needed.
3. Identify all the forces acting on the object: Consider forces such as gravity, normal force, tension, friction, applied forces, and air resistance.
4. Draw the forces as arrows:

• The length of each arrow represents the magnitude of the force.
• The direction of the arrow shows the direction in which the force acts.
• Label each force clearly (e.g., $F_{\text{gravity}}$ , $F_{\text{normal}}$ , $F_{\text{friction}}$ , etc.).

5. Check for equilibrium or net force:

• If the object is in equilibrium (stationary or moving at constant velocity), the forces should balance, meaning the arrows should add up to zero.
• If the object is accelerating, there will be a net force in the direction of acceleration.

Problem: A box of mass $5$ $kg$ is on a flat surface. A force of $20$ $N$ is applied horizontally to the right. The coefficient of friction between the box and the surface is $0.3$. Draw the force diagram.

Step 1: Identify forces acting on the box.

• Weight $( F_{\text{gravity}} )$: Downward, $F_{\text{gravity}} = mg = 5 \times 9.81 = :highlight[49.05 \, \text{N}]$ .
• Normal Force $( F_{\text{normal}} )$: Upward, balancing the weight, so $F_{\text{normal}} = :highlight[49.05 \, \text{N}]$ .
• Applied Force $( F_{\text{applied}} )$: $20$ $N$ to the right.
• Frictional Force $( F_{\text{friction}} )$: Opposes motion, calculated using $F_{\text{friction}} = \mu F_{\text{normal}} = 0.3 \times 49.05 = :highlight[14.715 \, \text{N}]$ to the left.

Step 2: Draw the diagram.

• Draw a box or point to represent the object.
• Draw arrows representing each force:
• Weight pointing downwards.
• Normal force pointing upwards.
• Applied force pointing to the right.
• Frictional force pointing to the left.

Final Diagram: The box will have:

• A downward arrow labelled $49.05 \, \text{N}$ for gravity.
• An upward arrow labelled $49.05 \, \text{N}$ for the normal force.
• A rightward arrow labelled $20 \, \text{N}$ for the applied force.
• A leftward arrow labelled $14.715 \, \text{N}$ for friction.

Question : Find the magnitude and direction of the resultant of the given forces.