Edexcel A Level (IAL) Physics-1.8 Free-body Force Diagrams- Study Notes- New Syllabus

Free-Body Force Diagrams

A free-body force diagram (FBD) is a simplified drawing showing all the forces acting on a single object, isolated from its surroundings. The diagram helps analyse motion, equilibrium, and forces on both particles and extended rigid bodies.

What Is a Free-Body Diagram?   

• A diagram showing an object separated from everything else.
• Only the forces acting on the object are shown.
• Each force is represented by an arrow starting from the object.
• The arrow’s direction shows the direction of the force.
• The length of the arrow represents the magnitude (if drawn to scale).

The purpose: To identify all forces clearly so they can be used in equations such as \( \mathrm{\sum F = ma} \).

Rules for Drawing Free-Body Diagrams

• Draw the object as a point (particle) or simple shape (rigid body).
• Represent each force with an arrow.
• Label each arrow with the type of force.
• Do NOT include forces the object exerts on other objects → only forces acting *on* it.
• Use the centre of gravity when drawing gravity on extended bodies.

 Common Forces in FBDs

• Weight \( \mathrm{W} \) → acts vertically downward through centre of gravity \( \mathrm{W = mg} \)
• Normal reaction \( \mathrm{N} \) → perpendicular to the surface
• Tension \( \mathrm{T} \) → along a rope/string
• Friction \( \mathrm{f} \) → opposite the direction of motion or impending motion
• Applied forces → pushes or pulls
• Air resistance/drag \( \mathrm{D} \) → opposite motion
• Upthrust → acts upward in fluids

Free-Body Diagrams for Particles

A particle is treated as a point mass.

Steps:

• Draw a dot for the object.
• Add arrows outward from the dot for each force.
• Label each force (e.g., \( \mathrm{W} \), \( \mathrm{N} \), \( \mathrm{T} \), \( \mathrm{f} \)).
• Use these to write equations of motion.

 Free-Body Diagrams for Rigid Bodies

A rigid body has size and shape, so forces may act at different points.

Key additional ideas:

• Weight acts at the centre of gravity (CoG).
• Multiple forces can act at different points.
• Turning effects (moments) must be considered.
• An extended body may rotate if there is a resultant moment.

Example: A ladder leaning against a wall

• Normal reaction at wall acts horizontally.
• Normal reaction at ground acts vertically.
• Friction may act at either wall or ground depending on motion tendency.

 Centre of Gravity (CoG) in FBDs

Centre of gravity: the point where the entire weight of the body can be considered to act.

• For a uniform rod → centre is at the midpoint.
• For irregular bodies → depends on shape.
• Weight arrow must always originate at the CoG when drawing FBDs for extended bodies.
• If CoG is not directly over the base, the body may topple.

Using FBDs in Calculations

• Resolve forces horizontally and vertically.
• Use \( \mathrm{\sum F_x = m a_x} \) and \( \mathrm{\sum F_y = m a_y} \).
• For rigid bodies, also consider moments: \( \mathrm{\sum M = 0} \) in equilibrium.
• If forces balance → object in equilibrium.
• If resultant force ≠ 0 → object accelerates.

Typical Situations

• Block on an incline (weight splits into components).
• Object on rough surface (friction present).
• Suspended object in equilibrium (tensions in strings).
• Ladder against wall (multiple reaction forces + friction).
• Beam supported at two points.