Unit 3.8 – Free Body Diagram

What is a Free Body Diagram (FBD)?

• Key Idea: An FBD focuses solely on the forces acting on a single body, ignoring internal forces or interactions with other objects.

Steps to Draw a Free Body Diagram

1. Identify the Object:
   • Clearly define the object or system you are analyzing.
2. Isolate the Object:
   • Remove all other objects and focus only on the forces acting on the chosen object.
3. Draw the Forces:
   • Represent all external forces acting on the object using arrows.
   • Include:
     • Weight ($𝑊=𝑚\cdot 𝑔$): Acts vertically downward due to gravity.
     • Normal Force ($𝑁$): Acts perpendicular to the surface in contact.
     • Frictional Force ($𝑓$): Acts parallel to the surface, opposing motion.
     • Applied Force (${𝐹}_{\text{applied}}$): Any external force applied to the object.
     • Tension ($𝑇$): Force transmitted through strings, ropes, or cables.
4. Choose a Coordinate System:
   • Assign directions for the $𝑥$-axis (horizontal) and $𝑦$-axis (vertical).
   • Resolve forces into components if necessary.
5. Label the Forces:
   • Clearly label each force with its magnitude and direction.

Examples of Free Body Diagrams

Example 1: A Box Resting on a Horizontal Surface

• Forces Acting:
  1. Weight ($𝑊=𝑚\cdot 𝑔$): Acts downward.
  2. Normal Force ($𝑁$): Acts upward, balancing the weight.
• FBD:

  1
  2
  ↑ N
  ↓ W
  

Example 2: A Block Being Pushed on a Rough Surface

• Forces Acting:
  1. Weight ($𝑊=𝑚\cdot 𝑔$): Acts downward.
  2. Normal Force ($𝑁$): Acts upward.
  3. Applied Force (${𝐹}_{\text{applied}}$): Acts horizontally to push the block.
  4. Frictional Force ($𝑓$): Acts horizontally, opposing the motion.
• FBD:

  1
  2
  3
  ↑ N
  ↓ W
  ← f       F_applied →
  

Example 3: A Hanging Object

• Forces Acting:
  1. Weight ($𝑊=𝑚\cdot 𝑔$): Acts downward.
  2. Tension ($𝑇$): Acts upward along the string.
• FBD:

  1
  2
  ↑ T
  ↓ W
  

Example 4: An Object Sliding Down an Inclined Plane

• Forces Acting:
  1. Weight ($𝑊=𝑚\cdot 𝑔$): Acts vertically downward.
     • Resolve into components:
       • ${𝑊}_{\parallel }=𝑚\cdot 𝑔\cdot \sin 𝜃$: Parallel to the incline.
       • ${𝑊}_{\perp }=𝑚\cdot 𝑔\cdot \cos 𝜃$: Perpendicular to the incline.
  2. Normal Force ($𝑁$): Acts perpendicular to the incline.
  3. Frictional Force ($𝑓$): Acts up the incline, opposing motion.
• FBD:

  1
  2
  3
  4
        N ↑
         ↖ W_⊥
  ← f      ↙ W_∥
         ↓ W
  

Applications of Free Body Diagrams

1. Equilibrium Problems:
   • If an object is at rest or moving at constant velocity, the net force is zero ($\mathrm{\Sigma }𝐹=0$).
   • Example: A book resting on a table.
2. Acceleration Problems:
   • Use Newton’s Second Law ($𝐹=𝑚\cdot 𝑎$) to find the net force and acceleration.
   • Example: A car accelerating on a road.
3. Inclined Planes:
   • Analyze forces on objects sliding up or down inclined surfaces.
4. Pulleys and Tension:
   • Study systems involving ropes, strings, and pulleys.

Examples to Understand Free Body Diagrams

Example 1:

• Solution:
  • Forces acting:
    1. Weight ($𝑊=𝑚\cdot 𝑔=5\cdot 9.8=49\text{N}$), acting downward.
    2. Normal Force ($𝑁$), acting upward.
  • Since the box is at rest, $𝑁=𝑊$.
  • FBD:

    1
    2
    ↑ N
    ↓ W
    

  • Normal Force: $𝑁=49\text{N}$.

Example 2:

• Solution:
  • Forces acting:
    1. Weight ($𝑊=𝑚\cdot 𝑔=10\cdot 9.8=98\text{N}$), acting downward.
    2. Normal Force ($𝑁=𝑊=98\text{N}$), acting upward.
    3. Applied Force (${𝐹}_{\text{applied}}=30\text{N}$), acting horizontally.
    4. Frictional Force ($𝑓={𝜇}_{𝑘}\cdot 𝑁=0.2\cdot 98=19.6\text{N}$), acting opposite to motion.
  • Net Force:
    $${𝐹}_{\text{net}}={𝐹}_{\text{applied}}-𝑓=30-19.6=10.4\text{N}\mathrm{.}$$
  • FBD:

    1
    2
    3
    ↑ N
    ↓ W
    ← f       F_applied →