Section 2.1: Free-body Diagrams
This section introduces free-body diagrams (FBDs), which are essential for visualizing all forces acting on a single object. FBDs are the first step in applying Newton’s Laws to solve mechanics problems.
Key Points:
- Identify the object of interest (the system).
- Draw all forces acting on it: weight, normal, tension, friction, applied forces, etc.
- Indicate direction of each force using arrows.
- Label forces clearly with symbols (F_N, F_g, F_f, T, etc.).
- Do not include forces exerted by the object on others.
Example 1
A block of mass 10 kg rests on a horizontal table. Draw the free-body diagram and identify all forces.
Weight: F_g = mg = 10*9.8 = 98 N, downward.
Normal force: F_N = 98 N, upward from table.
No friction or applied force in this case.
FBD: a box with two arrows, one down (F_g), one up (F_N).
Example 2
A 5 kg block is pulled on a frictionless horizontal surface by a 20 N horizontal force. Draw the FBD.
Weight: F_g = 5*9.8 = 49 N downward
Normal: F_N = 49 N upward
Applied force: F = 20 N to the right
Friction: 0 (frictionless)
Practice Problems
- Block of 8 kg rests on inclined plane (30°). Draw FBD including weight components and normal force.
- A 10 kg box pulled by 15 N at 25° above horizontal on frictionless surface. Draw FBD.
- Crate hanging from a rope of tension T. Draw FBD and identify forces.
- Car on flat road, friction present. Draw FBD showing weight, normal, friction, and applied engine force.
- Ball on a spring scale in elevator accelerating upward at 2 m/s². Draw FBD and indicate apparent weight.