Free-Body Diagrams
Teaches the systematic method of isolating an object and representing all external forces acting on it to analyze its motion.
What is Free-Body Diagrams?
A sketch isolating one body with every external force on it drawn as a vector: weight, normal reaction, tension, friction and applied force
Key formula / rule: Incline components
Key points
- Isolate a body, draw every external force on it and write Newton's second law along chosen axes
Common exam trap
Taking N = mg on an inclined surface
Definitions
- Name
Free-body diagram
- Definition
A sketch isolating one body with every external force on it drawn as a vector: weight, normal reaction, tension, friction and applied force
- Name
Key idea
- Definition
Only forces acting ON the body are drawn; choose axes along and perpendicular to the motion before resolving
- Name
Exam insight
- Definition
On an incline of angle θ the weight resolves into mg sin(θ) along it and mg cos(θ) across it, so N = mg cos(θ), not mg
- Name
Worked example
- Definition
2 kg block on a smooth 30 ° incline: a = g sin30 = 4.9 m/s2, N = 2 x 9.8 x cos30 ~ 17 N
Learning objectives
Isolate a body, draw every external force on it and write Newton's second law along chosen axes
Formulae
- Name
Incline components
- Expression
Along: m g sin(θ); Normal: N = m g cos(θ)
- Name
Equilibrium
- Expression
Sum Fx = 0 and Sum Fy = 0
Common mistakes
Taking N = mg on an inclined surface
Drawing 'ma' as if it were a force acting on the body
Keywords
free-body diagram
FBD
normal reaction
tension
friction
incline
newton
laws of motion
force