Free body diagrams are one of the most important tools in engineering mechanics because they turn a real object into a clear force model. Instead of trying to solve a messy physical situation all at once, you isolate one body and show every external force acting on it. This makes it possible to apply Newton's laws, predict motion, or check whether a structure is in equilibrium.
A careful diagram often determines whether the rest of the solution will be correct.
Key Facts
- A free body diagram shows one isolated object and all external forces acting on it.
- For equilibrium in 2D, sum Fx = 0 and sum Fy = 0.
- For rotational equilibrium, sum M = 0 about any chosen point.
- Weight acts downward through the center of mass: W = mg.
- For a block on an incline, weight components are W_parallel = mg sin theta and W_perpendicular = mg cos theta.
- Static friction adjusts up to a maximum value: fs <= mu_s N, while kinetic friction is fk = mu_k N.
Vocabulary
- Free body diagram
- A drawing of an isolated object showing all external forces and moments acting on it.
- Normal force
- The contact force exerted by a surface perpendicular to the surface.
- Friction
- A contact force that acts parallel to a surface and opposes relative motion or impending motion.
- Reaction force
- A force supplied by a support or connection to prevent certain types of motion.
- Moment
- The turning effect of a force about a point, calculated as M = Fd_perpendicular.
Common Mistakes to Avoid
- Drawing forces that the object exerts on other objects, which is wrong because a free body diagram only includes forces acting on the isolated object.
- Forgetting support reactions, which is wrong because pins, rollers, cables, and surfaces often supply unknown forces needed for equilibrium.
- Splitting weight into components and also drawing the original weight in the force equations, which double counts the same force.
- Assuming friction always equals mu N, which is wrong because static friction can be any value up to its maximum depending on what equilibrium requires.
Practice Questions
- 1 A 12 kg block rests on a 30 degree rough incline. Draw its free body diagram and calculate the components of its weight parallel and perpendicular to the plane using g = 9.8 m/s^2.
- 2 A simply supported beam is 6.0 m long with a 900 N downward point load located 2.0 m from the left support. Find the vertical reaction forces at the left and right supports.
- 3 A box is at rest on a rough horizontal floor while a person pushes it to the right, but it does not move. Explain the direction of friction and why the friction force does not have to equal its maximum possible value.