Free-body diagrams, resultant force and equilibrium
Draw every force on one object, find the resultant in one and two dimensions, and decide when the forces balance.
A book rests on a table and nothing moves, yet two forces act on it. How do you draw them, and how do you know they balance exactly?
Which arrow must NOT appear in a free-body diagram of a ball moving upwards through the air?
A 5.0 N force acts east and a 12 N force acts north on a body. The size of the resultant is…
A crate moves along a floor at a constant velocity of 2.0 m s⁻¹ while pulled forward by a 40 N rope. The friction on it is…
A 3.0 kg block rests on a rough slope inclined at 30°. The friction needed to hold it is (g = 9.81 m s⁻²)…
A lamp hangs at rest from two equal strings, each making 30° with the horizontal. Compared with the lamp’s weight W, each tension is…
A skydiver falls at terminal velocity. Draw (in words) the free-body diagram and use it to explain why the speed is constant.
If the resultant force is zero, the velocity is…
The weight and the normal force on a book at rest are…
Key points
- • A free-body diagram shows one object and only the forces acting on it.
- • Resultant: add with signs in 1D; in 2D add components, then Pythagoras.
- • Translational equilibrium means ΣF = 0, so a = 0.
- • On a slope: N = mg cos θ, friction needed = mg sin θ (until F_f reaches μN).
Formulas
- Fx = F cos θ, Fy = F sin θ
- Fnet = √(ΣFx² + ΣFy²)
Key terms
- Resultant force :
- the single force that has the same effect as all the forces together
- Equilibrium :
- resultant force zero: at rest or constant velocity
Common errors
- • Drawing a force that has no cause
- • Adding perpendicular forces by plain addition
- • Forgetting that equilibrium includes constant velocity, not just rest