Newton’s Third Law & Free-Body Diagrams
- State Newton’s third law and identify true action–reaction pairs
- Draw a free-body diagram showing every force on one object
- Resolve weight into components on an inclined plane
Forces come in pairs
Newton’s third law: if object A pushes on object B, then B pushes back on A with a force equal in magnitude and opposite in direction. The key subtlety is that the two forces act on different objects, so they never cancel each other — they appear in two separate free-body diagrams. When you jump, you push the Earth down and the Earth pushes you up; only the force on you accelerates you.
Free-body diagrams isolate one object
A free-body diagram (FBD) is a sketch of a single object with every force that acts on it drawn as an arrow from the object. Typical forces: weight (mg, always straight down), the normal force (N, perpendicular to and pushing away from a surface), tension (T, along a rope), friction (f, along a surface), and any applied push or pull. The normal force is not automatically equal to weight — it equals whatever it must to keep the object from sinking through the surface.
The incline: tilt your axes
On an inclined plane it pays to rotate your coordinate axes so one points along the slope and the other perpendicular to it. Then the normal force lies entirely on the perpendicular axis and only the mg sinθ slice of gravity drives motion down the ramp. For a frictionless incline, the acceleration is simply a = g sinθ — the mass cancels, so every object slides down at the same rate.
A 10 kg block sits on a frictionless 30° incline (g = 10 m/s²). Find the force pulling it down the slope and its acceleration. (sin30° = 0.5)
- 1.Weight is mg = 10 × 10 = 100 N, straight down.
- 2.The component along the incline is mg sinθ = 100 × sin30° = 100 × 0.5 = 50 N.
- 3.This is the only force along the (frictionless) slope, so ΣF = 50 N = ma.
- 4.Acceleration: a = 50 ÷ 10 = 5 m/s² down the incline (equivalently a = g sinθ = 10 × 0.5).
A book resting on a table: the reaction to Earth’s gravity pulling the book down is the book pulling the Earth up, not the table pushing the book up. Action–reaction partners are the same type of force on two different objects — never two forces on the same object.
A book rests on a table. Earth’s gravity pulls the book downward. By Newton’s third law, what is the reaction force to this gravitational pull?
A 4 kg block is released on a frictionless incline angled at 30° (g = 10 m/s², sin30° = 0.5). What is its acceleration down the slope?
Draw the free-body diagram before writing a single equation. On free response, a correct FBD with properly labeled forces earns points even if your algebra later slips — and it prevents you from inventing forces that are not there.
Answer the 2 checkpoints as you read.
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