Maths › Mechanics › Forces and Newton's laws
Forces and Newton's laws
Draw the forces, add them up, divide by the mass: Newton's second law is three instructions long, and almost every mechanics mark hangs off the first one, the diagram.
Builds on Kinematics with constant acceleration.
IN THIS TOPIC
- Draw free body diagrams with weight, normal reaction, tension, thrust and friction correctly placed.
- Apply F = ma along a chosen direction, and the equilibrium condition when a = 0.
- Combine F = ma with suvat when a constant force produces constant acceleration.
WHAT YOU PROBABLY THINK
A moving object always has a force pushing it along in the direction of motion.
The diagram is the physics
Every force on the object, and only forces on the object: weight mg down, normal reaction R perpendicular to the surface, tension pulling along a string, thrust pushing along a rod, friction opposing sliding. Forces the object exerts on other things belong on their diagrams, not this one.
Newton's laws at work
The first law says no resultant force means no change of velocity; rest and steady speed are the same condition, equilibrium. The second law quantifies the rest: resultant force equals mass times acceleration, applied along a chosen direction with consistent signs. The third law says forces come in equal and opposite pairs acting on different objects, which is why a diagram only ever shows one of each pair.
WORKED EXAMPLE
Resultant first, then divide
A 5 kg crate is dragged by a horizontal rope with tension 30 N against a constant resistance of 10 N. Find the acceleration, and the speed after 4 s from rest.
Along the motion: F = 30 − 10 = 20 N, so a = 20/5 = 4 m s⁻².
Constant force means constant acceleration, so suvat applies: v = 0 + 4 × 4 = 16 m s⁻¹.
Vertically, nothing moves: R = mg = 49 N, and the vertical equation quietly confirms the crate stays on the floor.
THE EXAM BIT
- Draw the free body diagram first; examiners award it and everything downstream leans on it.
- Write F = ma along a declared direction and keep every sign consistent with it.
- Equilibrium means resultant zero in each direction: resolve twice and solve.
- F = ma then suvat is the standard two-step; say when the force, and so the acceleration, is constant.
CHECK YOURSELF
A 1200 kg car accelerates at 2.5 m s⁻² against a total resistance of 600 N. Find the driving force.
Show a hint
F in F = ma is the resultant.
Show the answer
Resultant needed: ma = 1200 × 2.5 = 3000 N.
Driving force = 3000 + 600 = 3600 N.
Diagram first: every force on the object, nothing it exerts on anything else.
Resolve, sum with signs, apply F = ma; equilibrium is the a = 0 special case.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Draw free body diagrams with weight, normal reaction, tension, thrust and friction correctly placed.
- Apply F = ma along a chosen direction, and the equilibrium condition when a = 0.
- Combine F = ma with suvat when a constant force produces constant acceleration.
No animated video for this topic yet; these notes stand alone.