Newtonian models

Objective. Form equations of motion from free-body diagrams.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Newtonian models build equations of motion by drawing a free-body diagram showing every force on an object, then applying Newton's second law F = ma along chosen axes. Resolve forces into components, sum them in each direction, and set the total equal to mass times acceleration in that direction. For a block of mass m sliding down a frictionless slope at angle θ, resolving along the slope gives mg sinθ = ma, so a = g sinθ independent of mass. Including friction adds a term μmg cosθ opposing motion, which must be subtracted before dividing by m.

Worked example

A Newtonian model has a 4 kg block pushed by a horizontal force of 20 N on a frictionless surface. Find its acceleration.

1 $Apply Newton's second law: F = ma$
2 $Substitute known values: 20 = 4a$
3 $Solve for a: a = 20/4$
4 $Simplify: a = 5$

Answer: 5 m/s²

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Forgetting to resolve gravity into components along and perpendicular to an inclined surface, instead using mg directly as the force along the slope; only the component mg sinθ acts along the incline.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard