Jupiter2U School
Chapter 08

Newton's Laws & Forces

High School
At a glance
Core ideaNet force equals mass times acceleration; every force comes in an equal-and-opposite pair.
Key termFree-body diagram — every real force acting on one isolated object.
You can…Solve pulley, lift and friction problems with ΣF = ma.
Watch outMass ≠ weight; action–reaction pairs act on different bodies, so they never cancel.
Theory

The three laws of motion

Newton's laws connect force — a push or pull, a vector measured in newtons — to changes in motion.

First law (inertia): a body remains at rest or in uniform straight-line motion unless acted on by a net external force. This defines an inertial frame.

Second law: the net force equals the rate of change of momentum; for constant mass,

ΣF = dp/dt = ma

Third law: for every force there is an equal and opposite reaction — if A pushes B with force F, then B pushes A with −F. Crucially these act on different bodies, so they never cancel on a single object.

Common forces

Weight W = mg acts down. The normal force N acts ⟂ to a surface. Tension pulls along a string. Friction opposes relative sliding: kinetic f = μkN; static up to a maximum fmax = μsN.

Explanation

Free-body diagrams — the master tool

Nearly every mechanics problem is solved by drawing a free-body diagram: isolate one object, draw every force acting on it as an arrow, then apply ΣF = ma along each axis. The art is including all real forces (weight, normal, tension, friction, applied) and no imaginary ones — "the force of motion" does not exist; a moving object needs no forward force to keep moving (first law).

Step 1IsolatePick one object and mentally cut it free of everything else.
Step 2Draw forcesAdd every real force on it: weight, normal, tension, friction, applied.
Step 3Choose axesPick x and y (often along/across the surface) and resolve.
Step 4Apply ΣF = maWrite Newton's second law separately for each axis.
Step 5Solve & checkSolve for the unknown, then sanity-check the sign and size.

Mass and weight are distinct: mass (kg) is the amount of matter and the measure of inertia; weight (N) is the gravitational force on that mass, and changes with g. On the Moon your mass is unchanged but your weight is one-sixth.

Mass

  • Amount of matter; the measure of inertia
  • Measured in kilograms (kg)
  • A scalar — no direction
  • Same everywhere: Earth, Moon or deep space

Weight

  • The gravitational force on a mass, W = mg
  • Measured in newtons (N)
  • A vector — points toward the planet
  • Changes with g: one-sixth on the Moon, zero in free fall
Third-law traps. The reaction to your weight (Earth pulling you) is you pulling Earth — not the normal force from the floor. Weight and normal force act on the same body and are only equal in magnitude when there's no vertical acceleration; they are not a third-law pair.
Normal force N Weight mg
Two forces act on the book: the normal force up and its weight down — equal and opposite, so it stays still.
Practical

Worked example — two blocks and a pulley (Atwood-style)

Block A (mA = 3.0 kg) sits on a frictionless table connected over a pulley to hanging block B (mB = 2.0 kg). Find the acceleration and the tension. g = 9.81 m·s⁻².

  1. Free-body A (horizontal): tension T pulls it. T = mAa.
  2. Free-body B (vertical, down positive): mBg − T = mBa.
  3. Add the equations to eliminate T: mBg = (mA + mB)a.
  4. Solve: a = mBg / (mA+mB) = (2.0×9.81)/5.0 = 3.92 m·s⁻².
  5. Tension: T = mAa = 3.0 × 3.92 = 11.8 N.

Sanity check: T = 11.8 N is less than B's weight (19.6 N), which must be true or B could not accelerate downward. ✓

Q&A
A 70 kg person stands in a lift accelerating upward at 2.0 m·s⁻². What does the scale read?

The scale reads the normal force. N − mg = ma ⟹ N = m(g+a) = 70(9.81+2.0) = 827 N — heavier than the 687 N at rest. This apparent weight increase is why you feel pressed down as a lift starts up.

Why does a book on a table not accelerate, given gravity pulls it down?

The net force is zero: the downward weight mg is exactly balanced by the upward normal force from the table. By the first law, zero net force means zero acceleration. The table molecules compress slightly and push back.

A box needs 40 N to start sliding but only 30 N to keep it moving on a level floor. What does this tell you?

Static friction (max 40 N) exceeds kinetic friction (30 N), so μs > μk. If the weight is, say, 100 N then μs = 0.40 and μk = 0.30. This is why objects "break free" and then move more easily.

How does a rocket accelerate in the vacuum of space with nothing to push against?

By the third law. The rocket expels exhaust gas backward at high speed; the gas pushes the rocket forward with an equal and opposite force. No external medium is needed — it is momentum conservation (Chapter 10) in action.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

InertiaF = m*aAction-reactionFree-body diagramFrictionTension & normalNewton's Laws & Forces
Infographic

The process, step by step

Step 1Isolate bodyChoose one object to analyse
Step 2Draw forcesShow weight, normal, tension, friction as arrows
Step 3Pick axesAlign axes with the motion or incline
Step 4Sum per axisApply F_net = m*a along each axis
Step 5Solve systemCombine equations for the unknowns
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1A 2.0 kg box is pushed with a net force of 6.0 N. Find its acceleration.

  1. Newton second law: F = m*a
  2. a = F/m = 6.0 / 2.0

Example 2An Atwood machine has masses 3.0 kg and 5.0 kg. Find the acceleration. (g = 9.8)

  1. a = (m2 - m1)*g / (m1 + m2)
  2. a = (5.0 - 3.0)*9.8 / (3.0 + 5.0)
  3. a = 19.6 / 8.0
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1State Newton's first law.
An object stays at rest or moves at constant velocity unless a net force acts on it.
2A 10 kg object accelerates at 2 m/s^2. What net force acts?
F = m*a = 10*2 = 20 N.
3What is the reaction to Earth pulling you down?
You pull the Earth up with an equal and opposite force.
4Find the weight of a 4.0 kg mass. (g = 9.8)
W = m*g = 4.0*9.8 = 39.2 N.
5What is the normal force on a 5.0 kg box on a level floor? (g=9.8)
N equals the weight = 5.0*9.8 = 49 N.
6Friction is 8 N and applied force is 8 N. What is the acceleration?
Net force is zero, so acceleration is zero (constant velocity or at rest).