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Chapter 04 · Part I · Mechanics
Revised on ____________________

Chapter 04 · Newton's Laws of Motion

Draw the body, name every force, then write ΣF = ma

sheets
diagrams
results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

The three laws, and the diagram

NO FBD, NO MARKS

I.First law ΣF = 0 ⇒ v constant defines an inertial frame

II.Second law ΣF = m a = dpdt one equation per axis

III.Third law F_AB = − F_BA different bodies — they never cancel

IV.Weight W = m g always toward the centre of the Earth

V.Normal force N ⊥ to the surface, N ≥ 0 contact is lost when N = 0

VI.Tension same throughout a light, ideal string a massive string does not qualify

Only three kinds of force appear in mechanics: field forces (mg), contact forces (N, f, T) and, in an accelerating frame, the pseudo-force. If a fourth appears in your diagram, it is a mistake.

Systems, pulleys and constraints

THE STRING FIXES THE ACCELERATIONS

I.Blocks in contact a = Fm₁ + m₂ contact force N = m₂a

II.Atwood machine a = (m₁ − m₂) gm₁ + m₂

III.Its tension T = 2 m₁ m₂ gm₁ + m₂ T < both weights

IV.String constraint Σ (length along each segment) = constant differentiate twice for a

V.Movable pulley a_pulley = a₁ + a₂2

VI.Wedge constraint the block stays on the wedge face relative a along the face

III

Friction

STATIC IS A RANGE, KINETIC IS A VALUE

I.Static f_s ≤ μ_s N it takes whatever value equilibrium needs

II.Kinetic f_k = μ_k N opposes relative sliding

III.Down an incline a = g(sin θ − μ_k cos θ)

IV.Stopping distance d = v²2 μ_k g

V.Minimum pull at angle α F = μ m gcos α + μ sin α least at tan α = μ

VI.Block on block check the friction limit at each surface

Accelerating frames

ADD −ma, THEN WORK AS IF AT REST

I.Pseudo-force F_ps = − m a_frame no reaction pair; it is not a real force

II.Lift going up with a N = m(g + a) apparent weight

III.Effective gravity g_eff = g − a_frame

IV.Pendulum in a car tan θ = ag hangs along g_eff

Springs and equilibrium

THE LAST FEW RESULTS

I.Hooke's law F = − k x x from the natural length

II.In series 1k_eq = 1k₁ + 1k₂

III.In parallel k_eq = k₁ + k₂

Where marks are lost in this chapter

1“Friction opposes motion.” It opposes relative sliding — walking and pedalling are driven by it.

2Writing f_s = μ_sN always. That is the limit: push a stuck block with 10 N and friction is 10 N.

3Taking N = mg. True only on the level with no other vertical force — on an incline N = mg cos θ.

4Confusing apparent with true weight. The scale reads N; in a lift accelerating up that is m(g + a).