Week 4 Study Guide — Forces and Newton's Laws

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Directly supported by notes

The lecture and tutorial PDFs explicitly cover:

Topic	Direct source coverage
Definitions of common forces	Slides 11–17: gravity, spring, normal, tension, friction (static & kinetic), thrust, drag
Universal gravitation	Slide 13 + handwritten Cases 1 & 2 (two $1 kg$ masses; $1 kg$ at Earth’s surface)
Free body diagrams	Slides 19–22: construction recipe + common errors + worked FBDs (safe / furniture / pulley)
Newton’s three laws	Slide 24, with the 2nd law unpacked in component form on slide 25
Newton’s 2nd law in practice	Slides 27–30: train, motorboat, spring worked examples
Tutorial exercises	Tutorial 4 Exercises 1–6

The lecture / workshop expects you to be able to:

Identify every force acting on an isolated body (contact vs long-range).
Draw a clean FBD with axes and labelled vectors.
Write Newton’s 2nd law per axis: $\sum F_{x} = m a_{x}$ , $\sum F_{y} = m a_{y}$ .
Solve for the one unknown — either a force or an acceleration.
Recognise equilibrium ( $\sum F = 0$ ) as the special case.
Apply the four-step Model → Visualise → Solve → Assess approach (slide 9).

The lecture almost certainly covers, in this order:

The “productive failure” framing on slides 3–8 (try, fail, learn the technique).
The four-step problem-solving framework: Model · Visualise · Solve · Assess.
Two worked FBDs (safe + furniture + pulley) showing how to choose the body of interest.
The standard “Common Errors” slide on FBDs (slide 20) — most of those are echoed in the lecture notes and the cheatsheet’s mistakes list.

May appear in the lecture but is not in the workshop PDFs:

Mention of Newton’s law of universal gravitation as a special case of inverse-square forces (foreshadowing electromagnetism).
Numerical estimate of how small mutual gravitation between everyday objects is, framed as “why we can ignore it most of the time.”
Brief mention of apparent weight (anticipating elevator-style problems in the tutorial).

Whether Portfolio 3 specifically requires multi-body systems (e.g. coupled blocks on a pulley) or only single-body FBDs.
Whether the spring sign convention will be tested as a graded question on the exam, or only assumed in the workshop setting.
Whether inclined-plane problems (Tutorial Exercise 6) are in scope for this week’s portfolio, or held back for Week 5’s friction-on-inclines.

Two notes cover the topic at different depths:

Cheatsheet — every force, formula, and recipe in one page. Includes the full quiz (mixed difficulty, reshuffles every visit).
In-depth analysis — why each law works, intuition for $F_{n e t} = m a$ , fully worked FBD-to-answer example per scenario, and an exam-style template ending with a $603.2 N$ elevator-scale problem.

Treating $F$ as a scalar. Forces are vectors — write $F$ and decompose.
Drawing forces the body exerts instead of forces on the body.
Missing weight or normal on the FBD, especially when the problem doesn’t name them.
Confusing balanced forces with 3rd-law pairs. Gravity and normal on the same book are balanced, not paired.
Kinetic friction direction. Opposes the velocity, not the applied force.
Static friction set to $μ_{s} F_{N}$ always. It only equals that at the verge of slipping; otherwise $F_{f r i c} \leq μ_{s} F_{N}$ .
Ignoring drag/air resistance is the right move unless the question says otherwise.
Unit slips. $cm \to m$ before $F_{S} = k x$ . Check $N = kg \cdot m/s^{2}$ at the end.

Pick any from Tutorial 4. Recommended for a first pass:

Newton’s 2nd law warm-up: Exercise 1 (racing car — combine kinematics + 2nd law).
Apparent weight / 3rd law: Exercises 2 and 3 (elevator scenarios).
Spring equilibrium: Exercise 4 (fish on spring scale, $k x = m g$ ).
Static vs kinetic friction: Exercise 5 (two applied forces, check the threshold).
Stretch / next-week teaser: Exercise 6 (skier on a $2 5^{\circ}$ incline at constant velocity).

Also: Mastering Physics “Forces” set, Wolfson Chapter 3 (additional reading), and Portfolio 3 in Workshop.

Portfolio 3 is essentially “do this for a body of your choice.” Expect to be graded on FBD clarity, axis choice, and the $\sum F = ma$ line.
Exam questions on this material come in two shapes: (i) given forces, find $a$ ; (ii) given $a$ , find a force. Both reduce to $F_{n e t} = m a$ with a tidy FBD.
Spring, friction, and apparent-weight problems are common — they’re just $F_{n e t} = m a$ in disguise.

Directly supported: every formula, definition, and worked example listed above is from the lecture or tutorial PDF.
Inferred: the order in which the lecture presents the laws (catalogue of forces → FBD → laws → application) is reconstructed from slide numbers but not verified.
Gap: which specific exercises Portfolio 3 will require remains a check-with-instructor item.