Twenty minutes or less.

Week 4 — Forces and Newton's Laws. Pick a mode. Start a timer. That's it.

Pick a mode

The shortest path to walking in prepared.

Timer

5:00

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5-minute version

Three workflows. One sentence each.

Identify forces — list every push and pull on the body; tag each as contact / long-range.
Draw the FBD — body as a dot, every force as a labelled arrow, pick your axes.
Apply Newton’s 2nd law per axis — $\sum F_{x} = m a_{x}$ , $\sum F_{y} = m a_{y}$ , solve.

Open the cheatsheet quiz, do 3 easy questions, close it. You’re prepped.

Time	Action
0–5 min	Skim the cheatsheet — the catalogue-of-forces table and the FBD recipe.
5–10 min	Do one worked example longhand: the boat (Example 2) — it has both axes and all the trickiest sign work.
10–15 min	Take the cheatsheet quiz. Don’t worry about the score.
15–20 min	Read the matching “common mistakes” + apparent-weight worked example in the in-depth note.

Most students slip on three specific things in this week:

Drawing forces the body exerts instead of forces on the body. The FBD shows what acts on the dot, nothing else.
Confusing 3rd-law pairs with balanced forces. Gravity (Earth on book) and normal (table on book) act on the same body — they balance because of $\sum F = 0$ , not because they’re a 3rd-law pair.
Static friction set to its max value unconditionally. It only equals $μ_{s} F_{N}$ at the verge of slipping. Otherwise it adjusts to cancel the push.

F_{n e t} = m a ⟹ \sum F_{x} = m a_{x}, \sum F_{y} = m a_{y}

F_{G} = m g F_{S} = k x F_{f r i c} = μ F_{N} (kinetic : μ_{k}; static : F_{f r i c} \leq μ_{s} F_{N})

F_{A on B} = \frac{G m _{A} m _{B}}{r ^{2}}, G = 6.67 \times 1 0^{- 11} N m^{2} / kg^{2}

F_{A on B} = - F_{B on A} (Newton’s 3rd law)

Task type	What the setup usually looks like
Find a force	You’re given mass and acceleration. Apply $F = ma$ . (Example: train, Exercise 1 racing car.)
Find an acceleration	You’re given forces and mass. Apply $a = F / m$ . (Example: friction-overcome problems.)
Two-axis equilibrium + dynamics	One axis balances (gives you $F_{N}$ or $F_{B}$ ), the other has the acceleration. (Example: the boat.)
Spring equilibrium	Use $k x = m g$ for “mass on a spring at rest.” (Example: Exercise 4 fish scale.)
Apparent weight in elevator	Same as the boat — $\sum F_{y} = m a_{y}$ with $F_{N}$ as the unknown. (Example: Exercise 2.)
Static vs kinetic friction	Check whether the applied force exceeds $μ_{s} F_{N}$ before assuming sliding. (Example: Exercise 5.)

Forces drawn as scalars rather than vectors.
Forces drawn that the body exerts rather than that act on it.
Missing weight or normal on the FBD.
Confusing balanced pairs with 3rd-law pairs.
Using $μ_{k}$ when the block hasn’t broken loose yet.
Forgetting the unit conversion ( $cm \to m$ ) before $F_{S} = k x$ .
Skipping the Assess step — is the sign right, are the units right, is the magnitude believable?

Try these without notes. Five minutes total.

A $910 kg$ racing car starts from rest and travels $350 m$ in $4.85 s$ at constant acceleration. Find the net force on it.
A $6.7 kg$ fish hangs from a spring scale with $k = 340 N/m$ . How far does the spring stretch?
A $10 kg$ block on a horizontal surface has $μ_{s} = 0.4$ and $μ_{k} = 0.2$ . A $100 N$ horizontal force is applied. Find the block’s acceleration.

Answers:

Question	Working	Answer
1	$s = \frac{1}{2} a t^{2} \Rightarrow a = 2 s / t^{2} = 2 (350) /4.8 5^{2} \approx 29.76 m/s^{2}$ ; $F = ma = (910) (29.76)$	$F \approx 2.71 \times 1 0^{4} N$
2	Equilibrium: $k x = m g \Rightarrow x = (6.7) (9.8) /340$	$x \approx 0.193 m$
3	Max static $= 0.4 (10) (9.8) = 39.2 N < 100$ , so it slides. Kinetic $= 0.2 (10) (9.8) = 19.6 N$ . $a = (100 - 19.6) /10$	$a = 8.04 m/s^{2}$

Read the catalogue-of-forces table on the cheatsheet.
One worked example from the lecture summary (suggested: the boat) copied out longhand.
Cheatsheet quiz attempted.
Mini self-test attempted.
Glanced at “Common mistakes” once more.

That’s it. Close the laptop.