Week 6 Study Guide — Work, Energy, Conservation of Energy

Directly supported by notes

These topics are explicitly named in the lecture slides, handwritten notes, and tutorial:

Topic	Direct source coverage
System and energy definitions	Lecture slides 9–10
Work (constant, angled, variable)	Slides 11–14; Examples 1 and 2 in handwritten notes
Power	Slide 15
Kinetic, gravitational, elastic PE	Slide 19; tutorial Exercises 1, 2, 4, 5
Conservative vs non-conservative forces	Slide 21
Conservation of mechanical energy	Slide 22; Example 3 (skateboarder)
Work–energy balance with friction	Slide 23; Example 4 (Alice ramp); tutorial Exercises 3 and 5
Laboratory 1: spring constant, ${\mu }_k$, ramp displacement	Slides 26–28

The lecture directly states the master equation:

$K{E}_i+P{E}_i+W_{\text{on-system}}=K{E}_f+P{E}_f+W_{\text{by-system}}$

and all five tutorial exercises reduce to applying it (with one or more terms set to zero).

Strongly inferred from workshop materials

The lecture almost certainly emphasises, even where the slide text is terse:

• Why $W=0$ when force is perpendicular to motion (the “test force” twist in Example 1).
• The graphical interpretation of work as the area under the $F$ vs $s$ curve, including the km $\to$ m unit trap.
• Three equivalent paths for spring work (Tutorial 6 solutions explicitly do all three for Exercise 2).
• The need to decompose gravity into slope-parallel and slope-perpendicular components on an inclined plane ($mg\sin \theta$ along motion, $mg\cos \theta$ for the normal force).
• That kinetic friction always removes energy from the mechanical system regardless of motion direction.

Possible lecture content (not in notes)

These ideas often accompany Week 6 in an introductory physics course but are not explicitly visible in the provided PDFs:

• Energy conservation as a global law (link forward to thermodynamics).
• Work as a dot product $W=\vec{F}\cdot \vec{s}$ and the general line integral $\int \vec{F}\cdot d\vec{r}$.
• Discussion of “useful” vs “wasted” energy in real machines (efficiency).
• A formal proof that gravity’s work is path-independent (and hence has a PE function).

Gaps requiring official source check

• Confirm in the slides whether the energy diagram drawn for Example 3 uses "$W_{\text{hill}}$" as the symbol for the gravity-work term or as a separate boundary work term — the framing affects whether you write $W_{\text{on-system}}=mgh$ or fold the change into $P{E}_g$.
• Verify the lab worksheet’s exact data-recording requirements (number of trials, error analysis) — only summary slides are visible.

Worked examples

Two notes cover the topic at different depths:

• Cheatsheet — every rule, table, and recipe in one page. Includes the full quiz (mixed difficulty, reshuffles every visit).
• In-depth analysis — Newton II → work–energy theorem derivation, the cart, the variable-force graph, the spring (three equivalent calculations), the skateboarder, the snowboarder on a ramp with friction, and the spring-launched-package exam sample.

Tutorial 6 exercises (one-line outlines; full algebra in the lecture summary):

Exercise	Set-up	Final answer
1 — Car/truck same $KE$	$\frac{1}{2}{m}_c{v}_c^2=\frac{1}{2}{m}_T{v}_T^2$	$v_c\approx 116\text{km/h}$
2 — Spring compression	$W=\frac{1}{2}k{x}^2$	$59.25\text{J}$
3 — Box up $30^{\circ }$ ramp	$W_{\text{APP}}=mgh+{\mu }_{k}mg\cos \theta \cdot s$	$m\approx 35.16\text{kg}$
4 — Rocket	$W_{\text{thrust}}=\frac{1}{2}m{v}^2+mgh$	$v\approx 130\text{m/s}$
5 — Spring-launched package	$\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2+mgh(+W_{\text{fric}})$	(a) $3.2\text{m/s}$; (b) yes, $26\text{J}>8.82\text{J}$

Common mistakes

• Forgetting $\cos \theta$ when force is at an angle to motion (or, on a ramp, forgetting $\cos \theta$ in $F_N$).
• Treating spring work as $Fx$ when $F$ varies — must use $\frac{1}{2}k{x}^2$.
• Conservation of mechanical energy used in the presence of friction. Only valid when no non-conservative force acts.
• Mixing units (km vs m on graph axes; cm vs m on spring compression).
• Picking two different $P{E}_g$ references within one problem — choose zero once.
• Sign confusion between $W_{\text{on-system}}$ and $W_{\text{by-system}}$. Use the diagram: in = positive; out = positive on the other side; never both at once.
• Forgetting $m$ cancels in friction-on-slope problems — but it does not cancel when an applied force is given (e.g. Tutorial Exercise 3 solves for $m$).

Practice questions

Recommended order for a first pass:

• Conceptual warm-up: cheatsheet quiz Qs 1–6 (units, perpendicular force, area-under-curve, power, $KE$, spring).
• Conservative-only: Tutorial Exercise 1 (car/truck), Example 3 (skateboarder).
• Spring: Tutorial Exercise 2 (do all three methods — force formula, graphical area, energy formula).
• With friction: Example 4 (Alice ramp), Tutorial Exercise 3 (box up ramp).
• Multi-step: Tutorial Exercise 5 (spring + ramp + friction patch).

If you can do Example 4 and Exercise 5 cold, you’re ready for the lab and any exam question on this material.

Assessment relevance

• Laboratory 1 (this week) — spring constant, ${\mu }_k$, ramp displacement. Worksheet submission.
• Portfolio 5/6 — completed in the workshop class.
• Exam — work–energy balance problems with friction on an incline are a standard pattern; expect one. Power is sometimes a one-mark unit/conversion question.

Confidence report

• Directly supported: definitions, formulas, all four lecture worked examples, all five tutorial exercises with answers, lab structure.
• Strongly inferred: lecture framing of the “test force” twist; the link from Newton II to the work–energy theorem (shown in the in-depth note).
• Gap: full slide text in places where the PDF was terse; exact wording of the lab worksheet.

Source files used

• EGD102-Physics/Lecture6_CTP1.pdf — lecture slides
• EGD102-Physics/EGD102 - Lecture6 - Notes.pdf — handwritten worked solutions
• EGD102-Physics/Tutorial 6.pdf — five exercises
• EGD102-Physics/Tutorial 6_Solutions.pdf — worked solutions (with Ex. 2’s three methods and Ex. 5’s friction check)
• Wolfson, R. (2020) Essential University Physics, Vol. 1, 4th ed. SI, Chapters 6–7 — recommended reading