| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done against friction/resistance - inclined plane or slope |
| Difficulty | Moderate -0.8 This is a straightforward work-energy question requiring standard formulas: work = force × distance × cos(angle), PE = mgh, and energy conservation. All values are given directly, requiring only careful substitution and basic trigonometry with no problem-solving insight or novel approach needed. |
| Spec | 6.02b Calculate work: constant force, resolved component6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \([WD = 30 \times 20 \cos 10°]\) | M1 | For using \(WD = Fd \cos \beta\) |
| Work done is 591J | A1 | 2 |
| (ii) \([PE \text{ gain} = 8 \times 10 \times 20 \sin 15°]\) | M1 | For using \(PE = mgh\) and \(h = d \sin \alpha\) |
| PE gain is 414J | A1 | 2 |
| (iii) Work done is 177J | B1ft | 1 |
(i) $[WD = 30 \times 20 \cos 10°]$ | M1 | For using $WD = Fd \cos \beta$
Work done is 591J | A1 | 2
(ii) $[PE \text{ gain} = 8 \times 10 \times 20 \sin 15°]$ | M1 | For using $PE = mgh$ and $h = d \sin \alpha$
PE gain is 414J | A1 | 2
(iii) Work done is 177J | B1ft | 1 | $ft$ (ans(i) – ans(ii))1\\
\includegraphics[max width=\textwidth, alt={}, center]{d0fa61eb-f320-427e-8883-de224d293933-2_421_1223_267_461}
A box of mass 8 kg is pulled, at constant speed, up a straight path which is inclined at an angle of $15 ^ { \circ }$ to the horizontal. The pulling force is constant, of magnitude 30 N , and acts upwards at an angle of $10 ^ { \circ }$ from the path (see diagram). The box passes through the points $A$ and $B$, where $A B = 20 \mathrm {~m}$ and $B$ is above the level of $A$. For the motion from $A$ to $B$, find\\
(i) the work done by the pulling force,\\
(ii) the gain in potential energy of the box,\\
(iii) the work done against the resistance to motion of the box.
\hfill \mbox{\textit{CAIE M1 2006 Q1 [5]}}