| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Coplanar forces in equilibrium |
| Difficulty | Moderate -0.3 This is a standard coplanar forces equilibrium problem requiring resolution in two perpendicular directions. While it involves trigonometry and simultaneous equations, it's a routine textbook exercise with clear methodology (resolve horizontally and vertically, solve for unknowns). The 'show that' part guides students to one answer, making it slightly easier than average A-level mechanics questions. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(15 + F\cos60° = F\cos30°\) | M1 | For resolving forces in the \(x\) direction |
| \(F = 41.0\) | A1 | AG \(F = 15(1 + \sqrt{3})\) |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([G = F(\sin30° + \sin60°)]\) | M1 | For resolving forces in the \(y\) direction |
| \(G = 56.0\) | A1 | Allow \(15(2 + \sqrt{3})\) |
| Total: 2 |
# Question 1:
## Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $15 + F\cos60° = F\cos30°$ | M1 | For resolving forces in the $x$ direction |
| $F = 41.0$ | A1 | AG $F = 15(1 + \sqrt{3})$ |
| | **Total: 3** | |
## Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[G = F(\sin30° + \sin60°)]$ | M1 | For resolving forces in the $y$ direction |
| $G = 56.0$ | A1 | Allow $15(2 + \sqrt{3})$ |
| | **Total: 2** | |
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\includegraphics[max width=\textwidth, alt={}, center]{48f66bd5-33c1-4ce9-85f9-69faf10e871c-2_558_529_258_808}
Four horizontal forces act at a point $O$ and are in equilibrium. The magnitudes of the forces are $F \mathrm {~N}$, $G \mathrm {~N} , 15 \mathrm {~N}$ and $F \mathrm {~N}$, and the forces act in directions as shown in the diagram.\\
(i) Show that $F = 41.0$, correct to 3 significant figures.\\
(ii) Find the value of $G$.
\hfill \mbox{\textit{CAIE M1 2015 Q1 [5]}}