| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2009 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Equilibrium with applied force |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass problem requiring composite shapes (rectangle + semicircle), finding combined centre of mass, and resolving forces/moments at hinges. While it involves multiple steps and careful bookkeeping, the techniques are routine for M2 students with no novel insight required. Slightly easier than average A-level due to straightforward application of standard methods. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
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A door is modelled as a lamina $A B C D E$ consisting of a uniform rectangular section $A B D E$ of weight 60 N and a uniform semicircular section $B C D$ of weight 10 N and radius $40 \mathrm {~cm} . A B$ is 200 cm and $A E$ is 80 cm . The door is freely hinged at $F$ and $G$, where $G$ is 30 cm below $B$ and $F$ is 30 cm above $A$ (see diagram).\\
(i) Find the magnitudes and directions of the horizontal components of the forces on the door at each of $F$ and $G$.\\
(ii) Calculate the distance from $A E$ to the centre of mass of the door.
\hfill \mbox{\textit{OCR M2 2009 Q3 [10]}}