| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Prism or block on inclined plane |
| Difficulty | Standard +0.3 This is a straightforward moments problem requiring students to apply the toppling condition (weight acts through the pivot point) to find the maximum overhang, then use this constraint to determine how many books fit. The calculations are routine with clear geometric setup, though it requires careful bookkeeping of distances and the two-prism constraint. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04b Find centre of mass: using symmetry |
| Answer | Marks | Guidance |
|---|---|---|
| Identifies the distance of centre of mass from vertical face as \(\frac{1}{3}x\) base \([\frac{1}{3} \times 10/3]\) | B1 | |
| Maximum overhang is 6.67 cm (20/3) ft for 10 - \(\bar{x}\) | B1 A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Identifies the maximum possible width for books as \(100 - 2\bar{x}\) and divides by 5 \([100 - 20/3/5]\) | M1 | |
| Obtains greatest number as 18 | A1 | 2 marks |
**(i)**
| Identifies the distance of centre of mass from vertical face as $\frac{1}{3}x$ base $[\frac{1}{3} \times 10/3]$ | B1 |
| Maximum overhang is 6.67 cm (20/3) ft for 10 - $\bar{x}$ | B1 A1 | 2 marks |
**(ii)**
| Identifies the maximum possible width for books as $100 - 2\bar{x}$ and divides by 5 $[100 - 20/3/5]$ | M1 |
| Obtains greatest number as 18 | A1 | 2 marks |
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Two identical uniform heavy triangular prisms, each of base width 10 cm , are arranged as shown at the ends of a smooth horizontal shelf of length 1 m . Some books, each of width 5 cm , are placed on the shelf between the prisms.\\
(i) Find how far the base of a prism can project beyond an end of the shelf without the prism toppling.\\
(ii) Find the greatest number of books that can be stored on the shelf without either of the prisms toppling.
\hfill \mbox{\textit{CAIE M2 2002 Q2 [4]}}