| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Ladder on smooth wall and rough ground |
| Difficulty | Standard +0.3 This is a standard ladder equilibrium problem requiring moments about a point, resolving forces, and relating friction to normal reaction. The algebra is straightforward, and part (ii) involves recognizing that F increases with x and finding the critical coefficient of friction. While it requires multiple steps and careful setup, it follows a well-established template for Further Maths mechanics with no novel insights needed. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (i) | F (cid:32)S |
| Answer | Marks |
|---|---|
| (cid:159)F (cid:32)90(1(cid:14)x)tan20 | B1 |
| Answer | Marks |
|---|---|
| [4] | I |
| Answer | Marks |
|---|---|
| 2.1 | E |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (ii) | (A) |
| increases. | B1 | |
| [1] | 2.4 | Clearly explained |
| 7 | (ii) | (B) |
| Answer | Marks |
|---|---|
| 900 10 | B1 |
| Answer | Marks |
|---|---|
| [4] | 3.1b |
| Answer | Marks |
|---|---|
| 2.2a | N |
| Answer | Marks |
|---|---|
| Inequality clearly established | Set notation not required |
Question 7:
7 | (i) | F (cid:32)S
180(cid:117)4cos70 (cid:14)720(cid:117)xcos70 (cid:32)8Ssin70
P
(720(cid:14)720x)sin20(cid:113)(cid:32)8Fcos20(cid:113)
(cid:159)F (cid:32)90(1(cid:14)x)tan20 | B1
EM1
A1
E1
[4] | I
C
2.2a
3.3
1.1
2.1 | E
M
Moments equation with at least
two terms
Two terms correct
Correctly shown
7 | (ii) | (A) | All other terms constant so F increases as x
increases. | B1
[1] | 2.4 | Clearly explained
7 | (ii) | (B) | So worst case is x = 8
giving F (cid:32)810tan20 with R = 900
Since F(cid:100)F (cid:32)(cid:80)R
max
810tan20 9tan20
(cid:80)(cid:116) = (cid:32)0.3275...
900 10 | B1
B1
M1
A1
[4] | 3.1b
3.4
1.1
2.2a | N
E
Inequality clearly established | Set notation not requiredA uniform ladder of length 8 m and weight 180 N stands on a rough horizontal surface and rests against a smooth vertical wall. The ladder makes an angle of 20° with the wall. A woman of weight 720 N stands on the ladder. Fig. 7 shows this situation modelled with the woman's weight acting at a distance $x$ m from the lower end of the ladder.
The system is in equilibrium.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Show that the frictional force between the ladder and the horizontal surface is $F$ N, where $F = 90(1 + x)\tan 20°$. [4]
\item \begin{enumerate}[label=(\Alph*)]
\item State with a reason whether $F$ increases, stays constant or decreases as $x$ increases. [1]
\item Hence determine the set of values of the coefficient of friction between the ladder and the surface for which the woman can stand anywhere on the ladder without it slipping. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major Q7 [9]}}