| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2016 |
| Session | Specimen |
| Marks | 8 |
| Topic | Moments |
| Type | Rod against wall and ground |
| Difficulty | Standard +0.3 This is a standard statics problem requiring three equilibrium equations (horizontal/vertical forces and moments) to find the normal reaction at the wall, then comparing friction demand against available friction. The setup is straightforward with given coefficient of friction, making it slightly easier than average but still requiring systematic application of mechanics principles. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force |
From Question 8 in the mark scheme:
**(i)** Resolve vertically $N_B = 2 \times 10$ **M1**
Take moments about e.g. intersection of normals: $N_B \times 0.2\cos 60° = F \times 0.4\sin 60°$, moments equation correct (if in equilibrium) **M1, A1**
$F = 5.77$, $N_B = 20$ **A1**
$F > \mu N_B$ **M1**
Correctly deduce not in equilibrium therefore rod does slip **A1**
**(ii)** Consider forces horizontally $N_A$ non-zero **M1**
Correctly deduce impossibility hence leftwards force required for equilibrium **A1**9 The diagram shows a uniform rod $A B$ of length 40 cm and mass 2 kg placed with the end $A$ resting against a smooth vertical wall and the end $B$ on rough horizontal ground. The angle between $A B$ and the horizontal is $60 ^ { \circ }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{c4bbba86-2968-4247-b300-357217cf213b-4_657_647_1923_708}
Given that the value of the coefficient of friction between the rod and the ground is 0.2 , determine whether the rod slips.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2016 Q9 [8]}}