| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2002 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Ring on horizontal rod equilibrium |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of F=μR at limiting equilibrium. Part (a) involves routine trigonometry (tan α = 3/4 gives sin/cos values) and simultaneous equations. Parts (b) and (c) test understanding of equilibrium conditions without requiring full calculations. Slightly above average difficulty due to the three-part structure and the conceptual element in part (c), but all techniques are standard M1 material with no novel problem-solving required. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = \mu N \Rightarrow \mu = \frac{2}{4.44} \simeq 0.45\) | M1 A2,1,0 | M1 M1 A1 (8) |
| Answer | Marks | Guidance |
|---|---|---|
| Hence equilib. not possible | M1 B1 (2) | M1 |
## Part (a)
$R(\uparrow)$ $N = 0.3 \times 9.8 + 2.5\sin\alpha$
$(= 2.94 + 1.5 = 4.44\text{ N})$
$R(\leftarrow)$ $F = 2.5\cos\alpha$ $(= 2\text{ N})$
$F = \mu N \Rightarrow \mu = \frac{2}{4.44} \simeq 0.45$ | M1 A2,1,0 | M1 M1 A1 (8)
## Part (b)
$N' = 0.3 \times 9.8 - 2.5\sin\alpha = 1.44\text{ N}$
$F' = \mu N'$. $N' < N \Rightarrow F'_{\max} \text{ less}$
Bar $F'$ must $= 2.5\cos\alpha$ for equilib.
Hence equilib. not possible | M1 B1 (2) | M1 | A1 c.s.o.(12)
---\includegraphics{figure_2}
A ring of mass 0.3 kg is threaded on a fixed, rough horizontal curtain pole. A light inextensible string is attached to the ring. The string and the pole lie in the same vertical plane. The ring is pulled downwards by the string which makes an angle $\alpha$ to the horizontal, where tan $\alpha = \frac{3}{4}$ as shown in Fig. 2. The tension in the string is 2.5 N. Given that, in this position, the ring is in limiting equilibrium,
\begin{enumerate}[label=(\alph*)]
\item find the coefficient of friction between the ring and the pole. [8]
\end{enumerate}
\includegraphics{figure_3}
The direction of the string is now altered so that the ring is pulled upwards. The string lies in the same vertical plane as before and again makes an angle $\alpha$ with the horizontal, as shown in Fig. 3. The tension in the string is again 2.5 N.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the normal reaction exerted by the pole on the ring. [2]
\item State whether the ring is in equilibrium in the position shown in Fig. 3, giving a brief justification for your answer. You need make no further detailed calculation of the forces acting. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2002 Q7 [12]}}