| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough incline connected to particle on horizontal surface or other incline |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with connected particles requiring application of Newton's second law and SUVAT equations. While it involves multiple steps (finding acceleration from kinematics, then tension, then friction coefficient), each step follows a routine procedure taught in M1 with no novel insight required. The inclined plane component and resolving forces makes it slightly above average difficulty for M1, but still a textbook-style question. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.75 = \frac{1}{2}a(0.5)^2\) | M1 A1 | M1 for use of \(s = ut + \frac{1}{2}at^2\) (or 2 suvat formulae eliminating \(v\)) with \(u=0\), giving equation in \(a\) only; A1 correct equation |
| \(a = 6\) | A1 | A1 for \(a=6\) |
| \(0.5g\sin\theta - T = 0.5a\) | M1 A1 | M1 for resolving parallel to plane up or down for \(Q\) only; A1 correct equation (\(a\) need not be substituted) |
| \(T = 0.92\) N | A1 (6) | A1 for \(T = 0.92\) N |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = 0.1g\) | B1 | B1 for \(R = 0.1g\) |
| \(T - \mu R = 0.1a\) | M1 A1 | M1 resolving horizontally for \(P\) only; A1 correct equation (neither \(T\), \(R\) nor \(a\) need substituting) |
| \(0.92 - \mu \cdot 0.1g = 0.1 \times 6\) | M1 A1 | M1 for substituting \(T\), \(R\), \(a\) and solving for \(\mu\); A1 for \(\mu = 0.327\) or \(0.33\) (16/49, A0) |
| \(\mu = 0.327\) or \(0.33\) | (5) |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = 0.1g\) | B1 | |
| \(0.5g\sin\theta - \mu R = 0.6a\) | M1 A1 | M1 for 'whole system' equation; A1 correct (neither \(R\) nor \(a\) need substituting) |
| \(\mu = 0.327\) or \(0.33\) | M1 A1 (5) |
## Question 6:
### Part (a):
$0.75 = \frac{1}{2}a(0.5)^2$ | M1 A1 | M1 for use of $s = ut + \frac{1}{2}at^2$ (or 2 suvat formulae eliminating $v$) with $u=0$, giving equation in $a$ only; A1 correct equation
$a = 6$ | A1 | A1 for $a=6$
$0.5g\sin\theta - T = 0.5a$ | M1 A1 | M1 for resolving parallel to plane up or down for $Q$ only; A1 correct equation ($a$ need not be substituted)
$T = 0.92$ N | A1 (6) | A1 for $T = 0.92$ N
### Part (b):
$R = 0.1g$ | B1 | B1 for $R = 0.1g$
$T - \mu R = 0.1a$ | M1 A1 | M1 resolving horizontally for $P$ only; A1 correct equation (neither $T$, $R$ nor $a$ need substituting)
$0.92 - \mu \cdot 0.1g = 0.1 \times 6$ | M1 A1 | M1 for substituting $T$, $R$, $a$ and solving for $\mu$; A1 for $\mu = 0.327$ or $0.33$ (16/49, A0)
$\mu = 0.327$ or $0.33$ | (5) |
**Alternative:**
$R = 0.1g$ | B1 |
$0.5g\sin\theta - \mu R = 0.6a$ | M1 A1 | M1 for 'whole system' equation; A1 correct (neither $R$ nor $a$ need substituting)
$\mu = 0.327$ or $0.33$ | M1 A1 (5) |6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{fade35da-8dca-4d98-a07c-ed3a173fccda-16_398_860_210_543}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Two particles $P$ and $Q$ have masses 0.1 kg and 0.5 kg respectively. The particles are attached to the ends of a light inextensible string. Particle $P$ is held at rest on a rough horizontal table. The string lies along the table and passes over a small smooth pulley which is fixed to the edge of the table. Particle $Q$ is at rest on a smooth plane which is inclined to the horizontal at an angle $\theta$, where $\tan \theta = \frac { 4 } { 3 }$
The string lies in the vertical plane which contains the pulley and a line of greatest slope of the inclined plane, as shown in Figure 2. Particle $P$ is released from rest with the string taut. During the first 0.5 s of the motion $P$ does not reach the pulley and $Q$ moves 0.75 m down the plane.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string during the first 0.5 s of the motion.
\item Find the coefficient of friction between $P$ and the table.\\
\includegraphics[max width=\textwidth, alt={}, center]{fade35da-8dca-4d98-a07c-ed3a173fccda-19_72_59_2613_1886}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2014 Q6 [11]}}