| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with connected particles requiring kinematics (constant acceleration equations), Newton's second law for both particles, and friction calculations. While it has multiple parts and requires careful consideration of two phases of motion (before and after B hits the floor), the techniques are all routine M1 content with no novel insights needed. The multi-step nature and need to track motion in two phases elevates it slightly above average difficulty. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks |
|---|---|
| For \(B\): \(l = \frac{1}{2}a.2^2 \Rightarrow a = \frac{1}{2} \text{ m s}^{-2}\) | M1 A1 (2) |
| Answer | Marks |
|---|---|
| \(R = 3mg\); \(F=\mu R\) | B1 ; B1 |
| \(T - F = 3m \times 0.5\) | M1 A1ft |
| \(2mg - T = 2m \times 0.5\) | M1 A1 ft |
| Solving for \(\mu\) | DM1 |
| \(\mu = 0.58 \text{ or } 0.582\) | A1 (8) |
| Answer | Marks |
|---|---|
| \(v = \frac{1}{2} \times 2 = 1\) | B1 ft |
| \(-\mu 3mg = 3ma\) | M1 |
| \(0 = 1^2 - 2\mu gs\) | M1 |
| \(s = 0.0877\ldots(0.09 \text{ or better})\) | A1 |
| \(s < 0.3\) correct conclusion | DM1A1 cso (6) |
## Part (a)
For $B$: $l = \frac{1}{2}a.2^2 \Rightarrow a = \frac{1}{2} \text{ m s}^{-2}$ | M1 A1 (2) |
## Part (b)
$R = 3mg$; $F=\mu R$ | B1 ; B1 |
$T - F = 3m \times 0.5$ | M1 A1ft |
$2mg - T = 2m \times 0.5$ | M1 A1 ft |
Solving for $\mu$ | DM1 |
$\mu = 0.58 \text{ or } 0.582$ | A1 (8) |
## Part (c)
$v = \frac{1}{2} \times 2 = 1$ | B1 ft |
$-\mu 3mg = 3ma$ | M1 |
$0 = 1^2 - 2\mu gs$ | M1 |
$s = 0.0877\ldots(0.09 \text{ or better})$ | A1 |
$s < 0.3$ correct conclusion | DM1A1 cso (6) |
**Notes for Question 8(a):**
First M1 for a complete method to find $a$. M0 if $s = 1.3$ is used
First A1 for $a = 0.5$
**Notes for Question 8(b):**
First B1 for $R = 3mg$
Second B1 for $F = \mu R$ seen (could be on diagram)
First M1 for resolving horizontally for $A$ (this M mark can be scored if they just use $m$ for mass but M0 if no mass used)
First A1ft on their $a$, for correct equation. (allow $F$)
Second M1 for resolving vertically for $B$ (this M mark can be scored if they just use $m$ for mass but M0 if no mass used)
Second A1ft on their $a$, for correct equation.
(Allow M2A2 for 'whole system' equation but M0 if not using $5m$)
Third M1 dependent on both previous M marks for solving for $\mu$
N.B. If $m$ omitted consistently throughout (b), can score max B0B1M1A0M1A0M1A0
Third A1 for $\mu = 0.58$ or $0.582$
**Notes for Question 8(c):**
B1 ft for (their $a \times 2$) oe to find $v$
First M1 for resolving horizontally for $A$ with $T = 0$
Second M1 for a complete method (must have found a new '$a$') to find distance moved by $A$.
First A1 for $0.09$ or better $(0.087719\ldots)$
Third M1, dependent on first and second M marks, for comparison with $0.3$ or $1.3$ (Must explicitly refer to either $0.3$ or $1.3$ or an appropriate equivalent)
Second A1 cso for does not reach pulley.\includegraphics{figure_3}
A particle $A$ of mass $3m$ is held at rest on a rough horizontal table. The particle is attached to one end of a light inextensible string. The string passes over a small smooth pulley $P$ which is fixed at the edge of the table. The other end of the string is attached to a particle $B$ of mass $2m$, which hangs freely, vertically below $P$. The system is released from rest, with the string taut, when $A$ is 1.3 m from $P$ and $B$ is 1 m above the horizontal floor, as shown in Figure 3.
Given that $B$ hits the floor 2 s after release and does not rebound,
\begin{enumerate}[label=(\alph*)]
\item find the acceleration of $A$ during the first two seconds, [2]
\item find the coefficient of friction between $A$ and the table, [8]
\item determine whether $A$ reaches the pulley. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q8 [16]}}