| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| 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 system problem requiring kinematics to find acceleration, then Newton's second law for two connected particles, and finally friction calculation. It follows a well-established template with straightforward multi-step application of familiar techniques, making it slightly easier than the average A-level question. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Trapezium shape starting at origin, ending on \(t\)-axis | B1 | Trapezium starting at origin and ending on \(t\)-axis |
| Figures: \(22\) on speed axis; \(30\), \(30+T\), \(120\) on time axis | B1 | Allow missing \(0\) and a delineator oe for \(T\); allow if \(T=75\) used correctly on graph |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{(120+T)22}{2} = 2145\) | M1 A1 | Equation in \(T\) only; equating area of trapezium to 2145 with correct number of terms; if single trapezium, must see evidence of \(\frac{1}{2}\) × sum of parallel sides |
| \(T = 75\) | A1 | N.B. Use of single suvat equation \(s = t(u+v)/2\) for whole motion is M0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{(t + t - 30)22}{2} = 990\) | M1 A1 | Equation in \(t\) only (may use \((t-30)\) as variable); equating area of trapezium to 990; use of motorcycle motion is M0; use of \(v=22\) for motorcycle is M0 |
| \(t = 60\) | A1 | Allow \(30 + 30\) |
| Answer \(= 60 - 10 = 50\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(990 = 0.5a \cdot 50^2\) | M1 | Equation in \(a\) only |
| \(a = 0.79,\ 0.792,\ \frac{99}{125}\) oe | A1 | N.B. Use of \(v=22\) for motorcycle is M0 |
## Question 5:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Trapezium shape starting at origin, ending on $t$-axis | B1 | Trapezium starting at origin and ending on $t$-axis |
| Figures: $22$ on speed axis; $30$, $30+T$, $120$ on time axis | B1 | Allow missing $0$ and a delineator oe for $T$; allow if $T=75$ used correctly on graph |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{(120+T)22}{2} = 2145$ | M1 A1 | Equation in $T$ only; equating area of trapezium to 2145 with correct number of terms; if single trapezium, must see evidence of $\frac{1}{2}$ × sum of parallel sides |
| $T = 75$ | A1 | N.B. Use of single suvat equation $s = t(u+v)/2$ for whole motion is M0 |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{(t + t - 30)22}{2} = 990$ | M1 A1 | Equation in $t$ only (may use $(t-30)$ as variable); equating area of trapezium to 990; use of motorcycle motion is M0; use of $v=22$ for motorcycle is M0 |
| $t = 60$ | A1 | Allow $30 + 30$ |
| Answer $= 60 - 10 = 50$ | A1 | |
### Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $990 = 0.5a \cdot 50^2$ | M1 | Equation in $a$ only |
| $a = 0.79,\ 0.792,\ \frac{99}{125}$ oe | A1 | N.B. Use of $v=22$ for motorcycle is M0 |
---5.
Figure 4\\
\includegraphics[max width=\textwidth, alt={}, center]{94d9432d-1723-4549-ad5e-d4be0f5fd083-009_609_1026_301_516}
A block of wood $A$ of mass 0.5 kg rests on a rough horizontal table and is attached to one end of a light inextensible string. The string passes over a small smooth pulley $P$ fixed at the edge of the table. The other end of the string is attached to a ball $B$ of mass 0.8 kg which hangs freely below the pulley, as shown in Figure 4. The coefficient of friction between $A$ and the table is $\mu$. The system is released from rest with the string taut. After release, $B$ descends a distance of 0.4 m in 0.5 s . Modelling $A$ and $B$ as particles, calculate
\begin{enumerate}[label=(\alph*)]
\item the acceleration of $B$,
\item the tension in the string,
\item the value of $\mu$.
\item State how in your calculations you have used the information that the string is inextensible.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5}}