| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Force on pulley from string |
| Difficulty | Standard +0.8 This is a standard pulley problem requiring students to first find the system acceleration and tension (using F=ma for both masses), then calculate the resultant force on the pulley using vector addition at the correct angle. While the individual steps are routine A-level mechanics, combining them correctly and recognizing the need for vector resolution makes this moderately above average difficulty for AS-level students. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(4mg - T = 4ma\) | M1, A1 | Equation of motion for \(P\); M0 if \(m\)'s omitted i.e. \(4g - T = 4a\) |
| \(T - 3mg = 3ma\) | M1, A1 | Equation of motion for \(Q\); M0 if \(m\)'s omitted i.e. \(T - 3g = 3a\) |
| Solve for \(T\) | M1 | Does not need to be in terms of \(mg\); NB: whole system equation \(4mg - 3mg = 7ma\) also condoned |
| \(T = \frac{24mg}{7}\) | A1 | In any form |
| Force on pulley \(= 2T\) | M1 | \(T\) does not need to be substituted |
| \(\frac{48mg}{7}\) | A1 | Accept \(6.9mg\) or better; must be in terms of \(m\) and \(g\) as a single term |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Weight of the rope or extensibility of rope; or pulley may not be smooth | B1 | B0 if any incorrect extras are given |
# Question 2:
## Part (a)
| Working | Mark | Guidance |
|---------|------|----------|
| $4mg - T = 4ma$ | M1, A1 | Equation of motion for $P$; M0 if $m$'s omitted i.e. $4g - T = 4a$ |
| $T - 3mg = 3ma$ | M1, A1 | Equation of motion for $Q$; M0 if $m$'s omitted i.e. $T - 3g = 3a$ |
| Solve for $T$ | M1 | Does not need to be in terms of $mg$; NB: whole system equation $4mg - 3mg = 7ma$ also condoned |
| $T = \frac{24mg}{7}$ | A1 | In any form |
| Force on pulley $= 2T$ | M1 | $T$ does not need to be substituted |
| $\frac{48mg}{7}$ | A1 | Accept $6.9mg$ or better; must be in terms of $m$ and $g$ as a single term |
## Part (b)
| Working | Mark | Guidance |
|---------|------|----------|
| Weight of the rope or extensibility of rope; or pulley may not be smooth | B1 | B0 if any incorrect extras are given |
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0fd98465-9db5-4125-b53f-7a9a3467ac41-06_526_415_244_826}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
One end of a string is attached to a small ball $P$ of mass $4 m$.\\
The other end of the string is attached to another small ball $Q$ of mass $3 m$.\\
The string passes over a fixed pulley.\\
Ball $P$ is held at rest with the string taut and the hanging parts of the string vertical, as shown in Figure 1.
Ball $P$ is released.\\
The string is modelled as being light and inextensible, the balls are modelled as particles, the pulley is modelled as being smooth and air resistance is ignored.
\begin{enumerate}[label=(\alph*)]
\item Using the model, find, in terms of $m$ and $g$, the magnitude of the force exerted on the pulley by the string while $P$ is falling and before $Q$ hits the pulley.
\item State one limitation of the model, apart from ignoring air resistance, that will affect the accuracy of your answer to part (a).
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 2 2020 Q2 [9]}}