| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Lift with passenger or load |
| Difficulty | Moderate -0.3 This is a standard M1 lift problem requiring Newton's second law applied to connected particles. Part (a) is routine application of F=ma to find normal reaction. Part (b) requires setting up an inequality with tension constraint, but follows a predictable method. Slightly easier than average due to straightforward setup and clear given values. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(R - 60g = 60 \times 2\) | M1A1 | Equation in \(R\) only |
| \(R = 708\) N or \(710\) N (must be positive) | A1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(75n\) | B1 | Seen or implied |
| \(10000 - Mg - 100 = M \times 3\) | M1A2 | Equation in one unknown; \(a=3\) required for A1A1 |
| Using \(M = 250 + 75n \Rightarrow n = 6.9\ldots\) | DM1A1 | Dependent on first M1 |
| So 6 people | A1ft | (7 marks); ft on their \(n\) value |
# Question 5:
## Part 5(a):
| Working | Marks | Guidance |
|---------|-------|----------|
| $R - 60g = 60 \times 2$ | M1A1 | Equation in $R$ only |
| $R = 708$ N or $710$ N (must be positive) | A1 | (3 marks) |
## Part 5(b):
| Working | Marks | Guidance |
|---------|-------|----------|
| $75n$ | B1 | Seen or implied |
| $10000 - Mg - 100 = M \times 3$ | M1A2 | Equation in one unknown; $a=3$ required for A1A1 |
| Using $M = 250 + 75n \Rightarrow n = 6.9\ldots$ | DM1A1 | Dependent on first M1 |
| So 6 people | A1ft | (7 marks); ft on their $n$ value |
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4fd21e83-0bdf-4bb1-8a3f-76beada511ae-16_359_298_233_824}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
A lift of mass 250 kg is being raised by a vertical cable attached to the top of the lift. A woman of mass 60 kg stands on the horizontal floor inside the lift, as shown in Figure 3. The lift ascends vertically with constant acceleration $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. There is a constant downwards resistance of magnitude 100 N on the lift. By modelling the woman as a particle,
\begin{enumerate}[label=(\alph*)]
\item find the magnitude of the normal reaction exerted by the floor of the lift on the woman.
The tension in the cable must not exceed 10000 N for safety reasons, and the maximum upward acceleration of the lift is $3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. A typical occupant of the lift is modelled as a particle of mass 75 kg and the cable is modelled as a light inextensible string. There is still a constant downwards resistance of magnitude 100 N on the lift.
\item Find the maximum number of typical occupants that can be safely carried in the lift when it is ascending with an acceleration of $3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2018 Q5 [10]}}