| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Lift with passenger or load |
| Difficulty | Standard +0.3 This is a standard M1 lift problem requiring application of Newton's second law in multiple parts. Parts (a) and (b) involve routine F=ma calculations with weight and normal force, while parts (c) and (d) apply impulse-momentum theorem. All techniques are textbook standard with no novel insight required, making it slightly easier than average. |
| Spec | 3.03d Newton's second law: 2D vectors6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) resolve ↓ for man: \(90g - R = 90(0.5)\) so \(R = 837 \text{ N}\) | M2 A1 | |
| (b) resolve ↓ for lift: \(R + 70g - T = 70(0.5)\) \(837 + 686 - T = 35\) so \(T = 1488 \text{ N}\) | M2 A1, A1 | |
| (c) impulse \(= \Delta\) mom. \(= 160(0-2) = 320 \text{ Ns}\) | M1 A1 | |
| (d) \(Ft = 320\), so \(F = \frac{320}{2} = 160 \text{ N}\) | M1 A1 | (11) |
| (a) resolve ↓ for man: $90g - R = 90(0.5)$ so $R = 837 \text{ N}$ | M2 A1 | |
| (b) resolve ↓ for lift: $R + 70g - T = 70(0.5)$ $837 + 686 - T = 35$ so $T = 1488 \text{ N}$ | M2 A1, A1 | |
| (c) impulse $= \Delta$ mom. $= 160(0-2) = 320 \text{ Ns}$ | M1 A1 | |
| (d) $Ft = 320$, so $F = \frac{320}{2} = 160 \text{ N}$ | M1 A1 | (11) |4. A lift of mass 70 kg is supported by a cable which remains taut at all times. A man of mass 90 kg gets into the lift and it begins to descend vertically from rest with constant acceleration $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
Calculate, giving your answers correct to 3 significant figures,
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the force which the lift exerts on the man,
\item the tension in the cable.
Prior to slowing down, the lift is moving at $2 \mathrm {~ms} ^ { - 1 }$. It then uniformly decelerates until it is brought to rest.
\item Find the impulse exerted by the cable on the lift in bringing the lift to rest.
\item Given that it takes 2 seconds to come to rest, use your answer to part (c) to calculate the magnitude of the force exerted by the cable on the lift in bringing the lift to rest.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [11]}}