| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Maximum/minimum force for equilibrium |
| Difficulty | Standard +0.8 This is a non-trivial equilibrium problem requiring resolution of forces in two directions, consideration of limiting friction (μR), and optimization to find the minimum force T. Students must recognize that minimum T occurs at limiting friction and solve simultaneous equations involving trigonometry. More demanding than standard M1 equilibrium questions but uses only standard techniques. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.03r Friction: concept and vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((\uparrow)\ R + 200\sin 15° + T\sin 25° = 20g\) | M1A2 | M1 resolving vertically, correct no. of terms, condone sign errors and sin/cos confusion. A2: -1 each error |
| \((\leftarrow)\ 200\cos 15° - T\cos 25° - F = 0\) | M1A2 | M1 resolving horizontally, correct no. of terms, condone sign errors and sin/cos confusion. A2: -1 each error. Forces and angles must be paired correctly but allow slips |
| \(F = 0.3R\) | B1 | Seen anywhere, e.g. on diagram |
| Solving for \(T\) (192.31..) | DM1 | Dependent on previous two M marks |
| \(T = 190\) or \(192\) | A1 | cao, allow units |
# Question 3:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(\uparrow)\ R + 200\sin 15° + T\sin 25° = 20g$ | M1A2 | M1 resolving vertically, correct no. of terms, condone sign errors and sin/cos confusion. A2: -1 each error |
| $(\leftarrow)\ 200\cos 15° - T\cos 25° - F = 0$ | M1A2 | M1 resolving horizontally, correct no. of terms, condone sign errors and sin/cos confusion. A2: -1 each error. Forces and angles must be paired correctly but allow slips |
| $F = 0.3R$ | B1 | Seen anywhere, e.g. on diagram |
| Solving for $T$ (192.31..) | DM1 | Dependent on previous two M marks |
| $T = 190$ or $192$ | A1 | cao, allow units |
---3.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{ca445c1e-078c-4a57-94df-de90f30f8efd-06_156_1009_255_470}
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\caption{Figure 1}
\end{center}
\end{figure}
A parcel of mass 20 kg is at rest on a rough horizontal floor. The coefficient of friction between the parcel and the floor is 0.3
Two forces, both acting in the same vertical plane, of magnitudes 200 N and $T \mathrm {~N}$ are applied to the parcel. The line of action of the 200 N force makes an angle of $15 ^ { \circ }$ with the horizontal and the line of action of the $T \mathrm {~N}$ force makes an angle of $25 ^ { \circ }$ with the horizontal, as shown in Figure 1. The parcel is modelled as a particle $P$.
Find the smallest value of $T$ for which $P$ remains in equilibrium.\\
\hfill \mbox{\textit{Edexcel M1 2021 Q3 [9]}}