| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.8 This is a standard M1 equilibrium problem with three forces meeting at a point. Part (i) is routine diagram drawing, part (ii) uses basic triangle of forces or resolving with given angles and one known force, and part (iii) requires recognizing parallel strings create impossible equilibrium. All techniques are textbook standard with no novel problem-solving required. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Diagram with \(T_{BA}\), \(T_{BC}\) and \(400\) N with correct arrows | B1 | Different labels. All forces present with arrows in correct directions. Condone no angles. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Using triangle of forces (diagram with \(30°\), \(120°\), \(30°\) angles, \(T_{BC}\), \(T_{BA}\), \(400\) N) | M1 | Attempt at triangle of forces. Ignore angles and arrows. Accept 90, 60, 30 triangle. |
| Triangle, arrows, labels and angles correct | B1 | |
| Triangle isosceles so tension in BC is \(400\) N | A1 | cao |
| Tension in BA is \(2 \times 400 \times \cos 30 = 400\sqrt{3}\) N (\(693\) N, 3 s.f.) | F1 | FT BC only. [If resolution used: M1 for 1 eqn; M1 for \(2^{\text{nd}}\) eqn + attempt to elim; A1; F1. If Lami used: M1 first pair of equations in correct format, condone wrong angles. A1. M1 second pair in correct format, with correct angles. F1 FT their first answer if necessary.] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Resolve at B perpendicular to the line ABC | E1 | Attempt to argue unbalanced force |
| Weight has unbalanced component in this direction | E1 | Complete, convincing argument. [or Resolve horiz and establish tensions equal E1; Resolve vert to show inconsistency E1] |
# Question 6:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Diagram with $T_{BA}$, $T_{BC}$ and $400$ N with correct arrows | B1 | Different labels. All forces present with arrows in correct directions. Condone no angles. |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Using triangle of forces (diagram with $30°$, $120°$, $30°$ angles, $T_{BC}$, $T_{BA}$, $400$ N) | M1 | Attempt at triangle of forces. Ignore angles and arrows. Accept 90, 60, 30 triangle. |
| Triangle, arrows, labels and angles correct | B1 | |
| Triangle isosceles so tension in BC is $400$ N | A1 | cao |
| Tension in BA is $2 \times 400 \times \cos 30 = 400\sqrt{3}$ N ($693$ N, 3 s.f.) | F1 | FT BC only. [If resolution used: M1 for 1 eqn; M1 for $2^{\text{nd}}$ eqn + attempt to elim; A1; F1. If Lami used: M1 first pair of equations in correct format, condone wrong angles. A1. M1 second pair in correct format, with **correct** angles. F1 FT their first answer if necessary.] |
## Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Resolve at B perpendicular to the line ABC | E1 | Attempt to argue unbalanced force |
| Weight has unbalanced component in this direction | E1 | Complete, convincing argument. [**or** Resolve horiz and establish tensions equal E1; Resolve vert to show inconsistency E1] |6 A small box B of weight 400 N is held in equilibrium by two light strings AB and BC . The string $B C$ is fixed at $C$. The end $A$ of string $A B$ is fixed so that $A B$ is at an angle $\alpha$ to the vertical where $\alpha < 60 ^ { \circ }$. String BC is at $60 ^ { \circ }$ to the vertical. This information is shown in Fig. 5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{94f23528-931c-47b6-89aa-4b6edd25cc30-4_404_437_434_810}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
(i) Draw a labelled diagram showing all the forces acting on the box.\\
(ii) In one situation string AB is fixed so that $\alpha = 30 ^ { \circ }$.
By drawing a triangle of forces, or otherwise, calculate the tension in the string BC and the tension in the string AB .\\
(iii) Show carefully, but briefly, that the box cannot be in equilibrium if $\alpha = 60 ^ { \circ }$ and BC remains at $60 ^ { \circ }$ to the vertical.
\hfill \mbox{\textit{OCR MEI M1 Q6 [7]}}