| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.8 This is a straightforward statics problem requiring resolution of forces in equilibrium. Students draw a force diagram, then resolve vertically (T cos 30° = 15g) and horizontally (T sin 30° = tension in string). Standard two-step application of Newton's first law with no conceptual difficulty beyond basic trigonometry. |
| Spec | 3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Three forces diagram: \(T_R\) acting up-left, \(T_S\) acting horizontally right, \(15g\) acting downward | B1 | Three forces in approximately correct directions, with arrows and labels; tensions must be distinct. Accept \(W\) or \(mg\) for weight; condone missing \(g\) |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve vertically: \(T_R \cos 30° = 15g\) | M1 | Forming equilibrium equation (allow sin/cos interchange) |
| \(T_R = \frac{15 \times 9.8}{\cos 30°} = 98\sqrt{3} = 170\) N (3sf) | A1 | Oe |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve horizontally: \(T_S = T_R \sin 30°\) | M1 | Allow sin/cos interchange if consistent with (b) |
| \(T_S = 84.9\) N (3sf) | A1 | Oe. Accept \(T_S = 15g\tan 30°\) |
## Question 13:
**Part (a):**
Three forces diagram: $T_R$ acting up-left, $T_S$ acting horizontally right, $15g$ acting downward | B1 | Three forces in approximately correct directions, with arrows and labels; tensions must be distinct. Accept $W$ or $mg$ for weight; condone missing $g$
**Part (b):**
Resolve vertically: $T_R \cos 30° = 15g$ | M1 | Forming equilibrium equation (allow sin/cos interchange)
$T_R = \frac{15 \times 9.8}{\cos 30°} = 98\sqrt{3} = 170$ N (3sf) | A1 | Oe
**Part (c):**
Resolve horizontally: $T_S = T_R \sin 30°$ | M1 | Allow sin/cos interchange if consistent with (b)
$T_S = 84.9$ N (3sf) | A1 | Oe. Accept $T_S = 15g\tan 30°$
---13 A 15 kg box is suspended in the air by a rope which makes an angle of $30 ^ { \circ }$ with the vertical. The box is held in place by a string which is horizontal.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing the forces acting on the box.
\item Calculate the tension in the rope.
\item Calculate the tension in the string.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2019 Q13 [5]}}