| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Moderate -0.3 This is a straightforward two-force resolution problem requiring basic trigonometry. Part (i) involves resolving forces perpendicular to one direction and solving a simple equation for θ (show-that question reduces difficulty). Part (ii) is direct calculation of the resultant. Standard M1 mechanics with clear diagram and structured parts makes this slightly easier than average. |
| Spec | 3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For resolving forces in the i direction or for relevant use of trigonometry | |
| \(2.5 = 6.5\sin\theta\) | A1 | |
| \(\theta = 22.6°\) | A1 | 3 AG Accept verification |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For resolving forces in the j direction or for using Pythagoras or relevant trigonometry | |
| \(R = 6.5\cos 22.6°\) | A1 | |
| \(R = 6\) | A1 | 3 |
# Question 2:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For resolving forces in the **i** direction or for relevant use of trigonometry |
| $2.5 = 6.5\sin\theta$ | A1 | |
| $\theta = 22.6°$ | A1 | **3** AG Accept verification |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For resolving forces in the **j** direction or for using Pythagoras or relevant trigonometry |
| $R = 6.5\cos 22.6°$ | A1 | |
| $R = 6$ | A1 | **3** |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{8ee41313-b516-48cb-bc87-cd8e54245d28-2_620_711_543_717}
Forces of magnitudes 6.5 N and 2.5 N act at a point in the directions shown. The resultant of the two forces has magnitude $R \mathrm {~N}$ and acts at right angles to the force of magnitude 2.5 N (see diagram).\\
(i) Show that $\theta = 22.6 ^ { \circ }$, correct to 3 significant figures.\\
(ii) Find the value of $R$.
\hfill \mbox{\textit{OCR M1 2006 Q2 [6]}}