| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward two-part question on vector addition and equilibrium. Part (i) uses Pythagoras' theorem (F² + 8² = 17²) and basic trigonometry, while part (ii) simply requires recognizing that the equilibrant equals the resultant in magnitude but opposite direction. Both parts are routine applications of standard M1 techniques with no problem-solving insight required, making it easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(F^2 = 17^2 - 8^2\) | M1 | \(F^2 = 17^2 +/- 8^2\) |
| \(F = 15\) | A1 | Exact, accept 15.0 |
| \(\cos\alpha = 8/17\) | M1 | Correct method for angle between 8 N and 17 N forces |
| \(\alpha = 61.9°\) | A1 | Accept 62° from correct work |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(E = 17\) | B1 | Exact |
| Angle \(= 118(.1)°\) OR \(242°\) \((241.9°)\) | B1 FT | \(180 - \text{cv}(\alpha(\text{i}))\) OR \(180 + \text{cv}(\alpha(\text{i}))\) Must be 3sf or better |
# Question 1:
## Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $F^2 = 17^2 - 8^2$ | M1 | $F^2 = 17^2 +/- 8^2$ |
| $F = 15$ | A1 | Exact, accept 15.0 |
| $\cos\alpha = 8/17$ | M1 | Correct method for angle between 8 N and 17 N forces |
| $\alpha = 61.9°$ | A1 | Accept 62° from correct work |
## Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $E = 17$ | B1 | Exact |
| Angle $= 118(.1)°$ OR $242°$ $(241.9°)$ | B1 FT | $180 - \text{cv}(\alpha(\text{i}))$ OR $180 + \text{cv}(\alpha(\text{i}))$ Must be 3sf or better |
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\includegraphics[max width=\textwidth, alt={}, center]{f0813713-d677-4ed7-87e1-971a64bdb6ff-2_305_295_264_868}
Two perpendicular forces of magnitudes $F \mathrm {~N}$ and 8 N act at a point $O$ (see diagram). Their resultant has magnitude 17 N .\\
(i) Calculate $F$ and find the angle which the resultant makes with the 8 N force.
A third force of magnitude $E \mathrm {~N}$, acting in the same plane as the two original forces, is now applied at the point $O$. The three forces of magnitudes $E N , F N$ and $8 N$ are in equilibrium.\\
(ii) State the value of $E$ and the angle between the directions of the $E \mathrm {~N}$ and 8 N forces.
\hfill \mbox{\textit{OCR M1 2012 Q1 [6]}}