| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Resultant of three coplanar forces |
| Difficulty | Easy -1.2 This is a straightforward M1 mechanics question requiring only basic vector addition (adding components) and then using Pythagoras and inverse tangent to find magnitude and direction. It's routine bookwork with no problem-solving element, making it easier than average A-level questions overall. |
| Spec | 3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | \(X = 5\), \(Y = 12\) | B1 |
| 1(i) | B1 | |
| 1(ii) | \(R^2 = 5^2 + 12^2\) | [2] |
| 1(ii) | Magnitude is 13 N | M1 |
| 1(ii) | \(\tan\theta = 12/5\) | A1 |
| 1(ii) | Angle is 67.4° | M1 |
| 1(ii) | [4] |
1(i) | $X = 5$, $Y = 12$ | B1 | $X=5$ B0. Both may be seen/implied in (ii)
1(i) | | B1 | No evidence for which value is $X$ or $Y$ available from (ii) award B1 for the pair of values 5 and 12 irrespective of order
1(ii) | $R^2 = 5^2 + 12^2$ | [2] |
1(ii) | Magnitude is 13 N | M1 | For using $R^2 = X^2 + Y^2$
1(ii) | $\tan\theta = 12/5$ | A1 | Allow 13 from $X=5$
1(ii) | Angle is 67.4° | M1 | For using correct angle in a trig expression
1(ii) | | [4] | SR: $p=14.9$ and $Q=11.4$ giving $R=13±0.1$ B2, Angle = $67.5±/0.5$ B21\\
\includegraphics[max width=\textwidth, alt={}, center]{ae5d1e27-5853-48aa-9046-86ce1c1a154a-2_415_823_264_660}
Two horizontal forces $\mathbf { P }$ and $\mathbf { Q }$ act at the origin O of rectangular coordinates Oxy (see diagram). The components of $\mathbf { P }$ in the $x$ - and $y$-directions are 14 N and 5 N respectively. The components of $\mathbf { Q }$ in the $x$ - and $y$-directions are - 9 N and 7 N respectively.\\
(i) Write down the components, in the $x$ - and $y$-directions, of the resultant of $\mathbf { P }$ and $\mathbf { Q }$.\\
(ii) Hence find the magnitude of this resultant, and the angle the resultant makes with the positive $x$-axis.
\hfill \mbox{\textit{OCR M1 2007 Q1 [6]}}