| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Easy -1.3 This is a straightforward mechanics question requiring only basic vector addition (adding components) and then using Pythagoras and inverse tangent to find magnitude and direction. It's a standard textbook exercise with no problem-solving insight needed, making it easier than average for A-level. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.01c Moment unit: N m3.03a Force: vector nature and diagrams |
**Question 6**
(i) $x = 7$ [B1]
$y = 24$ (award B1 only if not identified) [B1]
(ii) $r^2 = 7^2 + 24^2$ [M1]
Magnitude is $25$ N [A1]
$\tan\theta = \frac{24}{7}$ [M1]
Angle is $73.7°$ [A1]
**Total: 6 marks**6\\
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The diagram shows two horizontal forces $\mathbf { P }$ and $\mathbf { Q }$ acting at the origin $O$ of rectangular coordinates $O x y$. The components of $\mathbf { P }$ in the $x$ - and $y$-directions are 12 N and 17 N respectively. The components of $\mathbf { Q }$ in the $x$ - and $y$-directions are - 5 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, or otherwise, calculate the magnitude of this resultant and the angle the resultant makes with the positive $x$-axis.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2016 Q6 [6]}}