| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2021 |
| Session | September |
| Marks | 7 |
| Topic | Vectors Introduction & 2D |
| Type | Forces in equilibrium (find unknowns) |
| Difficulty | Easy -1.3 This is a straightforward mechanics question testing basic equilibrium and vector addition. Part (a) requires simple addition of components and setting equal to zero (2 marks). Parts (b) and (c) involve standard magnitude and angle calculations using Pythagoras and arctangent. All techniques are routine with no problem-solving insight required, making it easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors3.03b Newton's first law: equilibrium3.03d Newton's second law: 2D vectors |
A particle $P$ is acted upon by three forces $\mathbf{F}_1$, $\mathbf{F}_2$ and $\mathbf{F}_3$ given by $\mathbf{F}_1 = (6\mathbf{i} - 4\mathbf{j}) \text{ N}$, $\mathbf{F}_2 = (-3\mathbf{i} + 9\mathbf{j}) \text{ N}$ and $\mathbf{F}_3 = (a\mathbf{i} + b\mathbf{j}) \text{ N}$, where $a$ and $b$ are constants. Given that $P$ is in equilibrium,
\begin{enumerate}[label=(\alph*)]
\item find the value of $a$ and the value of $b$. [2]
\end{enumerate}
The force $\mathbf{F}_3$ is now removed. The resultant of $\mathbf{F}_1$ and $\mathbf{F}_2$ is $\mathbf{R}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the magnitude of $\mathbf{R}$. [3]
\item Find the angle, to $0.1°$, that $\mathbf{R}$ makes with $\mathbf{i}$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Mechanics 2021 Q2 [7]}}