| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2002 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Single particle, Newton's second law – vector (2D forces) |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question testing basic vector addition, Newton's second law, and constant acceleration kinematics. All parts follow standard procedures: (a) add force vectors, (b) use arctangent for angle, (c) apply F=ma, (d) use v=u+at then find magnitude. No problem-solving insight required, just routine application of formulas with 11 marks total spread across simple steps. |
| Spec | 1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.03a Force: vector nature and diagrams3.03d Newton's second law: 2D vectors |
| Answer | Marks |
|---|---|
| \(F = (6i + 2j) + (3i - 5j) = (9i - 3j)\text{ N}\) | B1 (1) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\phi = 108.4°\) | M1 A1 (E) | A1 (3) |
| Answer | Marks |
|---|---|
| \(F = ma'' \Rightarrow a = (3i - j)\text{ m s}^{-2}\) | M1 A1 (E) (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Speed \(= \sqrt{(4^2 + 1^2)} \simeq 4.12\text{ m s}^{-1}\) | M1, M1, A1 (a) | M1 A1 (5) (11) |
## Part (a)
$F = (6i + 2j) + (3i - 5j) = (9i - 3j)\text{ N}$ | B1 (1)
## Part (b)
$\tan\theta = \frac{3}{9} \Rightarrow \theta \simeq 71.6°$
$\phi = 108.4°$ | M1 A1 (E) | A1 (3)
## Part (c)
$F = ma'' \Rightarrow a = (3i - j)\text{ m s}^{-2}$ | M1 A1 (E) (2)
## Part (d)
$v = (-2\xi + j) + 2(3\xi - j) = 4\xi - j$
Speed $= \sqrt{(4^2 + 1^2)} \simeq 4.12\text{ m s}^{-1}$ | M1, M1, A1 (a) | M1 A1 (5) (11)
---A particle $P$, of mass 3 kg, moves under the action of two constant forces (6$\mathbf{i}$ + 2$\mathbf{j}$) N and (3$\mathbf{i}$ - 5$\mathbf{j}$) N.
\begin{enumerate}[label=(\alph*)]
\item Find, in the form ($a\mathbf{i}$ + $b\mathbf{j}$) N, the resultant force $\mathbf{F}$ acting on $P$. [1]
\item Find, in degrees to one decimal place, the angle between $\mathbf{F}$ and $\mathbf{j}$. [3]
\item Find the acceleration of $P$, giving your answer as a vector. [2]
\end{enumerate}
The initial velocity of $P$ is (-2$\mathbf{i}$ + $\mathbf{j}$) m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find, to 3 significant figures, the speed of $P$ after 2 s. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2002 Q6 [11]}}