| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2007 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done by constant force - vector setup |
| Difficulty | Standard +0.3 This is a straightforward work-energy problem requiring calculation of displacement vector, dot product for work done, and application of work-energy theorem. All steps are standard M5 techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(\mathbf{d} = \mathbf{AB} = 3\mathbf{i} + \mathbf{j} - 5\mathbf{k}\) | B1 | |
| \(\frac{1}{2}(0.5)v^2 = \mathbf{F}\cdot\mathbf{d} = (4\mathbf{i}+7\mathbf{j}+2\mathbf{k})\cdot(3\mathbf{i}+\mathbf{j}-5\mathbf{k})\) | M1 A1 | |
| \(v = 6 \text{ m s}^{-1}\) | A1 | (4) |
## Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| $\mathbf{d} = \mathbf{AB} = 3\mathbf{i} + \mathbf{j} - 5\mathbf{k}$ | B1 | |
| $\frac{1}{2}(0.5)v^2 = \mathbf{F}\cdot\mathbf{d} = (4\mathbf{i}+7\mathbf{j}+2\mathbf{k})\cdot(3\mathbf{i}+\mathbf{j}-5\mathbf{k})$ | M1 A1 | |
| $v = 6 \text{ m s}^{-1}$ | A1 | **(4)** |
---\begin{enumerate}
\item A bead of mass 0.5 kg is threaded on a smooth straight wire. The only forces acting on the bead are a constant force ( $4 \mathbf { i } + 7 \mathbf { j } + 2 \mathbf { k }$ ) N and the normal reaction of the wire. The bead starts from rest at the point $A$ with position vector $( \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } ) \mathrm { m }$ and moves to the point $B$ with position vector $( 4 \mathbf { i } + 3 \mathbf { j } - 2 \mathbf { k } ) \mathrm { m }$.
\end{enumerate}
Find the speed of the bead when it reaches $B$.\\
(4)\\
\hfill \mbox{\textit{Edexcel M5 2007 Q1 [4]}}