| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2002 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Horizontal elastic string on smooth surface |
| Difficulty | Standard +0.3 This is a standard M3 elastic strings question requiring energy conservation (part a) and Hooke's law with equation of motion (part b). The setup is straightforward with clear given values, and both parts follow routine procedures taught in M3 with no novel problem-solving required. Slightly above average difficulty due to being Further Maths content and requiring careful application of EPE formula, but otherwise a textbook exercise. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2} \times 0.2 \times 5^2 - \frac{1}{3} \times 0.2 \times u^2 = \frac{1}{3} \times \frac{20(0.5)^2}{1.5}\) | M1 A1 A1 | |
| \(u^2 = \frac{25}{3}\) | M1 | |
| \(u = 2.89 \text{ ms}^{-1}\) | A1 | (5) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2} \times 0.2 \times 5^2 - \frac{1}{3} \times 0.2 \times 1.5^2 = \frac{1}{3} \times \frac{20x^2}{1.5}\) | M1 A1 | |
| \(x^2 = 0.34125\) | M1 | |
| \(T = \frac{20x}{1.5} = 7.8 \text{ N}\) | M1 A1 | (5) |
## Part (a)
$\frac{1}{2} \times 0.2 \times 5^2 - \frac{1}{3} \times 0.2 \times u^2 = \frac{1}{3} \times \frac{20(0.5)^2}{1.5}$ | M1 A1 A1
$u^2 = \frac{25}{3}$ | M1
$u = 2.89 \text{ ms}^{-1}$ | A1 | (5)
## Part (b)
$\frac{1}{2} \times 0.2 \times 5^2 - \frac{1}{3} \times 0.2 \times 1.5^2 = \frac{1}{3} \times \frac{20x^2}{1.5}$ | M1 A1
$x^2 = 0.34125$ | M1
$T = \frac{20x}{1.5} = 7.8 \text{ N}$ | M1 A1 | (5)
**Total: (10 marks)**
---A light elastic string $AB$ of natural length 1.5 m has modulus of elasticity 20 N. The end $A$ is fixed to a point on a smooth horizontal table. A small ball $S$ of mass 0.2 kg is attached to the end $B$. Initially $S$ is at rest on the table with $AB = 1.5$ m. The ball $S$ is then projected horizontally directly away from $A$ with a speed of 5 m s$^{-1}$. By modelling $S$ as a particle,
\begin{enumerate}[label=(\alph*)]
\item find the speed of $S$ when $AS = 2$ m.
[5]
\end{enumerate}
When the speed of $S$ is 1.5 m s$^{-1}$, the string breaks.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the tension in the string immediately before the string breaks.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2002 Q4 [10]}}