| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string on smooth inclined plane |
| Difficulty | Standard +0.3 This is a straightforward M3 elastic string problem requiring standard application of Hooke's law, resolution of forces on an incline, and Newton's second law. The calculation involves finding the weight component, spring tension (with compression given), and applying F=ma. While it requires multiple steps and careful handling of the compression case, it follows a standard textbook template with no novel insight required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03d Newton's second law: 2D vectors6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| HL: \(T = \frac{20 \times 0.4}{2} = 4\) | M1 A1 | accept \(-4\) |
| \(mg\sin\alpha + T = ma\) | M1 A1 | |
| \(0.8g \times 0.6 + 4 = 0.8a\) | M1 | |
| \(a = 10.88 \approx 10.9 \text{ ms}^{-2}\) | A1 | accept 11 |
| Total | [6] |
# Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| HL: $T = \frac{20 \times 0.4}{2} = 4$ | M1 A1 | accept $-4$ |
| $mg\sin\alpha + T = ma$ | M1 A1 | |
| $0.8g \times 0.6 + 4 = 0.8a$ | M1 | |
| $a = 10.88 \approx 10.9 \text{ ms}^{-2}$ | A1 | accept 11 |
| **Total** | **[6]** | |
---1.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{fecee25b-e5d9-4669-89a1-6ae445090126-2_336_624_306_683}
\end{center}
\end{figure}
A particle of mass 0.8 kg is attached to one end of a light elastic spring, of natural length 2 m and modulus of elasticity 20 N . The other end of the spring is attached to a fixed point $O$ on a smooth plane which is inclined at an angle $\alpha$ to the horizontal, where tan $\alpha = \frac { 3 } { 4 }$. The particle is held on the plane at a point which is 1.6 m down a line of greatest slope of the plane from $O$, as shown in Figure 1. The particle is then released from rest.
Find the initial acceleration of the particle.\\
(Total 6 marks)\\
\hfill \mbox{\textit{Edexcel M3 2005 Q1 [6]}}