| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string with compression (spring) |
| Difficulty | Standard +0.3 This is a standard M3 elastic spring problem requiring Hooke's law for equilibrium in part (a) and energy conservation in part (b). Both parts follow routine procedures taught in mechanics modules, with straightforward application of formulas and no novel problem-solving insight required. Slightly easier than average due to clear setup and standard method. |
| 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 principle |
\begin{enumerate}
\item A particle $P$ of mass 0.5 kg is attached to one end of a light elastic spring, of natural length 1.2 m and modulus of elasticity $\lambda$ newtons. The other end of the spring is attached to a fixed point $A$ on a ceiling. The particle is hanging freely in equilibrium at a distance 1.5 m vertically below $A$.\\
(a) Find the value of $\lambda$.
\end{enumerate}
The particle is now raised to the point $B$, where $B$ is vertically below $A$ and $A B = 0.8 \mathrm {~m}$. The spring remains straight. The particle is released from rest and first comes to instantaneous rest at the point $C$.\\
(b) Find the distance $A C$.\\
\hfill \mbox{\textit{Edexcel M3 2015 Q1 [7]}}