| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Vertical elastic string: projected from equilibrium or other point |
| Difficulty | Standard +0.3 This is a standard three-part Hooke's law and energy conservation question. Part (i) is routine equilibrium (showing given result), part (ii) applies energy conservation with elastic PE in a straightforward manner, and part (iii) requires recognizing that slack occurs at natural length. All techniques are standard M2 material with no novel insight required, making it slightly easier than average. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
3 A light elastic string has natural length 0.8 m and modulus of elasticity 16 N . One end of the string is attached to a fixed point $O$, and a particle $P$ of mass 0.4 kg is attached to the other end of the string. The particle $P$ hangs in equilibrium vertically below $O$.\\
(i) Show that the extension of the string is 0.2 m .\\
$P$ is projected vertically downwards from the equilibrium position. $P$ first comes to instantaneous rest at the point where $O P = 1.4 \mathrm {~m}$.\\
(ii) Calculate the speed at which $P$ is projected.\\
(iii) Find the speed of $P$ at the first instant when the string subsequently becomes slack.
\hfill \mbox{\textit{CAIE M2 2014 Q3}}