| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2016 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with elastic string or spring support |
| Difficulty | Challenging +1.8 This is a challenging Further Maths mechanics problem requiring geometric analysis to find the extended length of the elastic string, application of Hooke's law, and systematic use of equilibrium conditions (moments and forces). The geometry is non-trivial, requiring use of the cosine rule, and students must carefully resolve forces and take moments about an appropriate point. While the techniques are standard for FM students, the multi-step nature and geometric complexity place it well above average difficulty. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.02g 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 |
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The end $A$ of a uniform rod $A B$, of length $2 a$ and weight $W$, is freely hinged to a vertical wall. The end $B$ of the rod is attached to a light elastic string of natural length $\frac { 3 } { 2 } a$ and modulus of elasticity $3 W$. The other end of the string is attached to the point $C$ on the wall, where $C$ is vertically above $A$ and $A C = 2 a$. A particle of weight $2 W$ is attached to the rod at the point $D$, where $D B = \frac { 1 } { 2 } a$. The angle $A B C$ is equal to $\theta$ (see diagram). Show that $\cos \theta = \frac { 3 } { 4 }$ and find the tension in the string in terms of $W$.
Find the magnitude of the reaction force at the hinge.
\hfill \mbox{\textit{CAIE FP2 2016 Q11 EITHER}}