| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Elastic string – horizontal circle on surface |
| Difficulty | Standard +0.3 Part (i) requires setting up two simultaneous equations using Hooke's law (T = λx/a), which is straightforward algebra. Part (ii) applies circular motion (T = mv²/r) with the found values. Standard multi-step application of formulas with no novel insight required, slightly above average due to the combination of elasticity and circular motion topics. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(4 = \frac{\lambda(1.6-a)}{a}\) | B1 | Use \(T = \left(\frac{\lambda x}{l}\right)\) twice |
| \(6 = \frac{\lambda(2-a)}{a}\) | B1 | |
| \(1.5 = \frac{(2-a)}{(1.6-a)}\) | M1 | Attempt to solve the simultaneous equations |
| \(0.4 = 0.5(a),\ a = 0.8\) | A1 | |
| \(\lambda = 4\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 4 \times \frac{1.1}{0.8}\ (= 5.5)\) | B1 | FT Use \(T = \frac{\lambda x}{L}\), ft candidates \(\lambda\) and \(a\) |
| \(5.5 = \frac{0.2v^2}{1.9}\) | M1 | Use Newton's Second Law horizontally |
| \(v = 7.23\ \text{ms}^{-1}\) | A1 |
## Question 5(i):
| $4 = \frac{\lambda(1.6-a)}{a}$ | B1 | Use $T = \left(\frac{\lambda x}{l}\right)$ twice |
| $6 = \frac{\lambda(2-a)}{a}$ | B1 | |
| $1.5 = \frac{(2-a)}{(1.6-a)}$ | M1 | Attempt to solve the simultaneous equations |
| $0.4 = 0.5(a),\ a = 0.8$ | A1 | |
| $\lambda = 4$ | A1 | |
## Question 5(ii):
| $T = 4 \times \frac{1.1}{0.8}\ (= 5.5)$ | B1 | FT Use $T = \frac{\lambda x}{L}$, ft candidates $\lambda$ and $a$ |
| $5.5 = \frac{0.2v^2}{1.9}$ | M1 | Use Newton's Second Law horizontally |
| $v = 7.23\ \text{ms}^{-1}$ | A1 | |
---5 A light elastic string has natural length $a \mathrm {~m}$ and modulus of elasticity $\lambda \mathrm { N }$. When the length of the string is 1.6 m the tension is 4 N . When the length of the string is 2 m the tension is 6 N .\\
(i) Find the values of $a$ and $\lambda$.\\
One end of the string is attached to a fixed point $O$ on a smooth horizontal surface. The other end of the string is attached to a particle $P$ of mass 0.2 kg . The particle $P$ moves with constant speed on the surface in a circle with centre $O$ and radius 1.9 m .\\
(ii) Find the speed of $P$.\\
\hfill \mbox{\textit{CAIE M2 2019 Q5 [8]}}