| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Standard +0.3 This is a standard circular motion problem requiring resolution of forces and application of F=mrω². Part (i) involves straightforward use of Pythagoras, vertical equilibrium, and the circular motion equation. Part (ii) requires recognizing that maximum tension occurs when the normal reaction becomes zero, which is a common textbook scenario. The geometry is simple and the problem-solving is routine for M2 level. |
| Spec | 6.05a Angular velocity: definitions6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks |
|---|---|
| (ii) | θ(= tan–10.45/0.6 = 36.87..) = 36.9° |
| Answer | Marks |
|---|---|
| ω = 4.71 rads–1 | B1 |
| Answer | Marks |
|---|---|
| A1 | 3 |
| 4 | Or tanθ = 3/4 |
Question 5:
--- 5 (i)
(ii) ---
5 (i)
(ii) | θ(= tan–10.45/0.6 = 36.87..) = 36.9°
0.4v2/0.6 = 5cosθ
v = 2.45ms–1
Tsinθ = 0.4g
T = 6.67N
0.4ω2 x 0.6 = 6.67cosθ
ω = 4.71 rads–1 | B1
M1
A1
M1
A1
M1
A1 | 3
4 | Or tanθ = 3/4
Or 6
2
Accept 0.66, 6 , 20/3
3
Accept 4.72 rads–1A small ball $B$ of mass 0.4 kg moves in a horizontal circle with centre $O$ and radius 0.6 m on a smooth horizontal surface. One end of a light inextensible string is attached to $B$; the other end of the string is attached to a fixed point 0.45 m vertically above $O$.
\begin{enumerate}[label=(\roman*)]
\item Given that the tension in the string is 5 N, calculate the speed of $B$. [3]
\item Find the greatest possible tension in the string for the motion, and the corresponding angular speed of $B$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2016 Q5 [7]}}