| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Standard +0.3 This is a standard conical pendulum problem with straightforward application of circular motion formulas. Part (a) is simple unit conversion, part (b) requires resolving forces vertically (T cos 35° = mg), and part (c) uses horizontal force equation (T sin 35° = mrω²). All steps are routine M2 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks |
|---|---|
| 4 | m |
Question 4:
4
4 | m
8 An elastic string has natural length 1.5 metres and modulus of elasticity 120 newtons.
One end of the string is attached to a fixed point, A, on a rough plane inclined at 20(cid:2)
to the horizontal. The other end of the elastic string is attached to a particle of mass
4kg. The coefficient of friction between the particle and the plane is 0.8.
The three points, A, B and C, lie on a line of greatest slope.
The point C is x metres from A, as shown in the diagram. The particle is released
from rest at C and moves up the plane.
B
A
C
x
20(cid:2)
(a) Show that, as the particle moves up the plane, the frictional force acting on the
particle is 29.5N, correct to three significant figures.
[3 marks]
(b) The particle comes to rest for an instant at B, which is 2 metres from A.
The particle then starts to move back towards A.
(i) Find x.
[8 marks]
(ii) Find the acceleration of the particle as it starts to move back towards A.
[4 marks]
PMT
Donotwrite
19 outsidethe
box
QUESTION Answer space for question 8
PART
REFERENCE
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
.............................................................................................................................................................
END OF QUESTIONS
(19)
P/Jun14/MM2B
PMT
Donotwrite
20 outsidethe
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Copyrightª2014AQAanditslicensors. Allrightsreserved.
(20)
P/Jun14/MM2BA particle, of mass 0.8 kg, is attached to one end of a light inextensible string. The other end of the string is attached to the fixed point $O$. The particle is set in motion, so that it moves in a horizontal circle at constant speed, with the string at an angle of $35°$ to the vertical. The centre of this circle is vertically below $O$, as shown in the diagram.
\includegraphics{figure_4}
The particle moves in a horizontal circle and completes 20 revolutions each minute.
\begin{enumerate}[label=(\alph*)]
\item Find the angular speed of the particle in radians per second. [2 marks]
\item Find the tension in the string. [3 marks]
\item Find the radius of the horizontal circle. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2014 Q4 [9]}}