A ring of mass $$$0.3 \mathrm{~kg}$$$ is threaded on a horizontal rough rod. The coefficient of friction between the ring and the rod is $$$0.8$$$. A force of magnitude $$$8 \mathrm{~N}$$$ acts on the ring. This force acts at an angle of $$$10^{\circ}$$$ above the horizontal in the vertical plane containing the rod. Find the time taken for the ring to move, from rest, $$$0.6 \mathrm{~m}$$$ along the rod. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_42 Year：2021 Question No：3

Answer:

Resolving along or perpendicular to the rod
$ \begin{array}{l}
8 \sin 10+R=0.3 g \\
8 \cos 10-F=0.3 a \\
=0.8 R \quad[R=1.61081 \ldots, F=1.28865 \ldots] \\
{[a=21.966 \ldots]} \\
0.6=\frac{1}{2} \times 21.966 \times t^{2}
\end{array}
$
$t=0.234$ seconds
Alternative method for Question 3
Resolving perpendicular to the rod
$ 8 \sin 10+R=0.3 \mathrm{~g}
$
$ F=0.8 R \quad[R=1.61081 \ldots, F=1.28865 \ldots]
$

$8 \cos 10 \times 0.6=F \times 0.6+\frac{1}{2} \times 0.3 v^{2} \quad[v=5.134]$
$0.6=\frac{1}{2}(0+5.134) \times t$
$t=0.234$ seconds

Knowledge points:

4.1.1 identify the forces acting in a given situation； e.g. by drawing a force diagram.

4.1.2 understand the vector nature of force, and find and use components and resultants； Calculations are always required, not approximate solutions by scale drawing.

4.1.4 understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component

4.1.6 understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = nR or F G nR, as appropriate

4.2.4 use appropriate formulae for motion with constant acceleration in a straight line. （Questions may involve setting up more than one equation, using information about the motion of different particles.）

4.4.1 apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction, tension in an inextensible string and thrust in a connecting rod If any other forces resisting motion are to be considered (e.g. air resistance) this will be indicated in the question.

Answer:

Knowledge points:

Solution:

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