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Cambridge International AS and A Level

Name of student Date
Adm. number Year/grade Stream
Subject Mechanics 1 (M1) Variant(s) P42, P43
Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 4 4 6 6 7 11 38

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Question 1 Code: 9709/42/M/J/10/1, Topic: -


Question 2 Code: 9709/43/M/J/10/1, Topic: -


Three coplanar forces act at a point. The magnitudes of the forces are $5.5 \mathrm{~N}, 6.8 \mathrm{~N}$ and $7.3 \mathrm{~N}$, and the directions in which the forces act are as shown in the diagram. Given that the resultant of the three forces is in the same direction as the force of magnitude $6.8 \mathrm{~N}$, find the value of $\alpha$ and the magnitude of the resultant. $[4]$

Question 3 Code: 9709/42/M/J/21/2, Topic: -


Coplanar forces of magnitudes $34 \mathrm{~N}, 30 \mathrm{~N}$ and $26 \mathrm{~N}$ act at a point in the directions shown in the diagram.

Given that $\sin \alpha=\frac{5}{13}$ and $\sin \theta=\frac{8}{17}$, find the magnitude and direction of the resultant of the three forces. $[6]$

Question 4 Code: 9709/43/M/J/14/3, Topic: -


A particle $P$ of weight $1.4 \mathrm{~N}$ is attached to one end of a light inextensible string $S_{1}$ of length $1.5 \mathrm{~m}$, and to one end of another light inextensible string $S_{2}$ of length $1.3 \mathrm{~m}$. The other end of $S_{1}$ is attached to a wall at the point $0.9 \mathrm{~m}$ vertically above a point $O$ of the wall. The other end of $S_{2}$ is attached to the wall at the point $0.5 \mathrm{~m}$ vertically below $O$. The particle is held in equilibrium, at the same horizontal level as $O$, by a horizontal force of magnitude $2.24 \mathrm{~N}$ acting away from the wall and perpendicular to it (see diagram). Find the tensions in the strings. $[6]$

Question 5 Code: 9709/42/M/J/10/4, Topic: -

Question 6 Code: 9709/42/M/J/13/7, Topic: -


Particles $A$ of mass $0.26 \mathrm{~kg}$ and $B$ of mass $0.52 \mathrm{~kg}$ are attached to the ends of a light inextensible string. The string passes over a small smooth pulley $P$ which is fixed at the top of a smooth plane. The plane is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=\frac{16}{65}$ and $\cos \alpha=\frac{63}{65}. A$ is held at rest at a point $2.5$ metres from $P$, with the part $A P$ of the string parallel to a line of greatest slope of the plane. $B$ hangs freely below $P$ at a point $0.6 \mathrm{~m}$ above the floor (see diagram). $A$ is released and the particles start to move. Find

$\text{(i)}$ the magnitude of the acceleration of the particles and the tension in the string, $[5]$

$\text{(ii)}$ the speed with which $B$ reaches the floor and the distance of $A$ from $P$ when $A$ comes to instantaneous rest. $[6]$

Worked solutions: P1, P3 & P6 (S1)

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