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MATHEMATICS 9709

Cambridge International AS and A Level

Name of student Date
Adm. number Year/grade Stream
Subject Mechanics 1 (M1) Variant(s) P41, P42, P43
Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 7 Total
Marks 4 5 7 7 6 8 14 51
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject.
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Question 1 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 2 Code: 9709/43/O/N/13/1, Topic: -

A particle moves up a line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=0.28$. The coefficient of friction between the particle and the plane is $\frac{1}{3}$.

$\text{(i)}$ Show that the acceleration of the particle is $-6 \mathrm{~m} \mathrm{~s}^{-2}$. $[3]$

$\text{(ii)}$ Given that the particle's initial speed is $5.4 \mathrm{~m} \mathrm{~s}^{-1}$, find the distance that the particle travels up the plane. $[2]$

Question 3 Code: 9709/43/O/N/10/3, Topic: -

 

A small smooth pulley is fixed at the highest point $A$ of a cross-section $A B C$ of a triangular prism. Angle $A B C=90^{\circ}$ and angle $B C A=30^{\circ}$. The prism is fixed with the face containing $B C$ in contact with a horizontal surface. Particles $P$ and $Q$ are attached to opposite ends of a light inextensible string, which passes over the pulley. The particles are in equilibrium with $P$ hanging vertically below the pulley and $Q$ in contact with $A C$. The resultant force exerted on the pulley by the string is $3 \sqrt{3} \mathrm{~N}$ (see diagram).

$\text{(i)}$ Show that the tension in the string is $3 \mathrm{~N}$. $[2]$

The coefficient of friction between $Q$ and the prism is $0.75$.

$\text{(ii)}$ Given that $Q$ is in limiting equilibrium and on the point of moving upwards, find its mass. $[5]$

Question 4 Code: 9709/42/M/J/11/3, Topic: -

 

The velocity-time graph shown models the motion of a parachutist falling vertically. There are four stages in the motion:

$\circ$ falling freely with the parachute closed,

$\circ$ decelerating at a constant rate with the parachute open,

$\circ$ falling with constant speed with the parachute open,

$\circ$ coming to rest instantaneously on hitting the ground.

$\text{(i)}$ Show that the total distance fallen is $1048 \mathrm{~m}$. $[2]$

The weight of the parachutist is $850 \mathrm{~N}$.

$\text{(ii)}$ Find the upward force on the parachutist due to the parachute, during the second stage. $[5]$

Question 5 Code: 9709/42/O/N/17/3, Topic: -

A car travels along a straight road with constant acceleration. It passes through points $A, B$ and $C$. The car passes point $A$ with velocity $14 \mathrm{~m} \mathrm{~s}^{-1}$. The two sections $A B$ and $B C$ are of equal length. The times taken to travel along $A B$ and $B C$ are $5 \mathrm{~s}$ and $3 \mathrm{~s}$ respectively.

$\text{(i)}$ Write down an expression for the distance $A B$ in terms of the acceleration of the car. Write down a similar expression for the distance $A C$. Hence show that the acceleration of the car is $4 \mathrm{~m} \mathrm{~s}^{-2}$. $[4]$

$\text{(ii)}$ Find the speed of the car as it passes point $C$. $[2]$

Question 6 Code: 9709/43/M/J/10/5, Topic: -

A ball moves on the horizontal surface of a billiards table with deceleration of constant magnitude $d \mathrm{~m} \mathrm{~s}^{-2}$. The ball starts at $A$ with speed $1.4 \mathrm{~m} \mathrm{~s}^{-1}$ and reaches the edge of the table at $B, 1.2 \mathrm{~s}$ later, with speed $1.1 \mathrm{~m} \mathrm{~s}^{-1}$.

$\text{(i)}$ Find the distance $A B$ and the value of $d$. $[3]$

$A B$ is at right angles to the edge of the table containing $B$. The table has a low wall along each of its edges and the ball rebounds from the wall at $B$ and moves directly towards $A$. The ball comes to rest at $C$ where the distance $B C$ is $2 \mathrm{~m}$.

$\text{(ii)}$ Find the speed with which the ball starts to move towards $A$ and the time taken for the ball to travel from $B$ to $C$. $[3]$

$\text{(iii)}$ Sketch a velocity-time graph for the motion of the ball, from the time the ball leaves $A$ until it comes to rest at $C$, showing on the axes the values of the velocity and the time when the ball is at $A$, at $B$ and at $C$. $[2]$

Question 7 Code: 9709/42/M/J/18/7, Topic: -

 

As shown in the diagram, a particle $A$ of mass $1.6 \mathrm{~kg}$ lies on a horizontal plane and a particle $B$ of mass $2.4 \mathrm{~kg}$ lies on a plane inclined at an angle of $30^{\circ}$ to the horizontal. The particles are connected by a light inextensible string which passes over a small smooth pulley $P$ fixed at the top of the inclined plane. The distance $A P$ is $2.5 \mathrm{~m}$ and the distance of $B$ from the bottom of the inclined plane is $1 \mathrm{~m}$. There is a barrier at the bottom of the inclined plane preventing any further motion of $B$. The part $B P$ of the string is parallel to a line of greatest slope of the inclined plane. The particles are released from rest with both parts of the string taut.

$\text{(i)}$ Given that both planes are smooth, find the acceleration of $A$ and the tension in the string. $[5]$

$\text{(ii)}$ It is given instead that the horizontal plane is rough and that the coefficient of friction between $A$ and the horizontal plane is $0.2$. The inclined plane is smooth. Find the total distance travelled by $A$. $[9]$

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