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Cambridge International AS and A Level

Name of student GRADYACIFS Date
Adm. number Year/grade 1988 Stream Gradyacifs
Subject Mechanics 1 (M1) Variant(s) P41, P42, P43
Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 12 12 10 10 11 55

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Question 1 Code: 9709/41/M/J/15/7, Topic: -


Particles $A$ and $B$, of masses $0.3 \mathrm{~kg}$ and $0.7 \mathrm{~kg}$ respectively, are attached to the ends of a light inextensible string. Particle $A$ is held at rest on a rough horizontal table with the string passing over a smooth pulley fixed at the edge of the table. The coefficient of friction between $A$ and the table is $0.2$. Particle $B$ hangs vertically below the pulley at a height of $0.5 \mathrm{~m}$ above the floor (see diagram). The system is released from rest and $0.25 \mathrm{~s}$ later the string breaks. A does not reach the pulley in the subsequent motion. Find

$\text{(i)}$ the speed of $B$ immediately before it hits the floor, $[9]$

$\text{(ii)}$ the total distance travelled by $A$. $[3]$

Question 2 Code: 9709/42/M/J/15/7, Topic: -


A small ring $R$ is attached to one end of a light inextensible string of length $70 \mathrm{~cm}$. A fixed rough vertical wire passes through the ring. The other end of the string is attached to a point $A$ on the wire, vertically above $R$. A horizontal force of magnitude $5.6 \mathrm{~N}$ is applied to the point $J$ of the string $30 \mathrm{~cm}$ from $A$ and $40 \mathrm{~cm}$ from $R$. The system is in equilibrium with each of the parts $A J$ and $J R$ of the string taut and angle $A J R$ equal to $90^{\circ}$ (see diagram).

$\text{(i)}$ Find the tension in the part $A J$ of the string, and find the tension in the part $J R$ of the string. $[5]$

The ring $R$ has mass $0.2 \mathrm{~kg}$ and is in limiting equilibrium, on the point of moving up the wire.

$\text{(ii)}$ Show that the coefficient of friction between $R$ and the wire is $0.341$, correct to 3 significant figures. $[4]$

A particle of mass $m \mathrm{~kg}$ is attached to $R$ and $R$ is now in limiting equilibrium, on the point of moving down the wire.

$\text{(iii)}$ Given that the coefficient of friction is unchanged, find the value of $m$. $[3]$

Question 3 Code: 9709/41/O/N/15/7, Topic: -

A cyclist starts from rest at point $A$ and moves in a straight line with acceleration $0.5 \mathrm{~m} \mathrm{~s}^{-2}$ for a distance of $36 \mathrm{~m}$. The cyclist then travels at constant speed for $25 \mathrm{~s}$ before slowing down, with constant deceleration, to come to rest at point $B$. The distance $A B$ is $210 \mathrm{~m}$.

$\text{(i)}$ Find the total time that the cyclist takes to travel from $A$ to $B$. $[5]$

$24 \mathrm{~s}$ after the cyclist leaves point $A$, a car starts from rest from point $A$, with constant acceleration $4 \mathrm{~m} \mathrm{~s}^{-2}$, towards $B$. It is given that the car overtakes the cyclist while the cyclist is moving with constant speed.

$\text{(ii)}$ Find the time that it takes from when the cyclist starts until the car overtakes her. $[5]$

Question 4 Code: 9709/42/O/N/15/7, Topic: -

A car of mass $1600 \mathrm{~kg}$ moves with constant power $14 \mathrm{~kW}$ as it travels along a straight horizontal road. The car takes $25 \mathrm{~s}$ to travel between two points $A$ and $B$ on the road.

$\text{(i)}$ Find the work done by the car's engine while the car travels from $A$ to $B$. $[2]$

The resistance to the car's motion is constant and equal to $235 \mathrm{~N}$. The car has accelerations at $A$ and $B$ of $0.5 \mathrm{~m} \mathrm{~s}^{-2}$ and $0.25 \mathrm{~m} \mathrm{~s}^{-2}$ respectively. Find

$\text{(ii)}$ the gain in kinetic energy by the car in moving from $A$ to $B$, $[5]$

$\text{(iii)}$ the distance $A B$. $[3]$

Question 5 Code: 9709/43/O/N/15/7, Topic: -

A straight hill $A B$ has length $400 \mathrm{~m}$ with $A$ at the top and $B$ at the bottom and is inclined at an angle of $4^{\circ}$ to the horizontal. A straight horizontal road $B C$ has length $750 \mathrm{~m}$. A car of mass $1250 \mathrm{~kg}$ has a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ at $A$ when starting to move down the hill. While moving down the hill the resistance to the motion of the car is $2000 \mathrm{~N}$ and the driving force is constant. The speed of the car on reaching $B$ is $8 \mathrm{~m} \mathrm{~s}^{-1}$.

$\text{(i)}$ By using work and energy, find the driving force of the car. $[3]$

On reaching $B$ the car moves along the road $B C$. The driving force is constant and twice that when the car was on the hill. The resistance to the motion of the car continues to be $2000 \mathrm{~N}$. Find

$\text{(ii)}$ the acceleration of the car while moving from $B$ to $C$, $[3]$

$\text{(iii)}$ the power of the car's engine as the car reaches $C$. $[3]$

Worked solutions: P1, P3 & P6 (S1)

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