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ELOUISE STIDHAM

Cambridge International AS and A Level

Name of student ELOUISE STIDHAM Date
Adm. number 0 Year/grade Stream
Subject Mechanics 2 (M2) Variant(s) P41, P42, P43
Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 9 7 9 7 7 9 48
Score

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Question 1 Code: 9709/51/M/J/12/5, Topic: -

A particle $P$ of mass $0.4 \mathrm{~kg}$ is released from rest at the top of a smooth plane inclined at $30^{\circ}$ to the horizontal. The motion of $P$ down the slope is opposed by a force of magnitude $0.6 x \mathrm{~N}$, where $x \mathrm{~m}$ is the distance $P$ has travelled down the slope. $P$ comes to rest before reaching the foot of the slope. Calculate

$\text{(i)}$ the greatest speed of $P$ during its motion, $[7]$

$\text{(ii)}$ the distance travelled by $P$ during its motion. $[2]$

Question 2 Code: 9709/52/M/J/12/5, Topic: -

A ball is projected with velocity $25 \mathrm{~m} \mathrm{~s}^{-1}$ at an angle of $70^{\circ}$ above the horizontal from a point $O$ on horizontal ground. The ball subsequently bounces once on the ground at a point $P$ before landing at a point $Q$ where it remains at rest. The distance $P Q$ is $17.1 \mathrm{~m}$.

$\text{(i)}$ Calculate the time taken by the ball to travel from $O$ to $P$ and the distance $O P$. $[3]$

$\text{(ii)}$ Given that the horizontal component of the velocity of the ball does not change at $P$, calculate the speed of the ball when it leaves $P$. $[4]$

Question 3 Code: 9709/53/M/J/12/5, Topic: -

A light elastic string has natural length $3 \mathrm{~m}$ and modulus of elasticity $45 \mathrm{~N}$. A particle $P$ of mass $0.6 \mathrm{~kg}$ is attached to the mid-point of the string. The ends of the string are attached to fixed points $A$ and $B$ which lie on a line of greatest slope of a smooth plane inclined at $30^{\circ}$ to the horizontal. The distance $A B$ is $4 \mathrm{~m}$, and $A$ is higher than $B$.

$\text{(i)}$ Calculate the distance $A P$ when $P$ rests on the slope in equilibrium. $[3]$

$P$ is released from rest at the point between $A$ and $B$ where $A P=2.5 \mathrm{~m}$.

$\text{(ii)}$ Find the maximum speed of $P$. $[4]$

$\text{(iii)}$ Show that $P$ is at rest when $A P=1.6 \mathrm{~m}$. $[2]$

Question 4 Code: 9709/51/O/N/12/5, Topic: -

A particle $P$ is projected with speed $30 \mathrm{~m} \mathrm{~s}^{-1}$ at an angle of $60^{\circ}$ above the horizontal from a point $O$ on horizontal ground. For the instant when the speed of $P$ is $17 \mathrm{~m} \mathrm{~s}^{-1}$ and increasing,

$\text{(i)}$ show that the vertical component of the velocity of $P$ is $8 \mathrm{~m} \mathrm{~s}^{-1}$ downwards, $[2]$

$\text{(ii)}$ calculate the distance of $P$ from $O$. $[5]$

Question 5 Code: 9709/52/O/N/12/5, Topic: -

Question 6 Code: 9709/53/O/N/12/5, Topic: -

A small ball $B$ of mass $0.2 \mathrm{~kg}$ is attached to fixed points $P$ and $Q$ by two light inextensible strings of equal length. $P$ is vertically above $Q$, the strings are taut and each is inclined at $60^{\circ}$ to the vertical. $B$ moves with constant speed in a horizontal circle of radius $0.6 \mathrm{~m}$.

$\text{(i)}$ Given that the tension in the string $P B$ is $7 \mathrm{~N}$, calculate $[2]$

$\text{(a)}$ the tension in string $Q B$,

$\text{(b)}$ the speed of $B$. $[3]$

$\text{(ii)}$ Given instead that $B$ is moving with angular speed $7 \mathrm{rad} \mathrm{s}^{-1}$, calculate the tension in the string $Q B$. $[4]$

Worked solutions: P1, P3 & P6 (S1)

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