$\require{\cancel}$ $\require{\stix[upint]}$

Qtn No.	1	2	3	4	5	6	Total
Marks	6	7	7	7	6	6	39
Score

Question 1 Code: 9709/41/M/J/12/3, Topic: -

 

A load of mass $160 \mathrm{~kg}$ is pulled vertically upwards, from rest at a fixed point $O$ on the ground, using a winding drum. The load passes through a point $A, 20 \mathrm{~m}$ above $O$, with a speed of $1.25 \mathrm{~m} \mathrm{~s}^{-1}$ (see diagram). Find, for the motion from $O$ to $A$,

$\text{(i)}$ the gain in the potential energy of the load, $[1]$

$\text{(ii)}$ the gain in the kinetic energy of the load. $[2]$

The power output of the winding drum is constant while the load is in motion.

$\text{(iii)}$ Given that the work done against the resistance to motion from $O$ to $A$ is $20 \mathrm{~kJ}$ and that the time taken for the load to travel from $O$ to $A$ is $41.7 \mathrm{~s}$, find the power output of the winding drum. $[3]$

Question 2 Code: 9709/42/M/J/12/3, Topic: -

A particle $P$ moves in a straight line, starting from the point $O$ with velocity $2 \mathrm{~m} \mathrm{~s}^{-1}$. The acceleration of $P$ at time $t \mathrm{~s}$ after leaving $O$ is $2 t^{\frac{2}{3}} \mathrm{~m} \mathrm{~s}^{-2}$.

$\text{(i)}$ Show that $t^{\frac{5}{3}}=\frac{5}{6}$ when the velocity of $P$ is $3 \mathrm{~m} \mathrm{~s}^{-1}$. $[4]$

$\text{(ii)}$ Find the distance of $P$ from $O$ when the velocity of $P$ is $3 \mathrm{~ms}^{-1}$. $[3]$

Question 3 Code: 9709/43/M/J/12/3, Topic: -

A particle $P$ travels from a point $O$ along a straight line and comes to instantaneous rest at a point $A$. The velocity of $P$ at time $t \mathrm{~s}$ after leaving $O$ is $v \mathrm{~m} \mathrm{~s}^{-1}$, where $v=0.027\left(10 t^{2}-t^{3}\right)$. Find

$\text{(i)}$ the distance $O A$, $[4]$

$\text{(ii)}$ the maximum velocity of $P$ while moving from $O$ to $A$. $[3]$

Question 4 Code: 9709/41/O/N/12/3, Topic: -

 

A particle $P$ of mass $0.5 \mathrm{~kg}$ rests on a rough plane inclined at angle $\alpha$ to the horizontal, where $\sin \alpha=0.28$. A force of magnitude $0.6 \mathrm{~N}$, acting upwards on $P$ at angle $\alpha$ from a line of greatest slope of the plane, is just sufficient to prevent $P$ sliding down the plane (see diagram). Find

$\text{(i)}$ the normal component of the contact force on $P$, $[2]$

$\text{(ii)}$ the frictional component of the contact force on $P$, $[3]$

$\text{(iii)}$ the coefficient of friction between $P$ and the plane. $[2]$

Question 5 Code: 9709/42/O/N/12/3, Topic: -

A car travels along a straight road with constant acceleration $a \mathrm{~m} \mathrm{~s}^{-2}$. It passes through points $A, B$ and $C$; the time taken from $A$ to $B$ and from $B$ to $C$ is $5 \mathrm{~s}$ in each case. The speed of the car at $A$ is $u \mathrm{~m} \mathrm{~s}^{-1}$ and the distances $A B$ and $B C$ are $55 \mathrm{~m}$ and $65 \mathrm{~m}$ respectively. Find the values of $a$ and $u$. $[6]$

Question 6 Code: 9709/43/O/N/12/3, Topic: -

A particle $P$ is projected vertically upwards, from a point $O$, with a velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$. The point $A$ is the highest point reached by $P$. Find

$\text{(i)}$ the speed of $P$ when it is at the mid-point of $O A$, $[4]$

$\text{(ii)}$ the time taken for $P$ to reach the mid-point of $O A$ while moving upwards. $[2]$