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

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 | Total |
---|---|---|---|---|---|---|---|

Marks | 6 | 5 | 5 | 6 | 6 | 8 | 36 |

Score |

Question 1 Code: 9709/42/M/J/19/1, Topic: -

Coplanar forces of magnitudes $40 \mathrm{~N}, 32 \mathrm{~N}, P \mathrm{~N}$ and $17 \mathrm{~N}$ act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of $P$ and $\theta$. $[6]$

Question 2 Code: 9709/41/M/J/11/2, Topic: -

A load of mass $1250 \mathrm{~kg}$ is raised by a crane from rest on horizontal ground, to rest at a height of $1.54 \mathrm{~m}$ above the ground. The work done against the resistance to motion is $5750 \mathrm{~J}$.

$\text{(i)}$ Find the work done by the crane. $[3]$

$\text{(ii)}$ Assuming the power output of the crane is constant and equal to $1.25 \mathrm{~kW}$, find the time taken to raise the load. $[2]$

Question 3 Code: 9709/41/M/J/20/2, Topic: -

A car of mass $1800 \mathrm{~kg}$ is towing a trailer of mass $400 \mathrm{~kg}$ along a straight horizontal road. The car and trailer are connected by a light rigid tow-bar. The car is accelerating at $1.5 \mathrm{~m} \mathrm{~s}^{-2}.$ There are constant resistance forces of $250 \mathrm{~N}$ on the car and $100 \mathrm{~N}$ on the trailer.

$\text{(a)}$ Find the tension in the tow-bar. $[2]$

$\text{(b)}$ Find the power of the engine of the car at the instant when the speed is $20 \mathrm{~m} \mathrm{~s}^{-1}$. $[3]$

Question 4 Code: 9709/42/M/J/21/4, Topic: -

A particle of mass $12 \mathrm{~kg}$ is stationary on a rough plane inclined at an angle of $25^{\circ}$ to the horizontal. A pulling force of magnitude $P \mathrm{~N}$ acts at an angle of $8^{\circ}$ above a line of greatest slope of the plane. This force is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is $0.3$.

Find the greatest possible value of $P$. $[6]$

Question 5 Code: 9709/43/M/J/21/4, Topic: -

A particle is projected vertically upwards with speed $u \mathrm{~m} \mathrm{~s}^{-1}$ from a point on horizontal ground. After 2 seconds, the height of the particle above the ground is $24 \mathrm{~m}$.

$\text{(a)}$ Show that $u=22$. $[2]$

$\text{(b)}$ The height of the particle above the ground is more than $h \mathrm{~m}$ for a period of $3.6 \mathrm{~s}$.

Find $\mathrm{h}$. $[4]$

Question 6 Code: 9709/41/M/J/12/5, Topic: -

The diagram shows the vertical cross-section $O A B$ of a slide. The straight line $A B$ is tangential to the curve $O A$ at $A$. The line $A B$ is inclined at $\alpha$ to the horizontal, where $\sin \alpha=0.28$. The point $O$ is $10 \mathrm{~m}$ higher than $B$, and $A B$ has length $10 \mathrm{~m}$ (see diagram). The part of the slide containing the curve $O A$ is smooth and the part containing $A B$ is rough. A particle $P$ of mass $2 \mathrm{~kg}$ is released from rest at $O$ and moves down the slide.

$\text{(i)}$ Find the speed of $P$ when it passes through $A$. $[3]$

The coefficient of friction between $P$ and the part of the slide containing $A B$ is $\frac{1}{12}$. Find

$\text{(ii)}$ the acceleration of $P$ when it is moving from $A$ to $B$, $[3]$

$\text{(iii)}$ the speed of $P$ when it reaches $B$. $[2]$