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Name of student | Date | ||||

Adm. number | Year/grade | Stream | |||

Subject | Mechanics 1 (M1) | Variant(s) | P41 | ||

Start time | Duration | Stop time |

Qtn No. | 1 | 2 | 3 | 4 | 5 | Total |
---|---|---|---|---|---|---|

Marks | 4 | 5 | 6 | 7 | 9 | 31 |

Score |

Question 1 Code: 9709/41/O/N/17/1, Topic: -

A block of mass $3 \mathrm{~kg}$ is initially at rest on a smooth horizontal floor. A force of $12 \mathrm{~N}$, acting at an angle of $25^{\circ}$ above the horizontal, is applied to the block. Find the distance travelled by the block in the first 5 seconds of its motion. $[4]$

Question 2 Code: 9709/41/O/N/10/2, Topic: -

A car of mass $600 \mathrm{~kg}$ travels along a horizontal straight road, with its engine working at a rate of $40 \mathrm{~kW}$. The resistance to motion of the car is constant and equal to $800 \mathrm{~N}$. The car passes through the point $A$ on the road with speed $25 \mathrm{~m} \mathrm{~s}^{-1}$. The car's acceleration at the point $B$ on the road is half its acceleration at $A$. Find the speed of the car at $B$. $[5]$

Question 3 Code: 9709/41/O/N/20/4, Topic: -

A particle $P$ moves in a straight line. It starts from rest at a point $O$ on the line and at time $t \mathrm{~s}$ after leaving $O$ it has acceleration $a \mathrm{~m} \mathrm{~s}^{-2}$, where $a=6 t-18$.

Find the distance $P$ moves before it comes to instantaneous rest. $[6]$

Question 4 Code: 9709/41/O/N/14/5, Topic: -

A small block $B$ of mass $0.25 \mathrm{~kg}$ is attached to the mid-point of a light inextensible string. Particles $P$ and $Q$, of masses $0.2 \mathrm{~kg}$ and $0.3 \mathrm{~kg}$ respectively, are attached to the ends of the string. The string passes over two smooth pulleys fixed at opposite sides of a rough table, with $B$ resting in limiting equilibrium on the table between the pulleys and particles $P$ and $Q$ and block $B$ are in the same vertical plane (see diagram).

$\text{(i)}$ Find the coefficient of friction between $B$ and the table. $[3]$

$Q$ is now removed so that $P$ and $B$ begin to move.

$\text{(ii)}$ Find the acceleration of $P$ and the tension in the part $P B$ of the string. $[6]$

Question 5 Code: 9709/41/O/N/20/6, Topic: -

A car of mass $1500 \mathrm{~kg}$ is pulling a trailer of mass $750 \mathrm{~kg}$ up a straight hill of length $800 \mathrm{~m}$ inclined at an angle of $\sin ^{-1} 0.08$ to the horizontal. The resistances to the motion of the car and trailer are $400 \mathrm{~N}$ and $200 \mathrm{~N}$ respectively. The car and trailer are connected by a light rigid tow-bar. The car and trailer have speed $30 \mathrm{~m} \mathrm{~s}^{-1}$ at the bottom of the hill and $20 \mathrm{~m} \mathrm{~s}^{-1}$ at the top of the hill.

$\text{(a)}$ Use an energy method to find the constant driving force as the car and trailer travel up the hill. $[5]$

After reaching the top of the hill the system consisting of the car and trailer travels along a straight level road. The driving force of the car's engine is $2400 \mathrm{~N}$ and the resistances to motion are unchanged.

$\text{(b)}$ Find the acceleration of the system and the tension in the tow-bar. $[4]$