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### MATHEMATICS 9709

#### Cambridge International AS and A Level

 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

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions 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$\theta$.$$Question 2 Code: 9709/41/M/J/11/2, Topic: - A load of mass$1250 \mathrm{~kg}$is raised by a crane from rest on horizontal ground, to rest at a height of$1.54 \mathrm{~m}$above the ground. The work done against the resistance to motion is$5750 \mathrm{~J}$.$\text{(i)}$Find the work done by the crane.$\text{(ii)}$Assuming the power output of the crane is constant and equal to$1.25 \mathrm{~kW}$, find the time taken to raise the load.$$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.$\text{(b)}$Find the power of the engine of the car at the instant when the speed is$20 \mathrm{~m} \mathrm{~s}^{-1}$.$$Question 4 Code: 9709/42/M/J/21/4, Topic: - A particle of mass$12 \mathrm{~kg}$is stationary on a rough plane inclined at an angle of$25^{\circ}$to the horizontal. A pulling force of magnitude$P \mathrm{~N}$acts at an angle of$8^{\circ}$above a line of greatest slope of the plane. This force is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is$0.3$. Find the greatest possible value of$P$.$$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$u=22$.$\text{(b)}$The height of the particle above the ground is more than$h \mathrm{~m}$for a period of$3.6 \mathrm{~s}$. Find$\mathrm{h}$.$$Question 6 Code: 9709/41/M/J/12/5, Topic: - The diagram shows the vertical cross-section$O A B$of a slide. The straight line$A B$is tangential to the curve$O A$at$A$. The line$A B$is inclined at$\alpha$to the horizontal, where$\sin \alpha=0.28$. The point$O$is$10 \mathrm{~m}$higher than$B$, and$A B$has length$10 \mathrm{~m}$(see diagram). The part of the slide containing the curve$O A$is smooth and the part containing$A B$is rough. A particle$P$of mass$2 \mathrm{~kg}$is released from rest at$O$and moves down the slide.$\text{(i)}$Find the speed of$P$when it passes through$A$.$$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$B$,$\text{(iii)}$the speed of$P$when it reaches$B$.$\$

Worked solutions: P1, P3 & P6 (S1)

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