CAIE Mathematics (9709)

of greatest slope of an inclined plane. The top of the plane is at a vertical height of 1.6m above the level of the bottom of the plane. The speed of the block at the top of the plane is 2ms and the speed of the block at the bottom of the plane is 4ms Find the work done against the resistance to motion of the block.

2 N40Åmkg The diagram shows a smooth ring R, of massmkg, threaded on a light inextensible string. A horizontal force of magnitude 2N acts on vertical wall. The part ARof the string makes an angle of 30?with the vertical, the partBRmakes an angle of 40 ?with the vertical and the string is taut. The ring is in equilibrium. m.

30Å 120 N 10 kg A block of mass 10kg is at rest on a rough plane inclined at an angle of 30 ?to the horizontal. A force of 120N is applied to the block at an angle of 20 ?above a line of greatest slope (see diagram). There is a force resisting the motion of the block and 200J of work isdone against this force when the block has moved a distance of 5m up the plane from rest. Find the speed of the block when it has moved a distance of 5m upthe plane from rest.

4A particle Pof mass 0.2kg lies at rest on a rough horizontal plane. A horizontal force of 1.2N is applied to (a)Given that [3] travelled by Pin the third second of its motion.

5A particle Aof mass 0.5kg is projected vertically upwards from horizontal ground with speed 25ms (a)Find the speed of Awhen it reaches a height of 20m above the ground. [2] When Areaches a height of 20m, it collides with a particleBof mass 0.3kg which is moving downwards in the same vertical line as Awith speed 32.5ms . In the collision between the two particles, Bis brought to instantaneous rest. (b)Show that the velocity of Aimmediately after the collision is 4.5ms downwards.

(c)Find the time interval between AandBreaching the ground. You should assume thatAdoes not bounce when it reaches the ground.

6A railway engine of mass 120000kg is towing a coach of mass 60000kg up a straight track inclined at an angle of !to the horizontal where sin!=0.02. There is a light rigid coupling, parallel to the track, connecting the engine and coach. The driving force produced by the engine is 125000N and there are constant resistances to motion of 22000N on the engine and 13000N on the coach.

At an instant when the engine is travelling at 30ms , it comes to a section of track inclined upwards at an angle "to the horizontal. The power produced by the engine is now 4500000W and, as a result, the engine maintains a constant speed. ".

7A particle denoted byvms , where +1.8t The acceleration of Xis zero att=pandt=q, wherep<q. (a)Find the value of pand the value ofq. [4] It is given that the velocity of Xis zero att=14. (b)Find the velocities of Xatt=pand att=q, and hence sketch the velocity-time graph for the motion of

(c)Find the total distance travelled by Xbetweent=0 andt=15.

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