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This page covers Questions and Worked Solutions for CIE Mechanics Paper 41 May/June 2020, 9709/41.

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CIE May 2020 9709 Mechanics Paper 41 (pdf)

- Three coplanar forces of magnitudes 100 N, 50 N and 50 N act at a point A, as shown in the diagram.
The value of cos α is 4/5.

Find the magnitude of the resultant of the three forces and state its direction - A car of mass 1800 kg is towing a trailer of mass 400 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 m s
^{−2}. There are constant resistance forces of 250 N on the car and 100 N on the trailer.

(a) Find the tension in the tow-bar

(b) Find the power of the engine of the car at the instant when the speed is 20 m s^{−1} - A particle P is projected vertically upwards with speed 5 m s
^{−1}from a point A which is 2.8 m above horizontal ground.

(a) Find the greatest height above the ground reached by P.

(b) Find the length of time for which P is at a height of more than 3.6 m above the ground - The diagram shows a ring of mass 0.1 kg threaded on a fixed horizontal rod. The rod is rough and the
coefficient of friction between the ring and the rod is 0.8. A force of magnitude T N acts on the ring
in a direction at 30° to the rod, downwards in the vertical plane containing the rod. Initially the ring
is at rest.

(a) Find the greatest value of T for which the ring remains at rest

(b) Find the acceleration of the ring when T = 3.

- A child of mass 35 kg is swinging on a rope. The child is modelled as a particle P and the rope
is modelled as a light inextensible string of length 4 m. Initially P is held at an angle of 45Å to the
vertical (see diagram).

(a) Given that there is no resistance force, find the speed of P when it has travelled half way along the circular arc from its initial position to its lowest point.

(b) It is given instead that there is a resistance force. The work done against the resistance force as P travels from its initial position to its lowest point is X J. The speed of P at its lowest point is 4 m s^{−1}.

Find X. - A particle moves in a straight line AB. The velocity vm s
^{−1}of the particle ts after leaving A is given by v = k(t^{2}− 10t + 21), where k is a constant. The displacement of the particle from A, in the direction towards B, is 2.85 m when t = 3 and is 2.4 m when t = 6.

(a) Find the value of k. Hence find an expression, in terms of t, for the displacement of the particle from A

(b) Find the displacement of the particle from A when its velocity is a minimum - A particle P of mass 0.3 kg, lying on a smooth plane inclined at 30° to the horizontal, is released from
rest. P slides down the plane for a distance of 2.5 m and then reaches a horizontal plane. There is no
change in speed when P reaches the horizontal plane. A particle Q of mass 0.2 kg lies at rest on the
horizontal plane 1.5 m from the end of the inclined plane (see diagram). P collides directly with Q.

(a) It is given that the horizontal plane is smooth and that, after the collision, P continues moving in the same direction, with speed 2 m s^{−1}.

Find the speed of Q after the collision

(b) It is given instead that the horizontal plane is rough and that when P and Q collide, they coalesce and move with speed 1.2 m s^{−1}.

Find the coefficient of friction between P and the horizontal plane

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