CIE May 2021 9709 Mechanics Paper 43 (pdf)
- Particles P of mass 0.4 kg and Q of mass 0.5 kg are free to move on a smooth horizontal plane. P and
Q are moving directly towards each other with speeds 2.5 m s−1
and 1.5 m s−1
respectively. After P
and Q collide, the speed of Q is twice the speed of P.
Find the two possible values of the speed of P after the collision
- A cyclist is travelling along a straight horizontal road. She is working at a constant rate of 150 W. At
an instant when her speed is 4 m s−1, her acceleration is 0.25 m s−2. The resistance to motion is 20 N.
(a) Find the total mass of the cyclist and her bicycle
The cyclist comes to a straight hill inclined at an angle 1 above the horizontal. She ascends the hill at
constant speed 3 m s−1. She continues to work at the same rate as before and the resistance force is
(b) Find the value of θ.
- Four coplanar forces act at a point. The magnitudes of the forces are 20 N, 30 N, 40 N and F N. The
directions of the forces are as shown in the diagram, where sin α ° = 0.28 and sin α ° = 0.6.
Given that the forces are in equilibrium, find F and θ.
- A particle is projected vertically upwards with speed μ m s−1
from a point on horizontal ground. After
2 seconds, the height of the particle above the ground is 24 m.
(a) Show that μ = 22.
(b) The height of the particle above the ground is more than h m for a period of 3.6 s.
- A car of mass 1400 kg is towing a trailer of mass 500 kg down a straight hill inclined at an angle of 5Å
to the horizontal. The car and trailer are connected by a light rigid tow-bar. At the top of the hill the
speed of the car and trailer is 20 m s−1
and at the bottom of the hill their speed is 30 m s−1.
(a) It is given that as the car and trailer descend the hill, the engine of the car does 150 000 J of work,
and there are no resistance forces.
Find the length of the hill.
(b) It is given instead that there is a resistance force of 100 N on the trailer, the length of the hill is
200 m, and the acceleration of the car and trailer is constant.
Find the tension in the tow-bar between the car and trailer.
- A particle moves in a straight line and passes through the point A at time t = 0. The velocity of the
particle at time ts after leaving A is vm s−1, where
v = 2t2 − 5t + 3.
(a) Find the times at which the particle is instantaneously at rest. Hence or otherwise find the
minimum velocity of the particle.
(b) Sketch the velocity-time graph for the first 3 seconds of motion.
(c) Find the distance travelled between the two times when the particle is instantaneously at rest
- A particle P of mass 0.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where
sin θ = 7/25. A horizontal force of magnitude 4 N, acting in the vertical plane containing a line of
greatest slope of the plane, is applied to P (see diagram). The particle is on the point of sliding up the
(a) Show that the coefficient of friction between the particle and the plane is 3/4.
The force acting horizontally is replaced by a force of magnitude 4 N acting up the plane parallel to a
line of greatest slope.
(b) Find the acceleration of P.
(c) Starting with P at rest, the force of 4 N parallel to the plane acts for 3 seconds and is then removed.
Find the total distance travelled until P comes to instantaneous rest.
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