CASE STUDY 1
1. A plane takes off from a level runway with two gliders in tow, one behind the other. The first glider has a mass of 1600 kg and the second a mass of 800 kg. The frictional drag may be assumed as constant and equal to 2000 N on each glider. The towrope between the first glider and the plane can withstand a tension of 10 000 N.
(a) If a velocity of 40 m/s is required for takeoff, how long a runway is needed?
(b) How strong must the towrope between the two gliders be?
20 Marks
2. A small boy pulls his wagon, of mass 24 kg, giving it a horizontal acceleration of 1.5 m/s2. If the wagon’s handle makes an angle of 40° with the ground while the boy is pulling on it, and there is a frictional force of 6.0 N opposing the wagon’s motion, with what force is he pulling on the handle of the wagon? 15 marks
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Determine the moment of inertia of the shaded area shown with respect to each of the coordinate axes. 15 marks
CASE STUDY 2
- You have determined the following results when doing an investigation. Using proportioning techniques, find the new value for the centripetal force.
- marks
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(i) A speedboat is pulling two water skiers, using two ropes attached to the back of the boat. Each rope makes an angle of 30° on either side of the boat’s axis. The force exerted by each rope is 400 N. If the boat is moving in a straight line at constant speed, what force must it be exerting to keep the pair of skiers moving?
(ii) A block of mass 2.0 kg is placed on a smooth plane, inclined to the horizontal at an angle of 15°. The force of
gravity acting straight down on the block is 20 N.
(a) What is the acceleration of the block down the plane?
(b) How far up the plane was the block released, if it took 1.5 s to reach the bottom after it was released from rest?
(c) What is the force of gravity acting on a 1000 kg car resting on Earth? 20 marks
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An empty railway flatcar of mass 15 000 kg is being pulled along a smooth, horizontal track by a tractor travelling on a road parallel to the track. The rope joining the tractor and the flatcar makes an angle of 25° with the track.
(a) If the acceleration of the flatcar is 0.80 m/s2, what is the force exerted by the rope on the flatcar?
(b) Why does the flatcar have no sideways acceleration? A sideways force is exerted by the rope!
