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Transcript of Solucionario Kermode
Mechanics of flight Kermonde
Numerical questions Solutions
Chapter 1. Mechanics___________________________________________1. A car is travelling along a road at 50 km/h. If it accelerates uniformly at 1.5 m/s2 a) What speed will it reach in 12 s?
b) How long will it take to reach 150 km/h?
2. A train starts from rest with a uniform acceleration and attains a speed of 110 km/h in 2 min. Find a) the acceleration;
b) the distance travelled in the first minute;
c) the distance travelled in the two minutes.
3. If a motorcycle increases its speed by 5 km/h every second, find a) the acceleration in m/s2;
b) the time taken to cover 0.5 km from rest.
4. During its take-off run, a light aircraft accelerates at 1.5 m/s2. If it starts from rest and takes 20 s to become airborne, what is its take-off speed and what length of ground run is required?
5. A boy on a bicycle is going downhill at 16 km/h. If his brakes fail and he accelerates at 0.3 m/s2, what speed will he attain if the hill is 400 m long?
6. Assuming that the maximum deceleration of a car when full braking is applied is 0.8 g, find the length of run required to pull up from a) 50 km/h,
b) 100 km/h.
7. A rifle bullet is fired vertically upwards with a muzzle velocity of 700 m/s. Assuming no air resistance, what height will it reach? and how long will it take to reach the ground again?
8. The landing speed of a certain aircraft is 90 knots. If the maximum possible deceleration with full braking is 2 m/s2, what length of landing run will be required?
9. A 7000 kg aeroplane touches down at 100 knots and is brought to rest, the average resistance to motion due to brakes and aerodynamic drag being 6.867 kN. To reduce the landing run by 500 m a tail parachute is fitted. If the additional equipment increases the total mass of the aircraft by 200 kg and the landing speed by 5 knots, what additional average drag must the parachute supply?
10. An athlete runs 100 m in 11 seconds. Assuming that he accelerates uniformly for 25 m and then runs the remaining 75 m at constant velocity, what is his velocity at the 100 m mark?
11. An aircraft flying straight and level at a speed of 300 knots and at a height of 8000 m above ground level drops a bomb. Neglecting the effects of air resistance, with what speed will the bomb strike the ground? (Remember that the final velocity will have to be found by compounding the vertical and horizontal velocities.)
12. Two masses of 10 kg each are attached to the ends of a rope, and the rope is hung over a frictionless pulley. What is the tension in the rope?
13. One of the masses in Q12 is replaced by a 15 kg mass. What will be the tension in the rope when the system is released?
14. What force is necessary to accelerate a 133 kg shell from rest to a velocity of 600 m/s in a distance of 3.5 m?
15. What thrust is necessary to accelerate an aircraft of 5900 kg mass from rest to a speed of 90 knots in a distance of 750 m?
16. Calculate the thrust required to accelerate a rocket of 1 tonne mass from rest vertically upwards to a speed of 10 km/s in 10 s (neglect air resistance).
17. A train of 250 tonnes mass is moving at 100 km/h. What retarding force will be required to bring it to rest in 15 seconds?
18. A 76 kg man is standing on a weighing machine which is on the floor of a lift. What will the weighing machine record when a) the lift is ascending with velocity increasing at 0.6 m/s2?
b) the lift is ascending with velocity decreasing at 0.6 m/s2?
c) the lift is descending at a constant velocity of 1.2 m/s?
19. An engine of 50 tonnes mass is coupled to a train of 400 tonnes mass. What pull in the coupling will be required to accelerate the train up a gradient of 1 in 100 from rest to 50 km/h in 2 min if the frictional resistance is 70 N per tonne?
20. An aircraft of 5000 kg mass is diving vertically downwards at a speed of 500 knots. The pilot operates the dive brakes at a height of 10 000 m and reduces the speed to 325 knots at 7000 m. If the average air resistance of the remainder of the aircraft during the deceleration is 15 kN, what average force must be exerted by the dive brakes? (Assume that the engine is throttled back and is not producing any thrust.)
21. A 1 tonne truck is pulled on a level track by a force of 245 N in excess of the frictional resistance. How far will it travel from rest in 30 seconds?
22. A horizontal jet of water from a nozzle 50 mm in diameter strikes a vertical wall. If the water is diverted at right angles and none splashes back, what force is exerted on the wall when the speed of the jet is 6 m/s?
23. A truck is standing on an incline of 1 in 80. If the frictional resistance is50 N per tonne, how far will it travel in 15s if released from rest?
24. If the air resistance of a 500 kg bomb is equal to v2/18 N, where v is the velocity in m/s, what is the terminal velocity of the bomb?
25. An aircraft of 4000 kg mass has a take-off speed of 60 knots and a takeoff run of 300 m in conditions of no wind. If the thrust delivered by the engine is 15 000 N, and the frictional resistance is 1000 N, what is the average aerodynamic resistance during the take-off?
26. What force is necessary to stop a 500 kg car in 10 m from a speed of 50 km/h?
27. A solid 1 kg shot is fired from a barrel of 100 kg mass with a muzzle velocity of 850 m/s. If the barrel is free to recoil against a resistance of 5 kN, how far will the barrel move back when the shot is fired?
28. A fighter aircraft of 5000 kg mass is fitted with four cannon each of which fires 600 rounds per minute with a muzzle velocity of 900 m/s. If each shot has a mass of 110 g, and if all the recoil is taken by the aircraft, find the loss in speed that the aircraft would experience in a 5 second burst of fire.
29. A 9000 kg aircraft is flying straight and level at 300 knots; what thrust is necessary to accelerate it to 450 knots in half a minute if the average air resistance of the aircraft between these speeds is 15 kN?
30. A rifle of 4 kg mass fires a 30 g bullet with a muzzle velocity of 750 m/s. Find the force a rifleman must exert on the butt of the rifle to limit the recoil to 40 mm.
31. An aircraft is fitted with brakes capable of exerting a force of 10 kN, and reversible pitch propellers capable of producing a backward thrust of 25 kN. If the aircraft has a mass of 10 000 kg and a landing speed of 110 knots, find the minimum length of runway required for the landing run. (Neglect the effect of air resistance which will also help to decelerate the aircraft.)
32. An aircraft carrier is steaming at 20 knots against a head wind of 30 knots. An aircraft of 9000 kg mass lands on the deck with an air speed of 100 knots; if the arrester gear must be sufficiently powerful to stop the aircraft in a distance of 25 m in these conditions, without any aid from the brakes or air resistance, find the retarding force that the gear must exert.
33. A 5000 kg aircraft touches down on the deck of an aircraft carrier with an air speed of 90 knots. If the carrier is heading into wind at 20 knots, and the wind speed is 12 knots, what kinetic energy must be destroyed by the action of the arrester gear in bringing the aircraft to rest on the deck? If the average resistance exerted by the arrester gear is 55 kN, how far does the aircraft roll along the deck before coming to rest?
34. A propeller 3 m in diameter revolves at 2250 rpm. Find the angular velocity and the linear speed of the propeller tip.
35. The piston of an aircraft engine has a stroke of 150 mm and the engine runs at 3000 rpm. Find the angular velocity of the crankshaft and the average speed of the piston.
36. Find the acceleration of the propeller tip in Q34.
37. Find the acceleration of the crankpins in the engine in Q35.
38. A stone of mass 1 kg is whirled in a horizontal circle making 60 rpm at the end of a cord 1 m long; what is the pull in the string? If it is whirled in a vertical circle, what is the pull in the string a) when the stone is at the top?
b) when the stone is at the bottom?
39. A mass of 50 kg travelling at 7.905 km/s maintains a circular path of radius 6370 km. What is its acceleration towards the centre?
40. A sphere of mass 500 kg is travelling on a circular path of 12 800 km radius with an acceleration of 2.45 m/s2 towards the centre. How long does it take to complete one full circle?
41. At what speed (in km/h) is a bank angle of 45 required for an aeroplane to turn on a radius of 60 m?
42. An aeroplane has a mass of 1500 kg. It is turning on a horizontal circle of radius 100 m at an air speed of 80 knots. Calculate a) the centripetal force exerted by the air on the aircraft,
b) the correct angle of bank,
c) the total lift normal to the wings.
43. Find the work required to lift a mass of 5 tonnes to a height of 30 m. If this is done in 2 minutes, what power is being used?
44. Find the power required to propel a 3000 kg aircraft through the air at a speed of 175 knots if the air resistance is 3924 N.
45. Find the power required to propel the same aircraft at 350 knots when the air resistance is 14.715 kN.
46. A car of mass 750 kg can climb a gradient of 1 in 12 in top gear at 40 km/h. If the frictional resistance is 100 N per tonne, find the power developed by the engine in these conditions.
47. A projectile of mass 1 kg is fired from a gun with a muzzle velocity of 850 m/s. What is its kinetic energy? What will be its velocity when the kinetic energy has fallen to 90.3125 kJ?