(o) Find the magnitudes of the horizontal forces Fi and F2 that must be applied
ID: 1657696 • Letter: #
Question
(o) Find the magnitudes of the horizontal forces Fi and F2 that must be applied to hold the system in the position shown A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 710 kg, and the total each may be assumed constant and equal to 2490 N. The tension in the towrope between the transport plane and the first glider is not to exceed 11,550 N (air drag plus friction with the runway) on (a) If a speed of 40 m/'s is required for takeoff, what minimum length of runway is needed?Explanation / Answer
4. Given : Mass of glider, m=710 kg;
Total resistance (R)= 2×2490 = 4980 N
Maximum tension (T)= 11550 N
Solution :
Net force left for the acceleration can be given as :
F= 11550 N - 4980 N = 6570 N
By newton's second law:
F= ma
6570 N= (2×710) a
i.e. a = 6570/(2×710) = 4.63 m/s2
(a)At 4.63 m/s2, the time to reach 40 m/s : t= 40/4.63=8.65 s
The distance covered can be given as :
d= 1/2 at2= 1/2(4.63)(8.65)2= 170.03 m
(b) The tension between plane amd gliders can be given as
T= 11550/2 = 5775 N
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