A transport plane takes off from a level landing field with twogliders in tow, o

Question

A transport plane takes off from a level landing field with twogliders in tow, one behind the other. The mass of each glider is690 kg, and the total resistance (airdrag plus friction with the runway) on each may be assumed constantand equal to 2490 N. The tension inthe towrope between the transport plane and the first glider is notto exceed 11,600 N.
(a) If a speed of 40 m/s is required fortakeoff, what minimum length of runway is needed?


(b) What is the tension in the towrope between the two gliderswhile they are accelerating for the takeoff?
(a) If a speed of 40 m/s is required fortakeoff, what minimum length of runway is needed?


(b) What is the tension in the towrope between the two gliderswhile they are accelerating for the takeoff?

Explanation / Answer

For maximum force , Tension in the towrope between the transportplane and the first glider = 11600 N Also resistance = 2490 N So net force = 11600 - 2(2490) =6620 N So acceleration = Force /Total mass = 6620 / 2(690) =4.8m/s2 As they start from rest , Initial velocity(u) =0 Final velocity required (v)= 40 m/s Using the equation v2-u2=2aS So distance (S) = 402/(2*4.8) = 166.8 m b)Net force on second glider = mass*acceleration = 690*4.8 = 3312N As towrope between the two gliders provide the force required foracceleration Let the tension in it be T Then Net force = T -frictional losses So 3312 = T - 2490 T = 5802 N ~5.8*103 N

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