A transport plane takes off from a level landing field with two gliders in tow,

Question

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 700 kg , and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2200 N . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N . If a speed of 40 m/s is required for takeoff, what minimum length of runway is needed? B) What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

Explanation / Answer

  a)
First find the maximum acceleration.
(tension in rope) = (mass)×(force by acceleration) + (force by fraction)

12000 N = (2 × 700 kg)×a + (2 × 2700 N)
a = 4.71 m/s²

Now find the minimum length of the runway.
(Vf)² = (Vi)² + 2×a×d
where
Vf = final velocity = 40 m/s
Vi = initial velocity = 0 m/s
a = maximum acceleration = 4.71 m/s²
d = distance = ?
so
40² = 0² + 2×4.71×d
d = 169.85 m < - - - - - - - - answer

b)
(tension in rope) = (mass)×(force by acceleration) + (force by fraction)
T = (700 kg)×(5 m/s²) + 2700 N
T = 6200 N < - - - - - - - - answer

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