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 2500 N. The tension in the the towrope between the transport plane and the first glider is not to exceed 12,000 N. (b) What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

Explanation / Answer

1) Let the acceleration of plane is a m/s^2, and the mass is M Kg; Then:- =>12000 - [2500 + 2500] = Ma =>Ma = 7000 N =>a = 7000/M m/s^2 Now let the minimum distance taken by plane to reach 40 m/s speed from rest is s meter, than:- =>v^2 = u^2 + 2as =>40 x 40 = 0^2 + 2 x (7000/M) x s =>s = (1600/14000) x M =>s = 4M/35 meter 2)Let the tension in the tow rope between two gliders is T; than:- => T - 250 = 700 x a =>T - 250 = 700 x (7000/M) =>T = (4900000/M) + 250 Newton

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