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 1600 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N. A)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?

Answer 1

Answer:

The total resistance is 5000 N. So the net force left for acceleration is 7 000 N (12 000 - 5 000).

7000 N applied to 2x700 kg gives a maximum acceleration of

a = F/m = 7000/1400kg = 5 m/s^2

At 5m/s^2, it will take 8 s to reach 40 m/s. In 8 second the distance covered will be

d = 1/2 at^2 = 1/2 x 5 x 8^2 = 160 m

Because each glider has the same drag and inertia, the tension in the rope between the gliders will be exactly half of the tension between plane and the two gliders:

12 000/2 = 6 000N.