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

Question

A transport plane takes off from a level landing field with two gliders in two, one behind the other. The mass of each glider is 780.0 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed to be constant and equal to 2540.0 N. The tension in the towrope between the transport plane and the first glider is not to exceed 12200 N.

If a speed of 40 m/s is required for takeoff, what is the minimum length of runway needed for takeoff in meters (to 3 sig figs)?

What is the magnitude of the tension in N in the towrope between the two gliders while they are accelerating for takeoff? Use three sig figs.

Explanation / Answer

Assuming no tall trees, telephone lines, or buildings at the end of the runway, then S = Ux^2/2A is the minimum run of the gliders at Ux = 40 mps. P = 12200 N the max allowed tension, which is the pull force and d = 2540 N is the drag/friction force for each of the two gliders with mass m = 780 kg. A, the average rate of acceleration, is found from the net takeoff force, f = (2m)A = P - D = 12200 - 2*d = 12200 - 5080 = 7120 N so A = 7120/2m = 7120/1560= 4.56 m/s^2. Then S = 40^2/(2*4.56) = 175.43 m

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