The model airplane in the figure below has a mass of 0.95 kg and moves at a cons

Question

The model airplane in the figure below has a mass of 0.95 kg and moves at a constant speed on a circle that is parallel to the ground. The path of the airplane and its guideline lie in the same horizontal plane, because the weight of the plane is balanced by the lift generated by its wings. Assuming that there is no upward lift on the plane generated by its wings. Without such lift, the guideline slopes downward due to the weight of the plane. Find the tension T in the guideline (length = 18 m), for purposes of significant figures, use 0.950 kg for the mass of the plane, 18.0 m for the length of the guideline, and s1 = 22.0 and s2 = 36.0 m/s for the speeds.

Explanation / Answer

suppose the guideline make an angle of with respect to horizon

Tsin = mg                                    (1)

Tcos = mv2 /Rcos                       (2)

from (1), we have sin = mg/T

from (2) we have (cos)2 = mv2 / RT

using sin2 + cos2 = 1, we have

(mg/T)2 + mv2/RT = 1

or

T2 - (mv2/R) T - (mg)2 = 0

solve for T,

T = (mv2/2R) [1+ sqrt(1+ (2gR/v2)2)]

when v = 22 m/s, T = 28.6 N

when v = 36 m/s, T = 69.6 N

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