A 2.0 kg model airplane is attached to a 10.0 m cord as it flies at a constant s

Question

A 2.0 kg model airplane is attached to a 10.0 m cord as it flies at a constant speed of 5.00 m/s in a horizontal circular orbit with a radius of 5.0 m. Because of the air lift, the plane flies above the ground so that the cord makes an angle of 30 degree with the vertical, as shown in the figure. Assume the force exerted by the air is straight up. Draw a complete free-body diagram for the airplane. Write down the two equations that result from applying Newton's second law to the plane. Calculate the tension in the cord. Calculate the force exerted by the air on the plane.

Explanation / Answer

a) Refer below figure,

b) Applying Newton’s second law horizontally,

Tx = Fc

Tsin = mv^2/r ------------(1)

Applying Newton’s second law vertically,

Ty – mg =0

Tcos = mg -------------(2)

c) From (2)

Tcos = mg

T = mg/cos = (2*9.8)/(cos30) = 22.6 N

d) Force by air of the plane = Flift = Tcos = 22.6cos30 = 19.6 N

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