An airplane pulls a 21 kg banner on a cable as depicted in the figure below. Whe

Question

An airplane pulls a 21 kg banner on a cable as depicted in the figure below. When the plane has a constant cruising velocity the coble makes an angle of theta = 24 degree. What is the drag force exerted on the banner by the air? The weather changes abruptly and the pilot finds herself in a 20 minute rain storm. After the storm she finds that the cable now makes an angle of theta_water = 39 degree. Assuming the velocity and drag force are the same after the storm, what is the mass of the water absorbed by the banner's fabric during the storm?

Explanation / Answer

a) drag force is T*cos(theta)

in vertical direction

T*sin(theta) = m*g = 21*9.8 = 205.8

T*sin(24) = 205.8

T = 205.8/sin(24) = 506 N

then air drag force = T*cos(theta) = 506*cos(24) = 462.25 N

b) T*sin(theta) = m*g

T*sin(39) = m*g

T*cos(39) = 462.25

T = 462.25/cos(39) = 594.8 N

then T*sin(39) = m*g

594.8*sin(39) = m*9.81

mass m = 38.15 kg

mass of water absorbed is m_w = 38.15-21 = 17.15 kg

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