A model airplane of mass 0.820 kg flies with a speed of 35.0 m/s in a horizontal

Question

A model airplane of mass 0.820 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 64.0-m-long control wire as shown in Figure (a). The forces exerted on the airplane are shown in Figure (b): the tension in the control wire, the gravitational force, and aerodynamic lift that acts at = 20.0° inward from the vertical. Compute the radius, lift, and tension in the wire, assuming it makes a constant angle of = 20.0° with the horizontal.

A model airplane of mass 0.820 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 64.0-m-long control wire as shown in Figure (a). The forces exerted on the airplane nward from the vertical Compute the ad us, lift and tension are shown in Figure b): the tension in the control wire, the gravitational force, and aerodynamic lift that acts at in the wire, assuming it makes a constant angle of -20.0° with the horizontal 20.0 radius 64 Your response is within 10% of the correct value his may be due to roundof error, or you cou have a mistake n digit accuracy to minimize roundoff error. m lift tension 15.69 Your response differs from the correct answer by more than 10%. Double check your calculations. N ur calculation ar ut il intermediate e uit to at as our Circular path of airplane Wire mg

Explanation / Answer

there will be centripetal acceleration in horizontal towards the center of circle.

(to the left in this figure)

cos20 = r / L

r = 64 cos20 = 60 m .......Ans

centripetal acc. = v^2 / r = 35^2/ 60 = 20.4 m/s^2

Net force in horizontal,

Fnet = m a

F_lift sin20 + T cos20 = 0.820 x 20.4

F_lift sin20 + T cos20 = 16.7 ..........(i)

In vertical,

Fnet = m a

Flift cos20 - Tsin20 -mg = 0

F_lift cos20 - T sin20 = 8.04 ....... (ii)

solving two equations,

lift force = 13.3 N

Tension = 12.9 N

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