Question

The model airplane in figure below is flying at a speed of 23 m/s on a horizontal circle of radius 15 m. The mass of the plane is 0.99 kg. The person holding the guideline pulls it in until the radius becomes 13 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Answer 1

net work = 1/2I?^2 final - 1/2I?^2 initial

I = mr^2 = 1.1 x 17.7^2 = 344.619 kg-m^2

? = 24.8/17.7 = 1.4 rad/s

0.5 x 344.619 x 1.4^2 = 337.73 J

Initial tension = centripetal force = mass x v^2/radius

1.1 x 24.8^2/17.7 = 38.22 N


Four times = 38.22 x 4 = 152.88 N

152.88 / 1.1 = v^2/r = 138.98

138.98 x radius(13.7) = v^2 = 1904.05, sq-root = v = 43.64 m/s

43.64/r = ? = 3.185 rad/s

0.5 x 344.619 x 3.185^2 = 1748.38 J

1748.38 - 337.73 = 1410.66 J (answer)