**27. The model airplane in Figure 5.6 is flying at a speed of 22 m/s on a horizontal circle of radius 16 m. The mass of the plane is 0.90 kg. The person holding the guideline pulls it in until the radius becomes 14 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Sum of the forces in the radial direction gives

So at the initial radius , we have an initial tension given by

Then at the final radius , we have an final tension given by

Work-Energy gives us

From sum of force equations we can substitute for

And

Now substitute back for

So net work can be found by

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This page last updated on January 11, 2020