A toy plane with a mass of 0.97 kg is tied to a string and made to travel at a s

Question

A toy plane with a mass of 0.97 kg is tied to a string and made to travel at a speed of 25 m/s in a horizontal circle with a 18-m radius. The person holding the string pulls the plane in, increasing the tension in the string, increasing the speed of the plane and decreasing the radius of the plane's orbit. What is the net work done on the plane if the tension in the string increases by a factor of four and the radius decreases to 9 m.

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A toy plane with a mass of 0.97 kg is tied to a string and made to travel at a speed of 25 m/s in a horizontal circle with a 18-m radius. The person holding the string pulls the plane in, increasing the tension in the string, increasing the speed of the plane and decreasing the radius of the plane's orbit. What is the net work done on the plane if the tension in the string increases by a factor of four and the radius decreases to 9 m.

Explanation / Answer

m = 0.97 kg

V1 = 25 m/s

r1 = 18m

tension = mv^2/r

= 33.68 N

T' = 4T

134.72 N

r' = 9m

134.72 = mv^2/r

v = 35.35 m/s

work done = change in kinetic enrgy

= 1/2 *0.97 *(35.35^2 - 25^2)

= 303.125 J

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