An airplane flies with an air speed of 50.0 m/s [E]. If, according to an observe

Question

An airplane flies with an air speed of 50.0 m/s [E]. If, according to an observer on the ground, the velocity of the airplane is 23.0 m/s [N 45 degree E], what is the wind velocity? A 0.100 kg ball is swung in a vertical circle on the end of its 0.50 m long string. If the string can withstand a maximum tension of 50.0 N. What is the maximum speed of rotation of this ball that the string can withstand? Include a labelled free-body diagram with your answer. What will the least amount of tension be in the string as the object is swung in a vertical circle at this speed? Where will this minimum tension occur? Include a labelled free-body diagram with your answer.

Explanation / Answer

a) T at lowest is maximum

T = (mv^2 / r ) + mg

50/0.1 = (v^2/0.5) + 9.81

v^2 = (500-9.81)*0.5

v = 15.656 m/s

b) T minimum on the top of the circle

Tmin = (mv^2/r) - (mg)

Tmin = (0.1*15.656^2 / 0.5) - (0.1*9.81)

Tmin = 48.92 N

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