Electric Flying Model Airplanes
Need help with a physics problem–tension?
Consider a model airplane (1.9 kg) tied to a string and propelled by a small electric motor in a perfect horizontal circle with a circumference of 23 m at constant speed. The plane isn’t really flying, instead a component of the string’s tension is lifting the airplane up against it’s weight. If the string makes an angle of 75 degrees with respect to the vertical then:
Predict the tension in the string.
I already found that the length of the string is 3.789 meters.
Can you please help me find the tension and show me how to do it. Thanks.
Let:
m be the mass of the plane,
T be the tension in the string,
a be the angle between the string and the vertical,
g be the acceleration due to gravity.
For vertical equilibrium:
T cos(a) = mg
T = mg / cos(a)
= 1.9 * 9.81 / cos(75)
= 72.0N to 3sf.
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