(part 1 of 2) In civil aviation, a “standard turn” for level ight of a propeller

Question

(part 1 of 2) In civil aviation, a “standard turn” for level ight of a propeller-driven airplane is one in which the airplane makes a complete circular turn in 2 min. If the plane’s speed is 175 m/s, what is the radius of the circle? Answer in units of km.

What is the centripetal acceleration of the plane? Answer in units of m/s2.

A young boy swings a yo-yo horizontally above his head so that the yo-yo has a centripetal acceleration of 260 m/s2. If the yo-yo’s string is 0.82 m long, what is the yo-yo’s tangential speed? Answer in units of m/s.

Explanation / Answer

period is T = (2*pi*r)/v

given that T = 2*60 = 120 sec

r = ?

v = 175 m/sec

then

2*pi*r = T*v

2*3.142*r = 120*175

r = (120*175)/(2*3.142) = 3341.82 m = 3.34 km

centripetal accelaration is ac = V^2/R = (175^2)/3341.82 = 9.16 m/s^2

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ac = v^2/r = 260

v^2/0.82 = 260

v = sqrt(260*0.82) = 14.6 m/sec

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