A toy airplane is tied to the ceiling with a string. When the airplane\'s motor

Question

A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.21 m/s in a horizontal circle, as illustrated in the figure. If the angle the string makes with the vertical is 29, and the tension of the string is 1.2N:

(a) Find the radius of the horizontal circle of the plane. m

(b) Find the mass of the plane. g

A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.21 m/s in a horizontal circle, as illustrated in the figure. If the angle the string makes with the vertical is 29½, and the tension of the string is 1.2N: (a) Find the radius of the horizontal circle of the plane. m (b) Find the mass of the plane. g

Explanation / Answer

a)

x direction:

m v^2/R = T sin(29)

y direction:

m g = T cos(29)

divide them:

v^2/(R g) = tan(29)

==> R = v^2/(g tan(29)) = 1.21*1.21/(9.8*tan29) = 0.26952 = 0.270 m

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b)

y direction:

m g = T cos(29)

==> m = (T cos(29))/(g) = (1.2*cos29)/(9.8) = 0.1071 Kg = 110 grams

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