A 7.8×10 2 -kg toy airplane is tied to the ceiling with a string. When the airpl

Question

A 7.8×102-kg toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.10 m/s in a horizontal circle of radius 0.49 m , as illustrated in the figure(Figure 1) .

Part A

Find the angle the string makes with the vertical.

Express your answer using two significant figures.

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Part B

Find the tension in the string.

Express your answer using two significant figures.

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Figure 1 of 1

A 7.8×102-kg toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.10 m/s in a horizontal circle of radius 0.49 m , as illustrated in the figure(Figure 1) .

Part A

Find the angle the string makes with the vertical.

Express your answer using two significant figures.

=     

SubmitMy AnswersGive Up

Part B

Find the tension in the string.

Express your answer using two significant figures.

T =   N  

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Figure 1 of 1

Explanation / Answer

The net horizontal force is

F_x = T sin theta = mv^2/r

The net vertical force is

F_y = T cos theta -mg= 0

T cos theta = mg

T sin theta = (mg/ cos theta) sin theta

T sin theta = mg tan theta = mv^2/r

theta = tan^-1 ( v^2/ rg) = tan^-1 ( 1.10 m/s)^2/0.49 m ( 9.8 m/s^2) = 14.14 degree

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(b)

T = mg/ cos theta = 7.8×102-kg ( 9.8 m/s^2)/ cos 14.14 = 0.788 N

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