Question

Problem 6.85 Part A A7.9x102-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 1.25 m/s in a horizontal circle of radius 0.50 m, as illustrated in the figure (Figure 1) Find the angle the string makes with the vertical Express your answer using two significant figures Figure 1 of 1 Submit My Answers Give Up Part B Find the tension in the string Express your answer using two significant figures Submit My Answers Give Up VI ac Continue

Answer 1

From the force balance, assuming the tension in the string is T, we write
for horizontal force baance
   $T\sin\theta=\frac{mv^2}{r}$
And, for vertical force balance
   $T\cos\theta=mg$
Taking the ratio, we get
   $\tan\theta=\frac{v^2}{rg}=\frac{1.25^2}{0.5\times 9.8}$
   $\Rightarrow \theta=\tan^{-1}\left (\frac{1.25^2}{0.5\times 9.8} \right )=17.68^{\circ}$
Part-B:

   tension is
   $T=\frac{mg}{\cos\theta}=\frac{7.9\times 10^{-2}\times 9.8}{\cos17.68^\circ}$
   $\Rightarrow T=0.8126\hspace{1mm}N$