Question

A ball is on the end of a rope that is 1.72 m in length. The ball and rope are attached to a pole and the entire apparatus, including the pole, rotates about the pole's symmetry axis. The rope makes an angle of 64.0° with respect to the vertical. What is the tangential speed of the ball

Answer 1

Answer:

Tangential Speed equals 5.57m/s

Explanation:

In the figure shown for equilibrium along y- axis we have

$\sum F_{y}=0$

Resolving Forces along y axis we have

$Tcos(\theta )=mg............(i)$

Similarly along x axis

$\sum F_{x}=ma_{x}$

$Tsin(\theta )=m[tex]\frac{v^{2} }{r}$............(ii)[/tex]

Dividing ii by i we have

$tan(\theta )=\frac{v^{2}}{rg}$

In the figure below we have $r=lsin(\theta )$

Thus solving for v we have

$v=\sqrt{lgsin(\theta) tan(\theta )}$

Applying values we get

v=5.576m/s