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

Tangential Speed equals 5.57m/s

Step-by-step 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](v^(2) )/(r)`............(ii)[/tex]

Dividing ii by i we have

`tan(\theta )=(v^(2))/(rg)`

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

Thus solving for v we have

`v=√(lgsin(\theta) tan(\theta ))`

Applying values we get

v=5.576m/s