Question

Please show work and explain

In the game of tetherball, a 1.25-m rope connects a M=M= 0.590-kg ball to the top of a vertical pole so that the ball can spin around the pole as shown in the figure below.

1) What is the speed of the ball as it rotates around the pole when the angle θθ of the rope is 31.0° with the vertical? (Express your answer to three significant figures.)

Answer 1

the tension on rope has two compoent

the horizontal component

$Tcos\Theta =Mg \-----------------(1)$

the vertical component

$Tsin\Theta =\frac{Mv^{2}}{R} \-----------------(2)$

dividing equation 2 with one

$\frac{Tsin\Theta}{Tcos\Theta} =\frac{\frac{Mv^{2}}{R}}{Mg}$

$tan\Theta =\frac{v^{2}}{Rg}$

$v^{2}=Rgtan\Theta$

$v=\sqrt{Rgtan\Theta}$

$v=\sqrt{1.25\times 9.8tan31}m/sec$

in three significant figure

$v=2.71m/sec$