Question

A 1.0kg ball is swinging in a horizontal circle on the end of a 1.5m long string that makes an angle O with the horizontaol. The string passes through a tube and has a 2.0kg block hanging from the ned of the string. Find the speed of the ball if the block is to remain stationary?

Answer 1

Answer:

$v = 4.7 m/s$

Explanation:

As we know that the ball is swinging in a circle

so here net horizontal centripetal force on the ball is due to component of the tension force

so we will have

$T sin\theta = m\omega^2 r$

$T cos\theta = mg$

also we know that

$T = Mg$

so we have

$Mg cos\theta = mg$

$\theta = \frac{1}{2}$

$\theta = 60 degree$

now we have

$Mg sin\theta = m\omega^2 (Lsin\theta)$

$Mg = m\omega^2 L$

$2 \times 9.81 = 1 \omega^2 (1.5)$

$\omega = 3.62 rad/s$

now we have

$v = r\omega$

$v = (1.5 sin60) (3.62)$

$v = 4.7 m/s$