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

`v = 4.7 m/s`

Step-by-step 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 = (1)/(2)`

`\theta = 60 degree`

now we have

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

`Mg = m\omega^2 L`

`2 * 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`