Question

Ryan is swinging a 0.2 kg ball tied to a string around his head in a flat, horizontal circle. The radius of the circle is 0.40 m, and linear speed is 1.3 m/s. Find the centripetal force acting on the ball to keep it in the circular path. O 1.72 N O 2.04 N 0 0.046 N 0 0.845 N​

Answer 1

Hello!!

How you now, first we have to calculate centripetal aceleration, for that we know what:

`\boxed{\alpha =(v^(2) )/(r) }`

`\textbf{Being:}`

`\sqrt{}`
`\alpha = Centripetal\ aceleration= \ ?`

`\sqrt{}`
`r = Radius = 0,4\ m`

`\sqrt{}`
`v = Linear \ speed = 1,3\ m/s`

`\textbf{So let's replace and resolve it}`

`\alpha = ((1,3\ m/s)^(2))/(0,4\ m)`

`\alpha = 4.225 \ m / s^(2)`

And, for calculate centripetal force, lets applicate the formula:

`\boxed{ F = m * \alpha }`

`\textbf{Being:}`

`\sqrt{}`
`\alpha = Centripetal\ aceleration= \ 4,225\ m/ s^(2)`

`\sqrt{}`
`F = Centripetal \ force = ?`

`\sqrt{}`
`m = Mass = 0,2\ kg`

`\textbf{So let's replace and resolve it}`

`F = 0,2 \ kg * 4,225\ m /s^(2)`

`F = 0.845\ N`

`\text{The centripetal force is \textbf{0,845 N} }`

Good Luck!!