Answer:
1. Fc = 14212.3 N = 14.21 KN
2. ac = 1579.14 m/s²
Explanation:
First, we will find the linear velocity of the ball:
[tex]v = r\omega[/tex]
where,
v = linear velocity = ?
r = radius of circle = 2.5 m
ω = angular speed = (4 rotations/s)(2π rad/1 rotation) = 8π rad/s
Therefore,
[tex]v = (2.5\ m)(8\pi\ rad/s)\\v = 62.83\ m/s\\[/tex]
2.
Now, the centripetal acceleration can be given as:
[tex]a_{c} = \frac{v^2}{r}[/tex]
where,
ac = centripetal acceleration = ?
Therefore,
[tex]a_{c} = \frac{(62.83\ m/s)^2}{2.5\ m}[/tex]
ac = 1579.14 m/s²
1.
The centripetal force can be given as:
[tex]F_{c} = ma_{c}\\F_{c} = (9\ kg)(1579.14\ m/s^2)\\[/tex]
Fc = 14212.3 N = 14.21 KN
