To solve this problem we will apply the concepts related to centripetal acceleration and Newton's second law. In the case of acceleration, we will define how it is shaped, and we will equate that acceleration to that stipulated by Newton in his second law. We will clear the variable of the 'radius'. Centripetal acceleration is described as,
[tex]a_R = \frac{v^2}{r}[/tex]
Here,
v =Velocity
r = Radius
Now Newton's second law is,
[tex]F = ma_R[/tex]
Here,
m = mass
[tex]a_R[/tex] = Centripetal acceleration
Rearranging in function of the acceleration,
[tex]a_R = \frac{F}{m}[/tex]
Rearranging the first equation in function of the radius
[tex]a_R = \frac{v^2}{r} \rightarrow r=\frac{v^2}{a_R}[/tex]
Equating,
[tex]r = \frac{mv^2}{F}[/tex]
Replacing,
[tex]r = \frac{(83kg)(3.2m/s^2)}{560N}[/tex]
[tex]r = 1.518m[/tex]
Therefore the radius of the chamber is 1.518m
