Question

At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis (middle), with their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83kg person feels a 560N force pressing against his back. What is the radius of a chamber

Answer 1

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,

$a_R = \frac{v^2}{r}$

Here,

v =Velocity

r = Radius

Now Newton's second law is,

$F = ma_R$

Here,

m = mass

$a_R$ = Centripetal acceleration

Rearranging in function of the acceleration,

$a_R = \frac{F}{m}$

Rearranging the first equation in function of the radius

$a_R = \frac{v^2}{r} \rightarrow r=\frac{v^2}{a_R}$

Equating,

$r = \frac{mv^2}{F}$

Replacing,

$r = \frac{(83kg)(3.2m/s^2)}{560N}$

$r = 1.518m$

Therefore the radius of the  chamber is 1.518m