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, their backs against the outer wall.
At one instant the outer wall moves at a speed of 3.2 m/s, and an 83 kg person feels a 560N force pressing against his back.

What is the radius of a chamber?

a)1.2 m

b) 1.44 m

c) 1.5 m

d) 1.65 m

Please explain.

Answer 1

Answer:

C.

Explanation:

To solve the problem we need to use the concept related to Centripetal Force. According to Newton's second law, for an acceleration to occur, a force must act in the direction of that acceleration. Thus, if we consider a particle of mass m, in uniform circular motion, it will be subjected to a centripetal force given by:

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

Where,

m= mass

v= velocity

r = radius

Re-arrange for the radius

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

Our values are given by,

$m=83Kg$

$v=3.2m/s$

$F= 560N$

Replacing we have that

$r= \frac{83*3.2^2}{560}$

$r = 1.51m \approx 1.5m$

Therefore the correct answer is C.