At an amusement park there is a ride in which cylindrically shaped chambers spin

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 3.15 m/s, and an 57.4-kg person feels a 237-N force pressing against his back. What is the radius of a chamber? 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 3.15 m/s, and an 57.4-kg person feels a 237-N force pressing against his back. What is the radius of a chamber?

Explanation / Answer

Centripetal force, provided by the cylinder wall on the person,F

F = mw^2r

Where,  m = mass of person

r = radius of circular motion

w = angular velocity of motion

If v is the tangential velocity of motion, then

v = wr

F = mv^2 / r

r = mv^2 / F

= 57.4*3.15^2/237

= 2.40 m answer

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