Amusement Park Ride 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 3.03 m/s, and an 80.7 kg person feels a 576 N force pressing against his back. What is the radius of a chamber?

Amusement Park ride has a circular motion path.

At an instant, the speed of the is

v = 3.03m/s

Mass of a person is

M = 80.7kg

And he felt a force pressing against it back I. e centripetal force

Fc = 576N

Radius of the chamber

Using Circular motion.

Centripetal force is given as

Fc = m•ac

Where m is mass

And ac is centripetal acceleration.

Then, centripetal acceleration is give as

ac = v²/r

So,

Fc = mv²/r

Making r subject of formulas

r = mv² / Fc

Where,

m is mass m = 80.7kg

v is velocity v = 3.03m/s

Fc is centripetal force Fc = 576N

Then,

r = mv² / Fc

r = 80.7 * 3.03² / 576

r = 1.29m

The radius of the chamber is 1.29m

r = 1.29m

the radius of a chamber is 1.29m

Explanation:

Given;

Mass of person m = 80.7kg

Speed v = 3.03 m/s

Force felt = centripetal force F = 576N

r = Radius

The centripetal force F can be expressed as;

F = (mv^2) / r

making r the subject of formula;

r = (mv^2) / F

substituting the values;

r = (80.7*3.03^2) / 576

r = 1.29m

the radius of a chamber is 1.29m