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A 50 kg person is riding a Ferris wheel. The Ferris wheel consists of 8 metal cars, each with mass 1500 kg located 15 m from the center. The Ferris wheel starts from rest, and the motor applies a 500 N torque to it for 1 minute. The mass of the frame is small enough comparably that you can neglect it.

a) What is the angular acceleration of the Ferris wheel?

b) What is the speed of the car after the torque is applied?

c) Determine the person's apparent weight at the top and bottom of the Ferris wheel.

Added Fri, 26 Jun '15

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a) Calculate the moment of inertia of the Ferris wheel.

I = mr^2

m = 8(1500kg) = 12000kg

r = 15m

I = (12000kg)(15m)^2

= 2.7 x 10^6 kg*m^2 ---> I believe this answer is correct?

b) What is the angular acceleration of the Ferris wheel?

Torque = I * ?

5000 = 2.7 x 10^6 * ?

? = 5000 / (2.7 x 10^6) = 1.851851852 * 10^3

T(torque) = a(angular acc) mr^2

a =T/(mr^2)

mr^2 = I

a = T/I

a = (5000Nm)/(2.7 x 10^6 kg*m^2)

=1.85 x 10^-3 m/s^2 ---> I believe this answer is correct?

c) What is the speed of the car after the torque is applied?

Wf(final angular velocity) = Wi(initial angular velocity) + at (angular acceleration*time)

Wi = 0m/s

t = 1 min = 60s

a = 1.85 x 10^-3 m/s^2

Wf = 1.851851852 * 10^3 * 60 = 1/9 rad/s

Wf = 0m/s +at

Wf = at = (1.85 x 10^-3 m/s^2)(60s) = 0.11m/s

V=rw = (0.11m/s)(15m) = 1.65 m/s ---> I believe this answer is correct?

V = 15 * 1/9 = 1? m/s

This is a more accurate answer.

d) Determine the person's apparent weight at the top and bottom of the Ferris wheel.

When the person is at the top of the Ferris wheel, the apparent weight is equal to the difference of the actual weight and the centripetal force. According to your work, person's mass is 50 kg.

Weight = 50 * 9.8 = 490 N

Fc = 50 * 1?^2/15 = 9.259259259 N

Apparent weight = 490 - 9.2525259 = 480.7507407 N

When the person is at the bottom of the Ferris wheel, the apparent weight is equal to the sum of the actual weight and the centripetal force.

Apparent weight = 490 + 9.2525259 = 499.2592593 N

The only mistake you made is when you determined the centripetal force.

Let's use 1.65 m/s to determine this answer.

Fc = 50 * 1.65^2/15 = 9.075 N

Added Fri, 26 Jun '15

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