Question

Determining acceleration and forces on a carousel.

Jebediah puts his brother on a hippo that is 0.5m from the center of rotation. His sister rides a unicorn located 1.5m from the center. The carousel makes ten complete rotations at a constant speed in 2 minutes. a. What are the accelerations experienced by the sister and by the brother? b. What are the forces required to keep the sister and the brother rotating? What is the direction of these forces?

Answer 1

Angular Velocity disk

w = 10 * 2* 3.14 / (2* 60) = 0.523 rad/s

a)

Acceleration experienced by sister

As = r w^2 = 1.5* 0.523^2 = 0.41 m/s^2

Acceleration experienced by brother

Ab = 0.5* 0.523^2 = 0.1367 m/s^2

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B)

Force required for sister

Fs = 0.41 * mass of sister

Force required for brother

Fb = 0.1367* mass of brother

Both forces must directed towards center

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