A person gets on a ferris wheel as shown in this figure. The ferris wheel starts
ID: 1427508 • Letter: A
Question
A person gets on a ferris wheel as shown in this figure. The ferris wheel starts from rest and speeds up at a constant rate for 12.0 seconds, until it is rotating at 1 full rotation every 25.0 seconds. a) What is the tangential acceleration during the first 12 seconds. b) What is the centripetal acceleration that this person experiences, 6.00 seconds after the ferris starts to rotate.
The rotation in this problem is clockwise. A person gets on a ferris wheel as shown in this figure. The ferris wheel starts from rest and speeds up at a constant rate for 12.0 seconds, until it is rotating at 1 full rotation every 25.0 seconds. a) What is the tangential acceleration during those first 12.0 seconds, as experienced by the person sitting a distance of 14.0 m from the center? b) What is the centripetal acceleration that this person experiences, 6.00 seconds after the ferris wheel begins to rotate? c) sketch the acceleration vecto for the person, at t= 6.00 seconds.Explanation / Answer
a)
given
initial angular speed, w1 = 0
final angular speed, w2 = 2*pi/25
= 0.2513 rad/s
radius, R = 14 m
angular acceleration of the wheel, alfa = (w2 - w1)/t
= (0.2513 - 0)/12
= 0.0209 rad/s^2
Apply, a_tan = R*alfa
= 14*0.0209
= 0.293 m/s^2 <<<<<<<<<<---------Answer
b) at t = 6 s,
w = wo + alfa*t
= 0 + 0.0209*6
= 0.1254 rad/s
a_centripetal = R*w^2
= 14*0.1254^2
= 0.22 m/s^2 <<<<<<<<<<---------Answer
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