Passengers on a Ferris wheel sit in seats attached rigidly to the rim so that the…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Passengers on a Ferris wheel sit in seats attached rigidly to the rim so that the seats do not swing. The wheel has a radius of R=14m and rotates counter-clockwise in a vertical plane.
A rider in the lowest seat (point L) is located at a distance 0.8R from the axle, while another rider in a midway seat (point M) is at 0.5R from the axle along the same spoke. The wheel first accelerates uniformly from rest with an angular acceleration of α=0.10rads−2 until it reaches its operating angular speed of ω=0.75rads−1, which is then kept constant.
(a) During the acceleration phase, determine the magnitude of the tangential acceleration experienced by each rider.
(b) Once the wheel reaches its operating speed, calculate the magnitude of the centripetal (radial) acceleration for each rider.
(c) Compute the ratio of total acceleration magnitudes aL/aM for the riders (i) at the instant just after the wheel begins to move, (ii) at the end of the acceleration phase, and (iii) during steady-speed operation. Treat tangential and radial components as perpendicular when combining them.
(d) Discuss how the differing accelerations might affect the physical sensations experienced by riders at points L and M during the three stages identified in part (c). Support your discussion with quantitative references to your results.