On a popular amusement park ride, the rider sits in a chair suspended by a cable as shown in Figure P5.22. The top end of the cable is tied to a rotating frame that spins, hence moving the chair in a horizontal circle with r = 10 m. The ride makes one complete revolution every 10 s.
(a) Draw pictures showing the path followed by the chair. Give both a side view and a top view.
(b) In your diagrams in part (a), indicate all the forces on the chair. Also draw a free-body diagram for the chair.
(c) Find the components of the forces in the vertical direction and in the direction toward the center of the chair’s circular path. Express your answers in terms of the tension in the cable, the angle θ, and the mass m of the chair.
(d) Apply Newton’s second law in both the vertical and radial directions. What is the acceleration of the chair along y?
(e) Find the angle θ the cable makes with the vertical.
Figure P5.22
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