Question

The figure shows a photo of a swing ride at an amusement park. The structure consists of a horizontal, rotating, circular platform of diameter D from which seats of mass m are suspended at the end of massless chains of length d. When the system rotates at constant speed, the chains swing outward and make an angle θ with the vertical. Consider such a ride with the following parameters: D = 6.50 m, d = 2.50 m, m = 9.5 kg, and θ = 26.0°.

What is the speed of each seat (in m/s)?

(b)

Draw a diagram of forces acting on a 40.0-kg child riding in a seat.

(c)

Find the tension in the chain (in N).

What If? The chains holding each seat can withstand a maximum total tension of 700 N.

(d) What is the angle that the chains make with the vertical (in degrees) when they have this tension?

(e)What is the maximum angular speed (in rad/s) with which the ride can rotate?

Answer 1

D = 6.5mtr 3.25 m. d=2.som. m=a.steg. 77-sind 8=26.00 27x= drino. => R=r+x= 3.25tdsino 3.56 m Now, m ² Teoso, Tsino= mg. -T = mg sino 2 до «я (40 sino * ne = \PR Coto - 8.40m13 (as 1- 3 Sino (40 - 14.5 x 9 8 sim 260 (1) Ilo The chain should breate at T = 700 (a) Trind- ing. ef sind= mg 8- Sirt (ing) = ( 10 19.5) mRw² = Toso = ng lose war jeg coto R = 3.25xd sno= 5.63 7W = /109 rad's