An amusement park ride consists of a rotating circular platform 8 m in diameter from which bucket seats are suspended at the end of 2.5 m chains. When the system rotates the chains holding the seats make an angle θ = 28° with the vertical.
(a) What is the speed of the seats? Start by drawing a proper free body diagram.
(b) If a child of mass 40 kg sits in the 10 kg seat, what is the tension in the chain?
platform radius = 4 meters
seat radius = 4 + 2.5 sin 28 = 4.17 meters
tan 28 = m v^2/4.17 / m g = v^2 /( 4.17*9.81)
so v^2 = 21.8
v = 4.66 m/s
Tension = m g / cos 28 = 50 * 9.81 / cos 28 = 556 N