An amusement park ride consists of a rotating circular platform that is 8.00 m i

Question

An amusement park ride consists of a rotating circular platform that is 8.00 m in diameter, and from which 15.0 kg seats are suspended at the end of 2.50 m long cables. When rotating, the cables make an angle ? = 36.8° with the vertical. Timmy, a boy riding on the seat, has a mass of 25.0 kg. {Hint: you will have to add the radius of the circular platform to the distance of Timmy’s seat to the edge of the platform} Draw a free-body diagram.

(a) What is the magnitude of the tension force on the cable of Timmy’s seat?

(b) How long does it take for Timmy’s seat to complete one revolution? {Hint: you will need to know the orbital speed of the chair}

Explanation / Answer

a)
Balance force in vertical direction
T*cos thetha = m*g
T* cos 36.8 = 25*9.8
T = 306 N
Answer: 306 N

b)
r, distance from center of axis to timmy = (8/2) + L*sin thetha
r = 4 + 2.5*sin 36.8
= 5.5 m

T*sin thetha provides centrepatal force
so,
T*sin thetha = m*v^2/r
306*sin 36.8 = 15*v^2/5.5
v = 8.2 m/s

T = 2*pi*r/v
= 2*pi*5.5/8.2
= 4.2 s
Answer: 4.2 s

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