Circular Motion of amusement park ride

AI Thread Summary
The discussion revolves around calculating the speed of seats on a rotating amusement park ride with a circular platform. The platform has a diameter of 7.81m, and seats are suspended from 3.03m chains at an angle of 26.1 degrees with the vertical. The forces acting on the system are analyzed using a free body diagram, leading to equations involving tension (T) and gravitational force (mg). Participants discuss deriving the radius (r) and using it alongside the tension to find the speed (v) of the seats. The problem is ultimately resolved by applying the relevant physics equations.
rg67
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Homework Statement


An amusement park ride consists of a rotating circular platform 7.81m in diameter from which 10kg seats are suspended at the end of 3.03m massless chains. when the system rotates, the chains make an angle of 26.1 with the vertical. Gravity = 9.8m/s^2. what is the speed of each seat? answer in units of m/s.


Homework Equations


F=ma
acceleration centripetal = v^2/r

The Attempt at a Solution


Well i drew a free body diagram and the forces of on the y-axis are Tcos26.1=mg. the forces on the x-axis are (Tsin26.1)r/m=V^2
 
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Welcome to PF.

rg67 said:
Well i drew a free body diagram and the forces of on the y-axis are Tcos26.1=mg.

Good. So T = ____ ?

the forces on the x-axis are (Tsin26.1)r/m=V^2

If you figure out what r is, and use T from the previous equation, you'll have it solved.
 
thanks i solved it
 

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