An amusement park ride consists of a rotating circular platform 8.07m in diameter from which 10kg seats are suspended at the end of 2.87m massless chains. When the system rotates, it makes an angle of 37.3° with the vertical.
a) What is the speed of each seat?
b) If a child of mass 45.3kg sits in a seat what is the tension in the chain for the same angle?
m=55.3kg (mass of the seat + the mass of the child)
Vt=5.56565m/s (calculated from part A, confirmed as correct)
r=5.77419m (calculated from the length of the chain and the diameter of the circular platform, d/2+lsinѲ, which is its horizontal distance from the center of rotation, where d is the diameter of the platform and l is the length of the chain)
The Attempt at a Solution
I have the answer to A, and that part is verified as correct already. B is what I'm wondering about.
So, this swing is rotating in the z dimension, but in the x and y directions it is in equilibrium which means that the sum of the forces in the x direction and the y direction must be equal to 0.
Then the forces in the x are the horizontal tension in the cable in the x and the centrifugal (equal and opposite to the centripetal), and the forces in the y are the vertical tension in the cable and the force of gravity.
Since they're both equal to 0, they can be set equal to each other.
I rewrote these based on their definitions.
When I put all that together, I get T=681.28N. I have one more guess left for this problem so I need to be sure it's right beforehand. Can someone verify if this logic is correct please?