How Do You Calculate the Speed and Tension in a Rotating Amusement Park Ride?

[cdubsean]

Homework Statement

A) An amusement park ride consists of a rotating
circular platform 10.8 m in diameter from
which 10 kg seats are suspended at the end
of 2.34 m massless chains. When the system
rotates, the chains make an angle of 29.4◦ with
the vertical.
The acceleration of gravity is 9.8 m/s2 .

What is the speed of each seat?
Answer in units of m/s.

B) If a child of mass 42.6 kg sits in a seat, what is
the tension in the chain (for the same angle)?
Answer in units of N.

Homework Equations

∑F=ma_(c)= m (v^2/r)

The Attempt at a Solution

If this where talking about the string starting from origin of pole, wouldn't be that hard. But since they added the top diameter, I am not sure how to tackle this problem.

 

[Doc Al]

If this where talking about the string starting from origin of pole, wouldn't be that hard. But since they added the top diameter, I am not sure how to tackle this problem.

The chains are attached to the edge of the circular platform and angle outward as the entire thing rotates. The axis of rotation is the center of the platform.

 

[cdubsean]

I am aware of this, but from what my book has and what I have been trying to find out, I can't seem to figure out where to start since I have to factor in the radius of the axle the chains are attached to. Which is where I am stuck trying to figure out how to start.

 

[Doc Al]

Do you have a diagram to work from? I'm not sure what you mean by "radius of the axle". You certainly have to add the radius of the platform to any calculation, but that's given. And you know the angle that the chains make, so you can figure out how much they add to the total radius.

 

[cdubsean]

Here is a diagram :

http://img525.imageshack.us/img525/7149/captureni.jpg"

 

[Doc Al]

Good. So what's the issue? Can you calculate the radius of the circular path of the chairs?

 

[cdubsean]

Yes, it is the diameter of 10.8 plus the 2.34sin(29.4) then divide by 2 to find radius, but I am still trying to find relations to get from not having a time and not having a velocity to finding them.

 

[Doc Al]

Yes, it is the diameter of 10.8 plus the 2.34sin(29.4) then divide by 2 to find radius, but I am still trying to find relations to get from not having a time and not having a velocity to finding them.

Analyze the forces acting on the chairs and apply Newton's 2nd law. (Consider vertical and horizontal components.)