Centripetal Motion and Masses at the Fair

[catenn]

Hi, I was told about Centripetal Motion and learned some about rides at the fairs. There is one ride with chairs hanging by a chain in a circle that simply rotates at a certain speed without turning at any angle. Does anyone understand why all of the chairs move up at the same angle even though each person will have a different mass, and even the empty chairs move the same. How can all of the masses cancel? Thanks.

 

[Doc Al]

It turns out that the angle a chair rises depends on the ratio of the centripetal force (which is proportional to mass) to the weight (which is also proportional to mass). So the mass does cancel. As long as the chains are the same length, the seats will rise to the same angle for a given angular speed regardless of the mass of the person.

 

[catenn]

Thank you very much!

 

[student85]

What procedure do you exactly follow to determine the height each chair is going to rise?

 

[Doc Al]

Apply Newton's 2nd law. The chairs are centripetally accelerated, so there is a net force in the horizontal direction. Realizing that the tension in the chain acts along its length allows you to calculate the angle the chain makes with the vertical.