Resolving Forces for Periodic Motion in a Suitcase

[Angello90]

Hi all,

Everything is in the pdf file. I did the question, but I'm not sure if its correct. My lecture is using Wiley, and I think it is really confusing service for assignments.

Anyways, my questions are:
Is the question done out right?
Why is there θ given, if I don't really need to use it? Or do I need to use it?

Thanks in advance everyone.

Kind regards

 

[Delphi51]

Welcome to PF, Angello90!
You have quite an interesting problem. It has to be more complex than you took it to be. The angle matters! If the angle was 90 degrees, for instance, then the suitcase would fall before it made a quarter of a turn. When the angle is smaller, the carousel can spin faster without the suitcase sliding.

It seems to me you have to make a free body diagram of all the forces on the suitcase, resolve them into forces down the ramp and into the ramp (normal). I find these problems make more sense when I take the view from the moving object so there is a centrifugal force rather than a centripetal one. Then you can find the friction force and write the condition that the total force down the ramp is zero - spinning as fast as you can without it slipping. It will be kind of like your u*m*g = m*v^2/r, but you'll have more terms and every term will have a sinθ or cosθ factor.

 

[Angello90]

Thanks Delphi51 for that, can you tell me whether I am correct with this solution in pdf?

 

[Delphi51]

I don't think so, Angello. Seems to me you have to think like this:

Both the gravity and centrifugal forces need to be resolved into parallel and normal components. The total normal force N will have two expressions added together (one from Fc and one from Fg).