Forces, marble on side of spinning bowl

In summary, a marble is dropped into a hemispherical bowl with a radius of 15 cm that is spinning at a rate of one full turn in 0.72 s. The marble comes to rest against the inside surface of the bowl and rotates at the same rate as the bowl. The angle theta, which is the angle between a line straight up from the center of the bowl and the point where the marble rests, can be solved using centripetal force equations.
  • #1
bang
18
0

Homework Statement


A bowl has a hemispherical inside surface with radius R = 15
cm, and is sitting in the exact center of a spinning table that completes
one full turn in 0.72 s. A small marble is dropped into the bowl. After
the marble has stopped rolling around, it will come to rest against the
inside surface of the bowl, rotating around the center of the table at the
same rate as the bowl. You can ignore the size of the marble. The
angle θ, as defined in the figure, is closest to ___?

DIAGRAM SHOWING THE PROBLEM
http://imgur.com/0pKoAKT

Homework Equations


I guess F=ma
a=v^2/r
Ff=Fnμ

The Attempt at a Solution


No idea how to start even approaching this, sum of all forces?
 
Last edited:
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  • #2
It would probably help us to see the figure stated in the problem.

Looks like you've got a centripetal force problem.
 
  • #3
I don't really have access to a diagram, but basically its a semi-circle, with a marble resting on the side of the bowl. The angle theta is the angle from a line that is straight up from the center of the bowl.
 
  • #4
I put a picture up now.
 
  • #5
Draw a free body diagram for the marble. As functions of theta, what forces act on it? What is the resultant force for equilibrium?
 

What is the force that keeps the marble on the side of the spinning bowl?

The force that keeps the marble on the side of the spinning bowl is centrifugal force.

Does the speed of the spinning bowl affect the force on the marble?

Yes, the faster the bowl spins, the greater the centrifugal force on the marble.

What would happen if the marble was placed on the bottom of the spinning bowl?

If the marble was placed on the bottom of the spinning bowl, it would likely roll to the center due to the force of gravity being greater than the centrifugal force.

How does the shape of the bowl affect the force on the marble?

The shape of the bowl does not affect the centrifugal force on the marble. As long as the bowl is spinning at a constant speed, the force will remain the same.

Can the centrifugal force on the marble be greater than the force of gravity?

Yes, if the bowl is spinning fast enough, the centrifugal force on the marble can be greater than the force of gravity, allowing the marble to remain on the side of the bowl.

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