Coin and Marble on a Frictionless Dome: When Will They Hit the Ground?

[Elo21]

Harder Basic Physics Question..Please Help!

Homework Statement

A Perfectly hemispherical dome with a 10. meter radius is treated with a frictionless coating. A marble and a coin are released from the top of the dome simultaneously. We will assume there is no air friction. The coin will slide, not roll.



2. Questions

a)Will the objects hit the ground at the same time, or if not, which will hit first and why?

b)Show mathematically whether or not the coin will stay in contact with the dome until it reaches the ground. If it does not, what will the coin's vertical displacement be at the instant it loses contact with the dome, and how far from the base of the dome will the coin hit the ground? (be clear and include explanations where necessary)

3. Attempt at the solution

a) This is what I put as an answer-- They will hit the ground at the same time because there is no friction.

Am I right? When there is no fiction objects fall at the same rate?

b) This part is where I am confused. Would I have to use equations using radians? Do I need to use multiple different kinds of equations?

Please Help!

 

[minimark1234]

well i don't know how in depth you book is, but I am going to assume that the marble will have angular momentum from rolling along with the sliding (unless its rolling at a speed of which there is no sliding), and the question makes a point of saying the coin won't roll so it might have something to do with that. i don't remember if the rolling object will go faster or slower, but I am going to think slower because some of the kinetic energy is being lost to angular rolling moment. i could be wrong and it could be it gains speed, id have to look it up in my old book to be certain, but its to late for me to rummage though my stuff for it.

 

[rl.bhat]

As the coin slides its velocity increases. The centripetal force increases and hence normal reaction increases. At the same time component of the weight of the coin along the radius decreases. As long as component of the weight is greater than the normal reaction, the coin will be on the hemisphere. When the normal is greater than the component of the weight, the coin will loss the contact of the dome.