phy
posted by Naso .
A marble slides without friction in a vertical plane around the inside of a smooth, 21 cmdiameter horizontal pipe. The marble's speed at the bottom is 4.5 m/s this is fast enough so that the marble makes a complete loop, never losing contact with the pipe.What is its speed at the top?

At the top, it needs to have centripetal acceleration of v^2/r>g
So is v^2/r greater than g?
Now its speed at the top is determined by the bottom speed minus losses to gravity.
speed at top^2 =speedbottom^22g*.21
so figure speed at top, and see if it is greater than required. 
2.2