A marble slides without friction in a vertical plane around the inside of a smooth, 21 cm-diameter 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?

Answer 1

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^2-2g*.21
so figure speed at top, and see if it is greater than required.

Answer 2

2.2