Solve Tricky Homework Problem: Ice Flake Speed in Hemispherical Bowl

[lbofin1]

In this problem, a 1.90 g ice flake is released from the edge of a hemispherical bowl whose radius r is 15.0 cm. The flake-bowl contact is frictionless.
a) What is the speed of the flake when it reaches the bottom of the bowl?
(b) If we substituted a second flake with twice the mass, what would its speed be?

*Our teacher gave us these problems and they are from a totally different book than we are using, and we haven't been able to find any examples like this in our book. We don't even know where to begin..*
Please help!

 

[mrjeffy321]

This problem can be easily soved with a simple application of Conservation of Energy.

Energy the flake has at the beginning (before it it dropped) = the Energy at the end (when it reaches the bottom of the bowl)

The ice flakes "Total" energy = Kinetic Energy + Potential Energy

The flake starts off with all its energy being potential, and no kinetic since it is not moving. When the flake gets to the bottom of the bowl, all that potential energy is converted into Kenitic energy.
change in KE = Change in PE

KE = 1/2 mv^2
PE = mgh

m is the mass, v is the velocity, g is the gravitational acceleration, and h is the height.