A.1-kilogram ball rolls across the floor at a speed of 2 meters per second. another .1 kilogram ball rests on a shelf 1 meter above the floor. which ball has more energy?

First, we need to fight the weight of the balls instead of their mass.  We do this by multiplying their weight it kg by 9.8.  This gives us .98 N.  To find the potential energy of the rolling ball, we find its kinetic energy.  The formula for this is KE=mass*velocity^2*1/2.  

Plugging in our numbers, we have Kinetic energy = .1 * 1^2*1/2 which gives us .05 joules.

Now we find the potential energy of the ball on the shelf.  For this we do:

Potential energy = .1*9.8*1, and our answer is .98 joules.  Clearly, the ball on the shelf has more energy.

The answer is frictional force