1. The problem statement, all variables and given/known data 2 identical bowls are rolling on 2 different routes. The first one has a convexity and the second one has a concavity in their middle parts. The convexity fits perfectly the concavity. Both bowls had the same initial velocities. Bowls are rolling without slipping and jumping. Which one will reach the goal first? Why? What can you tell about their final velocities and kinetic energy of rotational motion? Consider 2 cases: a) there are no wastes of energy b) there appears friction. How many times deeper or wider should be the concavity so that both bowls reach the goal simultaneously? 2. Relevant equations KE = (mV^2)/2 kinetic energy E = (Iw^2)/2 kinetic energy of rotational motion T=fN friction 3. The attempt at a solution The first part I did in such a way - consider an average velocities of both bowls. When the first one reaches the goal its average velocity is less than the second, because when the first one climbed the convexity its velocity decreased and thus affectioned average velocity in a negative way. The second bowl behaved just in opposite. Energies are the same, because there are no wastes. However, I have a big problem with b). Actually, I have no idea how to solve this one.