So please review them before you begin.
A solid ball of mass M and radius r sits at rest at the top of a hill of height H leading to
a circular loop-the-loop. The center of mass of the ball will move in a circle of radius R if it
goes around the loop. Recall that the moment of inertia of a solid ball is Iball = 2MR2. 5
a) Find the minimum height Hmin for which the ball barely goes around the loop stay- ing on the track at the top, assuming that it rolls without slipping the entire time independent of the normal force.
b) where it was a block that slid around a frictionless track? Does this answer make sense? If it is higher, where did the extra potential energy go? If it is lower, where did the extra kinetic energy come from?

c) Discussion question for recitation: The assumption that the ball will roll around the track without slipping if released from this estimated minimum height is not a good one. Why not?

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?