1. A chain is help on a frictionless table with one-fourth of its length hanging over the edge. If the chain has length L and mass M, how much work is required to pull the hanging part back on the table? i dont think i could have W = mgL/4 will the work change each time a new chain ring is on the table? is there work from the horizontal chain if the table is frictionless? 2. A small solid marble of mass m and radius r rolls without slipping along the loop the loop track having been released from rest somewhere on the straight section of the track. a) from what minimum height above the the bottom of the track must the marble be released in order that it just stay on the track at the top of the loop? (the radius of the loop is R , assume R>>r ) b) If the marble is released from height 6R above the bottom of the track, what is the horizontal component of the force acting on it when it is at height R in the loop. Ui + Ki = Uf + Kf mgh = mg2R h = 2R same as height it reaches how can I account for friction?