5. A block whose mass is M1 rests on a friction-free table and is connected by a string to a second block M2 hanging over the table. The system is released. a) How fast are the blocks moving after M2 has fallen a distance h? Find a numerical answer if h =1 m; M1 = 1 kg; M2 = 4 kg? c) What if there were a coefficient of friction, u , between block 1 and the table.

 

  red block = m1

green block = m2

  Because we have for now, at least, neglected friction, the red block on the table will start slipping as soon as it is released.
 

 With more than one object moving, the law of conservation of energy takes a different form. Where does the energy come from? = where did it go?

See line 3. The blocks have the same speed because they are tied together. The third bar in the equal sign means "equal by definition".
     
   

 If friction enters the pictuure, we treat it as another place for energy to go.

Note that in the bottom line, if um1 is greater than m2, the radicand goes negative and the blocks do not move when released.