Potential Energy EX 2

When the two blocks are released from rest, one of the blocks moves up while the other goes down. It is important to make a decision about which one of them will go up and which one will go down. There is a rule of thumb for making such decisions when dealing with an attractive interaction such as the gravitational attraction. When released from rest a system always moves towards the lowest possible level of potential energy. It means that the change in gravitational potential energy is always negative when an object is released from rest. It also means that we have "a test" for evaluating whether our solution is correct:

1. Let's say $m_{1}$ moves up and the change in its gravitational potential energy is positive. Then, $m_{2}$ moves down and the change in its gravitational energy is negative. The total change of the system $m_{1}$-$m_{2}$-Earth is
   
   $\Delta U=m_{1}gh+(-m_{2}gh)=(4)(10)(0.2)+(-(8)(10)(0.2))=8-16=-8J$
   
   This is a possible result.
   
   
2. Let's say $m_{2}$ moves up and the change in its gravitational potential energy is positive. Then, $m_{1}$ moves down and the change in its gravitational energy is negative. The total change of the system $m_{1}$-$m_{2}$-Earth is
   
   $\Delta U=m_{2}gh+(-m_{1}gh)=(8)(10)(0.2)+(-(4)(10)(0.2))=16-8=8J$
   
   This is an impossible result.

Therefore, the block $m_{1}$ moves up and the change of the gravitational potential is -8 J.