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In the diagram above, assume that the tabletop is frictionless. Determine the acceleration of the blocks once they're released from rest. |
Answer» Solution :There are two blocks, so we need to DRAW two free-body diagrams.  To get the acceleration of each one, we use Newton's Second Law, `F_("net")=ma`.  Notice that there are two unknowns, `F_(y)` and a , but we can eliminate `F_(T)` by adding the two equations, and then we can solve for a.  A quicker way of solving for the acceleration is to treat the entire SYSTEM (blocks plus string) as one object. Since we are only concerned with forces acting on the object, we can ignore tension. The string is part of the object. Then we only need to CONSIDER forces acting in the direction of motion (Mg) and forces opposite the direction of motion (none). Our mass in Newton's Second Law becomes M+ m, so `F_("net")=ma` becomes Mg=(M+m)a , giving us the same ANSWER for acceleration. |
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