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Acceleartion of hanging block connected to a sliding block

  • Thread starter emauer
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1. The Problem
Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a smooth (frictionless) tabletop as shown above, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block B is then released from rest at a distance h above the floor at time t = 0.
Express all algebraic answers in terms of h, m, and g. Assume the string rests on a pulley at the edge of the table instead of being in direct contact with the table itself as in picture.
a. Determine the acceleration of block B as it descends.




2. Relevant equations
F=ma



3. The attempt at a solution
It is my understanding that because there is no friction there is no force pulling block A to the left therefore no force counteracting the force of gravity pulling block B down. The acceleration of both blocks should therefore be 9.8m/s^2. I am told this is not the answer however.
 
I had a problem loading the picture last time so here it is.
 

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It is my understanding that because there is no friction there is no force pulling block A to the left therefore no force counteracting the force of gravity pulling block B down.
There are two forces acting on B (gravity and the rope tension) and only one force acting on A (rope tension). If the rope tension were zero, then you'd be correct. But it's not zero.
The acceleration of both blocks should therefore be 9.8m/s^2. I am told this is not the answer however.
The acceleration of both blocks would be 9.8m/s^2 if they were in free fall. But they are not: there's a table constraining their motion. The gravitational force on A is countered by the normal force of the table, thus the rope must drag A along without the help of gravity.

Analyze the forces on A and on B and apply Newton's 2nd law to each. Then you can solve for the acceleration (and the rope tension).
 

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