Acceleartion of hanging block connected to a sliding block

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The problem involves two blocks connected by a string, with one block (B) hanging off a frictionless tabletop and the other (A) resting on it. The initial assumption that both blocks would accelerate at 9.8 m/s² is incorrect due to the presence of tension in the rope affecting their motion. Block B experiences gravitational force and rope tension, while block A is only influenced by the rope tension. To find the correct acceleration, it's essential to apply Newton's second law to both blocks and account for the forces acting on them. The solution requires analyzing these forces to derive the correct acceleration and tension in the rope.
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.




Homework Equations


F=ma



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.
 
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emauer said:
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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