In solution of this problem the acceleration of all the blocks is taken same as $a$ . But won't the acceleration of Block $A$ and $B$ be different and the acceleration of Block $C$ would be the sum of acceleration of $A$ and $B$. Please explain.
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$\begingroup$ How can the string still be attached to all the blocks if they move at different acceleration or speed? Unless of course the string can stretch. $\endgroup$– slebetmanCommented Jul 24, 2020 at 15:46
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$\begingroup$ do you consider that the problem would be different if A and B were on the same side? What if they were attached together? What if it was a single 12kg block? $\endgroup$– njzk2Commented Jul 24, 2020 at 16:58
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4 Answers
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Solving this problem requires additional assumptions which are not stated.
For this type of high-school/freshman question you should assume block C is frictionlessly constrained to move only vertically and to remain level by the channel in which it runs.
If it is not constrained to be level, or if it can move from side to side, then it could either tilt (if the strings are attached at different points) or move from side to side. This complicates the analysis, and I haven't attempted to solve for that.
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4$\begingroup$ Right, the issue could be fixed by constraining C to a narrow shaft, or by attaching the ropes at a single point. Without those constraints, the unequal tensions will result in a torque around C's center of mass, resulting in the left side of C falling faster than the right, so A will initially accelerate faster than B, until C has twisted enough to balance the torque. $\endgroup$ Commented Jul 24, 2020 at 13:54
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1$\begingroup$ The given diagram seems to support this idea for the constraint. $\endgroup$– wyphanCommented Jul 24, 2020 at 17:06
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Notice, both the strings of blocks A & B are tied to the (same) block C which moves vertically downward with a certain acceleration. Block C pulls & causes both the blocks A and B to move with the same acceleration. However the tensions in both the strings will be different depending on the masses of blocks and the friction conditions.
answered Jul 24, 2020 at 1:12
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It can be explained by string constraint.Block A and C share the same rope and also the blocks B and C.So,for the string to remain taut(between A and C)both should have the same acceleration and also the same reason for B and C.
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Block C can only accelerate in one manner, and because they are tied by strings, Blocks A and B must accelerate at that same rate. Otherwise the strings would either go slack or snap -- in either case the block attached to that string would cease to accelerate because there wouldn't be any force on it.
