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Constrained Motion of 7 Masses and 3 Pulleys
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[QUOTE="Lnewqban, post: 6391860, member: 673625"] I don’t believe that setting the directions of positive one way or the other makes a difference in the result. The sign of the value that you obtain at the end always tells you whether or not your initial assumption regarding the direction of that magnitude was correct. Your error was assigning a negative value to ##4a_b##. When in doubt, it is better to assume all as positive and let the result decide. The original data is telling us that: 1) The length Xc is growing as block C is moving to the right. 2) The four lengths Xb are growing as block B is moving downwards. 3) The three lengths Xa are shrinking as block A can only move upwards as result of conditions 1) and 2) above. $$\begin{align} a_C+4a_B+3a_A&=0\nonumber\\ 75+4(480/2)+3a_A&=0\nonumber\\ -75-960&=3a_A\nonumber\\ -1035/3&=a_A\nonumber\\ a_A&=-345~mm/s^2\nonumber\\ \end{align}$$ Note that the negative sign here means that the actual direction of the acceleration of block A is opposed to the originally assumed. [/QUOTE]
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Constrained Motion of 7 Masses and 3 Pulleys
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