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FIGURE CP7.54 shows three hanging masses connected by massless strings over two massless, frictionless pulleys. a. Find the acceleration constraint for this system....

Question

FIGURE CP7.54 shows three hanging masses connected by massless strings over two massless, frictionless pulleys. a. Find the acceleration constraint for this system. It is a single equation relating $a_{1 y}$ $a_{2 y}$ and $a_{3 y}$ Hint: $y_{\mathrm{A}}$ isn't constant. b. Find an expression for the tension in string $\mathbf{A}$ Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns. Hint: You should be able

FIGURE CP7.54 shows three hanging masses connected by massless strings over two massless, frictionless pulleys. a. Find the acceleration constraint for this system. It is a single equation relating $a_{1 y}$ $a_{2 y}$ and $a_{3 y}$ Hint: $y_{\mathrm{A}}$ isn't constant. b. Find an expression for the tension in string $\mathbf{A}$ Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns. Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns. c. Suppose: $m_{1}=2.5 \mathrm{kg}, m_{2}=1.5 \mathrm{kg},$ and $m_{3}=4.0 \mathrm{kg} .$ Find the acceleration of cach. d. The $4.0 \mathrm{kg}$ mass would appear to be in equilibrium. Explain why it accelerates.



Answers

Two blocks, one of mass $5.0 \mathrm{kg}$ and the other of mass $3.0 \mathrm{kg},$ are tied together with a massless rope as in Figure $4-24 .$ This rope is strung over a massless, resistance-free pulley. The blocks are released from rest. Find the following. a. the tension in the rope b. the acceleration of the blocks Hint: you will need to solve two simultaneous equations. CANT COPY THE FIGURE


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