A block with mass m1 hangs from a rope that is extended over an ideal pulley and attached to a second block with mass m2 that sits on a ledge. The second block is also connected to a third block with mass m3 by a second rope that hangs over a second ideal pulley as shown in Figure P5.47. If the friction between the ledge and the second block is negligible, m1 = 3.00 kg, m2 = 5.00 kg, and m3 = 8.00 kg, find the magnitude of the tension in each rope and the acceleration of each block.
FIGURE P5.47
What is the magnitude of tension on each rope and the acceleration on each block?
Answer to Problem 47PQ
The magnitude of tension on each rope is
Explanation of Solution
From the given condition the
Applying Newton’s laws.
For
Here,
For
Here,
For
Here,
Write the equation for gravitational force.
Here,
Conclusion:
Using equation V find the gravitational force on each object.
Substitute the above values in equation I, II and IV to generate another three equation with unknown factors.
Solve the equation VI and VIII to get tension and substitute in equation VII.
Then equation VII becomes,
Substitute
Therefore, the magnitude of tension on each rope is
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Chapter 5 Solutions
Physics for Scientists and Engineers: Foundations and Connections, Advance Edition, Volume 2
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- Two blocks are connected by a rope that passes over a massless and frictionless pulley as shown in Figure P5.41. Given that m0 = 15.93 kg and m2 = 10.45 kg, determine the magnitudes of the tension in the rope and the blocks acceleration. FIGURE P5.41arrow_forwardAn object of mass m = 1.00 kg is observed to have an acceleration a with a magnitude of 10.0 m/s2 in a direction 60.0 east of north. Figure P4.29 shows a view of the object from above. The force F2 acting on the object has a magnitude of 5.00 N and is directed north. Determine the magnitude and direction of the one other horizontal force F1 acting on the object. Figure P4.29arrow_forwardAn object of mass m1 = 5.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2 = 9.00 kg as shown in Figure P4.28. (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects and (c) the tension in the string. Figure P4.28arrow_forward
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