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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