Pulley and Blocks: Is My Answer Correct?

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The discussion focuses on the calculations involving two blocks connected by a pulley system. The user derives equations for the tensions and accelerations of the blocks, ultimately expressing the acceleration of block m2 as a2 = m2g / (4m1 + m2) and that of block m1 as a1 = 2m2g / (4m1 + m2). Other participants confirm the correctness of these calculations. The consensus indicates that the user's approach and final answers are accurate. The thread highlights the importance of proper application of Newton's laws in solving pulley problems.
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Homework Statement
In term of m1, m2 and g, find the acceleration of each block. There is no friction anywhere in the system
Relevant Equations
∑F= ma
1 1.png
155434234_755501075359888_7661044753117238048_n.jpg

  • Block m2:
    m2g - 2T = m2a2 (1)
  • Block m1:
    ∑F= ma
    T= m1a1 = m1.2a2 (2)

    Cancel T in (1) and (2) I have :
    m2g = a2 (4m1 + m2) => a2 = m2g / (4m1 + m2)

    => a1 = 2m2g / (4m1 + m2)
Is my answer correct ? Thank you
 
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Your work looks correct to me.
 
TSny said:
Your work looks correct to me.
Thank you
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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