Help with 3 objects/masses connected by string over frictionless pulley?

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The discussion revolves around solving a physics problem involving three masses connected by strings over a frictionless pulley. The user attempts to calculate the downward acceleration of mass M2 using free body diagrams and Newton's second law but struggles with the correct application of the formulas. After several incorrect attempts, including using different masses and equations, the user finds a solution using the formula A = [(M1-M2)/(M1+M2)] * g, arriving at an acceleration of 1.413 m/s². The user also requests assistance with a diagram to clarify the setup but ultimately resolves the issue independently. The thread highlights the importance of correctly applying physics principles in problem-solving.
miamirulz29
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Homework Statement


Three masses connected by light strings are shown in the figure below (I will try my best in describing the figure):
There is light, frictionless pulley with two masses, M2 and M3, on the left and one mass, M1, on the right. They are all connected by light strings. Given m1 = 10 kg, m2 = 7.48 kg, m3 = 8.01 kg, and g = 9.8 m/s2. The acceleration of gravity is 9.8 m/s2 . Find the downward acceleration of m2 mass. answer in units of m/s^2


Homework Equations


SigmaF= ma
mg=fg

The Attempt at a Solution



I drew three separate free body diagrams for each of the masses.
For M1:
Ft-MG=MA
Ft-98=10a

For M2:
MG-Ft=MA
7.48(9.8)-Ft=7.48a
73.304-Ft=7.48a

So I combined the two equations and got -1.413 m/s^2. I though because it is downward, I didn't need the negative, so I put in UT, 1.413, it was wrong, I also put -1.413, it was also wrong. Then I tried using M3 and combined the acceleration of M3 and M2, which was 8.387, which is also wrong. Then I read on another thread that you can use the equation:
A= [(M1-M2)/(M1+M2)] * G. I got 1.413. I honestly don't know what to do at this point, can somebody please help me. Thanks in advance.
 
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Anybody? Please?
 
miamirulz29 said:
Anybody? Please?

If you could post the diagram that would help a lot so we would know where to start...
 
Diagram posted. It is on the last page, number 018 (part 1of 3).
 

Attachments

Please can anybody help? I even posted the diagram.
 
Nevermind, figured it out.
 
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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