Acceleration of two blocks connected by a pulley

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The discussion centers on understanding the acceleration of two blocks connected by a pulley. The original poster questions why the combined mass of both blocks is used in their solution instead of just the mass of M1. They initially believed that only the forces acting on M1 should determine its acceleration, but they realize that the tension in the rope and the forces on M2 also play a critical role. The clarification highlights that if the tension equals the weight of M2, then M2 would not accelerate, indicating that both masses must be considered for accurate calculations. Ultimately, the interaction between the two blocks is essential for determining the system's overall acceleration.
Esoremada
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http://puu.sh/4DtNc.png

I solved this question, but I don't understand why this worked. I feel like for the final line in my solution it should just be divided by M1, not the combined mass of both blocks.

Isn't this synonymous with just M1 being pulled up the ramp by a guy at the top pulling with a force of 2.91*9.8 N? I thought I made an equation for the net force of just M1. The tension in the rope is 2.91*9.8, the friction is 3.19113*9.8*cos(18.5)*0.396, the gravity component pointing down the ramp is 3.19113*9.8*sin(18.5). So why does the mass of M2 have any place in solving for the acceleration of M1?

I feel like it should just be.
[2.91*9.8 - 3.19113*9.8*sin(18.5) - 3.19113*9.8*cos(18.5)*0.396] / (3.19113)
 
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Once the system has an acceleration, the tension in the rope will no longer equal the weight of ##m_2##.

You can see why this is true by considering the forces acting on ##m_2##. If the tension acting on ##m_2## equals the weight acting on ##m_2##, then the forces acting on ##m_2## would add to zero and ##m_2## would have zero acceleration.
 
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Ah I get it, thank you.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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