Analyzing Frictionless Motion: Va vs Vb

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In a frictionless pulley system with two masses, m1 on a table and m2 hanging, the discussion centers on the velocities Va and Vb. As m2 descends, it is suggested that Vb, the velocity of the hanging mass, is greater than Va, the velocity of the mass on the table. The reasoning is based on the principles of constant acceleration due to gravity and the conservation of energy. A diagram is recommended for clarity in understanding the dynamics of the system. Ultimately, Vb is concluded to be greater than Va due to the mechanics involved.
kuuooomar
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Homework Statement


va=va vb=vb m1>m2
frictionless

Homework Equations





The Attempt at a Solution


So i got this question where m1 is on a table and connected to a pully and m2 is hanging off the table, which have a Va (velocity). Then a few seconds later the pully is drawing in and the distance from m1 and the pully decreases, basically the pully is going down. This was considered Vb(velocity). The instructor asked us which had more velocity or did it stay the same, my intution is telling me that the velocity increased but through energy of conservation I feel like it stayed constant and went to the hanging mass. I have no idea, I already took the quiz and just want some reassurance on whether i was right or wrong >_<
 
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I'd like to help, but I just don't understand the question as written. Actually a diagram is pretty much necessary to sort out pulley problems.
 
I agree a diagram would be helpful... From my understanding of the problem is that you have two masses connected via a pulley, one of the masses is on a table (assuming the table is not angled...) and the other mass is hanging freely.

It sounds to me like you are asking if V(t) is increasing so assuming that is actually the problem then Vb is greater than Va since the table is frictionless and you have a constant acceleration due to gravity.
 
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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