Two masses attached to spring w/ pulley

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The discussion revolves around a physics problem involving two masses connected to a spring and a pulley system. Key questions include calculating the combined kinetic energy of the blocks after one block has fallen a specific distance, the kinetic energy of the hanging block, and the maximum distance the hanging block will fall before stopping. Participants suggest using conservation of energy principles, considering both gravitational and spring potential energies, and emphasize the importance of determining the relationship between the speeds and distances of the two blocks. The confusion expressed by the original poster highlights the complexity of applying these concepts correctly. Clarifying these relationships and applying the conservation of energy equation is essential for solving the problem.
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Homework Statement



Two blocks, of masses M = 1.7 kg and 2M are connected to a spring of spring constant k = 180 N/m that has one end fixed, as shown in the figure below. The horizontal surface and the pulley are frictionless, and the pulley has negligible mass. The blocks are released from rest with the spring relaxed.

http://img686.imageshack.us/img686/1376/stupidness.jpg

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(a) What is the combined kinetic energy of the two blocks when the hanging block has fallen a distance of 0.090 m?

(b) What is the kinetic energy of the hanging block when it has fallen that 0.090 m?

(c) What maximum distance does the hanging block fall before momentarily stopping?


Homework Equations



KEi + PEi = KEf + PEf

Fs = kx


The Attempt at a Solution



I've tried to use the two masses as one system, and also have tried to separate them into two different systems. Neither way seems to be working for me, and I am just thoroughly confused. I would really like to believe that I only need a push in the correct direction.

Thanks for any help offered! :D
 
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You should first determine if the speeds and distance traveled by each block are the same. Then using your conservation of energy equation, applied to the system, should give you the answer. Be sure to consider both gravitational and spring potential energies associated with spring-block system. Please show the values you are using in your equation.
 
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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