Acceleration, friction, pulleys

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The discussion revolves around calculating the acceleration of a system involving a 27.5kg box and a 13.75kg box connected by a frictionless pulley. The initial question seeks clarification on whether the acceleration calculation includes both horizontal and vertical components, and how to isolate the downward acceleration. There is confusion about the setup, specifically whether both boxes are suspended or if one is on a surface. Ultimately, the original poster resolves their query independently. The conversation highlights the importance of clearly defining physical setups in physics problems.
jshaner858
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a 27.5kg box is connected to a 13.75kg box on a frictionless pulley. my question is if you calculate the acceleration does that include horizontal and vertical acceleration, and if so, how do you just find the downward acceleration?
 
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This is too vague, please explain the setup better. Are they both in the air, one on a table the other in the air?
 
nevermind, i figured it out myself...thanks
 
my work here is done! :-P
 
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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