Two masses connected by a rope on a pulley on a ramp

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SUMMARY

The discussion focuses on solving a physics problem involving two masses connected by a rope over a pulley on a ramp. Participants emphasize the importance of using distinct symbols for each mass to avoid confusion. They recommend writing force balance equations for each mass, either by separating forces into horizontal and vertical components or by analyzing forces parallel and normal to the slope. This structured approach simplifies the problem-solving process.

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  • Understanding of free body diagrams
  • Knowledge of Newton's laws of motion
  • Familiarity with force balance equations
  • Basic concepts of inclined planes in physics
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Homework Statement
If the left-hand slope in the figure makes a 58° angle with the horizontal, and the right-hand slope makes a 32° angle, how should the masses compare if the objects are not to slide along the frictionless slopes?
Relevant Equations
F=ma
I have no clue how to do the problem. I created a free body diagram for each block. I assume that it is simpler than I am making it out to be.
 

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First, use a different symbol for each mass. Calling them both "m" will confuse.

Next, write the force balance equations for each mass.
You can write an equation for each of horizontal and vertical or for parallel to the slope(s) and normal to them. Your choice.
 
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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