Solving Lever (Moment) Homework Problem

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To solve the problem, the pole's weight is 500 N, and one brother applies an upward force of 100 N, requiring an additional force of 400 N from the other brother to maintain balance. The key is to determine the distance from the end where the second brother should lift to ensure the pole remains horizontal. Using moments about the fulcrum, the upward forces must equal the downward force, and the moments around the fulcrum must also balance. The discussion emphasizes understanding the application of forces and moments in maintaining equilibrium.
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Homework Statement


A uniform 10 m long, 50 kg pole is lying on the ground. You get your little brother to lift at one end with an upward force of 100 N. How far from the other end will you need to lift so the pole stays horizontal (in m)? [Hint: Using your little brother as the fulcrum, what upward force, in N will you need to apply?]


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The Attempt at a Solution



Hi, I am really confused as to how to answer this. I know its to do with moments but i don't understand how to use the brother as the fulcrum because how much force does the other brother have to apply? the question doesn't say
 
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I think this is a poorly conceived question.
The other brother must lift with at least a force that will, when combined with the first brother, equal the weight of the the pole. In round figures (taking g as 10m/s²)
The weight is 500N and the one guy has an upward force of 100N, so you need at least 400N upwards. The question is, where do you apply that 400N to keep the pole horizontal; that is, there is no overall turning moment.
(At least that's what I think they mean!)
 
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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