Solving a Homework Problem with Mass, String, and Friction

AI Thread Summary
Two blocks of mass m_A and m_B are connected by an ideal string, with block A descending at a constant speed and no friction involved. The discussion centers on determining the correct relationship between the masses based on the forces acting on them, particularly using Newton's laws. The initial reasoning suggests that since the speed is constant, the forces must balance, leading to the conclusion that m_A (1/2) = m_B (sqrt(3)/2). After further analysis, it is confirmed that the first answer is correct, as 1/sqrt(3) falls between 0.25 and 0.6. The solution emphasizes the importance of breaking down gravitational components to arrive at the correct answer.
SqueeSpleen
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Homework Statement


There's two blocks of mass m_{A} and m_{B} which are linked by an ideal string. The block of mass A descends at constant speed. There's no friction. If the pulley is ideal, which one of the following is true[/B]
upload_2017-5-19_0-33-15.png

Homework Equations


Newton laws and trigonometry I think.[/B]

The Attempt at a Solution


I think that the correct answer is the second one, but the first one is marked as correct so I wanted a second opinion.
My reasoning is the following: If the speed is constant it means there is no acceleration, so the sum of the forces is 0. Then I decomposed gravity in the component that's compensated by the normal force done by the triangle and it's perpendicular component. So I arrived to
m_{A} (1/2) = m_{B} sqrt(3)/2
Now that I check, it isn't item 2. it would fall in item 1 as 1/sqrt(3) is between 0.25 and 0.6
Right?

sorry for the typos, I broke my keyboard yesterday (I won't drink coffee while on computer again) and I'm with a rubber one until a new one arrives, at least it's better thanthe one that windows have to use with the mouse.

[/B]
 

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Working it out very quickly, and thus prone to error, I think the first answer is correct.
 
SqueeSpleen said:
it would fall in item 1 as 1/sqrt(3) is between 0.25 and 0.6
Right?
Yes.
 
Absolutely correct! Way of solving by simply taking their Sine components of 'g' and solve it.
 
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