Find Max Mass B for Mass A to Move on Slope of 30°

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To determine the maximum mass (B) that can hang without causing mass (A) to move down a 30° slope, the static friction must be considered along with the gravitational force acting on mass (A). The equation M(B) ≤ μsM(A) is insufficient alone, as the angle of the slope affects the forces involved. The gravitational force component parallel to the slope and the frictional force must be calculated to find the correct maximum mass (B). The correct approach involves using the angle to resolve the forces acting on mass (A) and applying the equilibrium conditions. Understanding these dynamics is crucial for solving the problem accurately.
Mary O'Donovzn
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Homework Statement



A mass(A) of 12kg is on a slope with an angle of 30 degrees.
The static coefficient of friction of the slope = 0.5 (μs)
The kinetic coefficient of friction 0.3
The length of the slope from the block= 5m

However the The mass(A) is connected to another mass(B) which is hanging over the edge.

Q. What is the maximum mass (B) can be before mass (A) will begin to move.
IMG_20141031_170401.jpg



Homework Equations



M(B) ≤ μsM(A)

The Attempt at a Solution


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I just subbed into this 0.5 x 12 = 6 Kg

but my teacher marked it wrong on the test.
Is it possible the fact its on a slope will have anything to do with it so do I use the angle in some way?
 
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Yes, so your equation is not correct.
 
Okay is it that it is incorrect as in doesn't exist or i used the wrong one
 
Suppose that the mass MB wasn't there. Would you know how determine whether of not the mass A slides down the slope? If so, show us how you would do it. Once you do this problem, you will know what to do with the present problem in which MB is trying to make MA slide up the slope.

Chet
 
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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