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

[Mary O'Donovzn]

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.

Homework Equations

M(B) ≤ μsM(A)

The Attempt at a Solution

[/B]
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?

 

[Chestermiller]

Yes, so your equation is not correct.

 

[Mary O'Donovzn]

Okay is it that it is incorrect as in doesn't exist or i used the wrong one

 

[Chestermiller]

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

 

[HalfLostAndSearching]

The maximum mass (B) that can be hung over the edge before mass (A) begins to move can be calculated using the equation M(B) ≤ μsM(A), where μs is the static coefficient of friction and M(A) is the mass of the object on the slope. In this case, the maximum mass (B) would be equal to 6 kg, as you have calculated correctly. However, it is possible that your teacher marked it wrong because they were looking for a more detailed explanation or solution.

To take into account the fact that the slope has an angle of 30 degrees, you could use the equation M(B) ≤ μsM(A)sinθ, where θ is the angle of the slope. This would give you a slightly different value for the maximum mass (B), but it would still be less than or equal to 6 kg.

It is also important to note that this calculation assumes ideal conditions and does not take into account other factors such as the mass of the rope connecting the two objects or the distribution of mass within the objects. In real-world scenarios, the maximum mass (B) may be slightly lower than the theoretical value calculated using this equation.