Connected particle problem involving rough inclined plane

[James10492]

Dear math-helpers,

I have come across the following problem which yet again has presented me with difficulty. Observe the diagram that I made in MS paint:



"Box A of masss 6kg rests on a rought plance which is inclined at an angle x to the horizontal, where tan x = .75. The coefficient of friction between the box and the plane is m. Box A is attached to one end of a light inextensible string, which passes over a smooth pulley. The string is attached to a second box B, of mass 2kg, which hangs freely below the pulley.

The system is released from rest: given that A begin to slide down the incline, what is the range of possible values of m?"

I would begin by trying to formulate equations of motion for each particle as is the normal procedure in these pulley-problems:

[math]T - 2g = 2a \\ 6g\sin{x} - F - T = 6a \\ 6g\sin{x} - m[6g\cos{x}] - T = 6a[/math]
You want to show that the downward sliding force of A is greater than the combined resistive forces of the friction and the tension in the rope, and for what range of m this would be true.

I don't see how you are supposed to proceed from here, as both a and T are unknown quantities. I don't see how you can solve using a simultaneous equation. Adding the equations of motion leads to an expression for a that involves the undefined 'm'.

This was only a 3 mark question so I think I am probably missing a trick here.

 

[topsquark]

[math]T - 2g = 2a \\ 6g\sin{x} - F - T = 6a \\ 6g\sin{x} - m[6g\cos{x}] - T = 6a[/math]

You have left number m's off of these equations, you have too many T's, and I don't really know what you are trying to say in the last equation.

Aside from the missing m's the first equation is correct.

Sketch a Free-Body diagram and decompose the forces into vectors with positives down the slope and perpendicular to it. Let us know what you get when you do that and we can talk from there.

-Dan

 

[lex]

This was only a 3 mark question so I think I am probably missing a trick here.

You can work out sinx and cosx from tanx=3/4
Now substitute T from the 1st equation into your third equation.
That will give you an equation with [imath]\mu[/imath] and 'a'.
Use the fact that a≥0 to get the restriction on [imath]\mu[/imath].