Dynamics - Blocks on an Incline Plane

[fobbz]

Homework Statement

In the diagram below find the 1) acceleration of the system 2) T1 and T2
The ramp is angled 35degrees to the horizontal and coeff of friction is 0.15

Homework Equations

The image at the top is the problem's figure.
http://img155.imageshack.us/img155/4176/centralkootenayj2011122.jpg

The Attempt at a Solution

Basically, I've redone this problem and I believe my answers are now correct. In my picture all necessary FBDs are drawn. Do I have the right idea?

Thanks

 

[PhanthomJay]

Your answers appear correct, but I have the following comments:

1.) Drawing a Free Body Diagram of the system of 3 blocks, which you have done to calculate the acceleration of the system, is generally not a good idea for these particular type problems where motion of all blocks is not in the same direction, even though you did get the correct answer.
2.) Are the 5kg blocks accelerating up the plane or down the plane?

 

[fobbz]

Your answers appear correct, but I have the following comments:

1.) Drawing a Free Body Diagram of the system of 3 blocks, which you have done to calculate the acceleration of the system, is generally not a good idea for these particular type problems where motion of all blocks is not in the same direction, even though you did get the correct answer.
2.) Are the 5kg blocks accelerating up the plane or down the plane?

Fair enough, I see your point on the direction. As you point out, the blocks are going up while the 20kg block is going down, so what is correct for the acceleration? Would it be correct to say that the 20kg block accelerates at 4.26m/s² [down], but the other blocks accelerate at 4.26m/s₂ [up] ? I suppose however this would change the tensions would it not? ahhh...

 

[ehild]

You can consider such problems one-dimensional, saying that the motion happens along the rope and all objects move with the same acceleration. Decide the direction of the acceleration: this is the "forward" direction, and the forces act along the rope forward or backward.
Write the equation of motion for each body, and add up all three: the tensions cancel and you get an equation with the acceleration of the system as variable. The hanging body will move downward, and those on the slope will slide upward. Your arrow points in the wrong direction.
I suggest to type in the solution, I can not follow your handwriting.

ehild

 

[PhanthomJay]

Would it be correct to say that the 20kg block accelerates at 4.26m/s² [down], but the other blocks accelerate at 4.26m/s₂ [up] ?

yes, correct

I suppose however this would change the tensions would it not? ahhh...

No, you have the correct tensions, because you assumed the correct direction of motion in your FBD's, even though your arrow shows otherwise.

 

[fobbz]

yes, correct No, you have the correct tensions, because you assumed the correct direction of motion in your FBD's, even though your arrow shows otherwise.

Oh, I now see the arrow you're referring to. That was a silly error, due to the net force the 20kg block would be successful in accelerating downwards. Sorry about that arrow.Thanks though guys!