Motion of blocks with kinetic friction

[tmacarel]

Homework Statement

Two blocks with masses 4.00 kg and 8.00 kg are connected by a string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00 kg and plane is .25; that between the 8.00 kg block and the plane is .35.

a) Calculate the acceleration of each block.

b) calculate the tension in the string

c) what happens if the positions of the blocks are reversed, so the 4.00 kg block is above the 8.00 kg block?

Homework Equations

$$\Sigma$$ = ma

?

The Attempt at a Solution

I have drawn the free body diagram but not complete sure if I did that correctly. I need major help with this problem.

 

[PhanthomJay]

Homework Statement

Two blocks with masses 4.00 kg and 8.00 kg are connected by a string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00 kg and plane is .25; that between the 8.00 kg block and the plane is .35.

a) Calculate the acceleration of each block.

b) calculate the tension in the string

c) what happens if the positions of the blocks are reversed, so the 4.00 kg block is above the 8.00 kg block?

Homework Equations

$$\Sigma$$ = ma

?

The Attempt at a Solution

I have drawn the free body diagram but not complete sure if I did that correctly. I need major help with this problem.

tmacarel, welcome to PF!
You should be generally familiar with the use of free body diagrams in identifying forces acting on an object or objects. This problem has a level of difficulty up a notch from the more basic types. You should first note that ropes and strings and cords and the like can support tension forces only, that is, they can pull on an object but not push on them. So do your FBD's of the blocks or system of blocks, and use Newton 2, assuming the blocks move together with the same acceleration. If you find that the tension force in the string is negative, that is, pushing rather than pulling on the block, then you must set the tension equal to zero (as if the string were not there), and start over by looking at each block separately in order to determine each block's individual acceleration. You should show or describe what you are getting for your FBD's before we can be of further assistance.

 

[tmacarel]

Here is what I got for the accelerations in x and y directions for each box:

40 kg box
a_x = (323.634 - Tcos$$\theta$$) / 40

a_y = (560.553 - Tsin$$\theta$$) / 40

80 kg box

a_x =( Tcos$$\theta$$ + 417.089) / 80

a_y = (722.328 + Tsin$$\theta$$) / 80

** Please let me know if I got these values right. If I didn't, please explain where I could have screwed up. And if I did, how do I go about getting the tension experienced by the rope between the blocks? **