acceleration on a pulley system with 3 blocks

1. The problem statement, all variables and given/known data

Three objects are connected on an inclined table. The objects have masses 8.0 kg, 4.0 kg and 2.0 kg as shown, and the pulleys are frictionless. The tabletop is rough, with a coefficient of kinetic friction of 0.47, and makes an angle of 20.0° with the horizontal. The 8.0kg block hangs on the left, the 4.0kg block in the middle on the table (20.0° t the left and above horizontal), and the 2.0kg is hanging on the right.



Draw a free-body diagram for each object. (did this but can't display on the forum)

Determine the acceleration and direction of motion of the system.

Determine the tensions in the two cords.







2. Relevant equations

εF=ma

trig

T-mg=ma





3. The attempt at a solution

I can do this with two blocks but 3 on a angle through me off.

mg for the 8.0kg block =78.4N and mg for the 2 kg block is 19.6kg



I know that for the block on the table:

Fgx = sin 20 (39.2) = 13.4N

Fgy = cos 20 (39.2)= 36.83N - Force normal and Fgy are equal

Ff=0.47(36.83)



The using εFx=max

19.6=13.4-17.3-78.4 = (14)a

a= -4.5m/s/s or 4.5 m/s/s moving to the left.



Not sure if I did this right and when calculating tension in a 3 block pulley system on a angle.



Thanks