Tension and acceleration?

Question

An 8kg box and a 10kg box that are attached by a rope that passes over a frictionless pulley slide on a frictionless inclines.

a.Find the acceleration of the boxes and the tension in the rope.

Here is a picture of the boxes
http://img521.imageshack.us/my.php?image=ps3dm6.jpg

Answer 1

Start by looking at FBDs of each box. Since there is no friction, and their accelerations are equal, and using T as the tension in the rope
T-10*sin(50)*g=10*a
8*sin(40)*g-T=8*a

assuming that the 8kg box will slide downward and the 10 will slide upward
solving for T in each
T=10*(sin(50)*g+a)
T=8*(sin(40)*g-a)
or
8*(sin(40)*g-a)=
10*(sin(50)*g+a)

this equation can be solved for a
which can then be used to solve for T
a= -1.37 m/s^2
T=61.42 N

using g=9.81
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