How Do You Calculate Tension in a String Connecting Two Blocks on a Ramp?

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To calculate the tension in the string connecting two blocks on a ramp, consider the forces acting on each block. For block 1, the net force equation incorporates the kinetic friction and tension, while for block 2, it includes the gravitational component along the ramp and tension. The equations derived from free body diagrams should be combined to solve for tension. A tilted frame of reference can simplify the analysis by separating forces into parallel and perpendicular components. The net force is determined by the difference between the gravitational force on block 2 and the frictional force on block 1.
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Homework Statement


In Fig. 6-48, block 1 of mass 1.8 kg and block 2 of mass 2.9 kg are connected by a string of negligible mass and are initially held in place. Block 2 is on a frictionless surface tilted at = 38o. The coefficient of kinetic friction between block 1 and the horizontal surface is 0.20. The pulley has negligible mass and friction. Once they are released, the blocks move. What then is the tension in the string?
**image attached**

Homework Equations


For m1, fxnet=Uk(FN)-T=ma and fynet=FN-mg=0 and for m2, fxnet=T-mgsin(theta)=ma and fynet=FN-mgcos(theta)=0... I don't know if these are correct or not, that's what I got when I did the free body diagrams.


The Attempt at a Solution


I don't really know how to go about solving this problem... should I add any two equations together in order to get T?
 

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As a shortcut, use a tilted frame of reference for m2. Instead of x and y, consider the forces that are parallel and perpendicular to the surface. The force down the slope is a component of the gravitational force (on m2). The tension acts up the slope.

The net force on this system ends up being (the down-slope component of gravitational force on m2) - (frictional force on m1)
 
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