Solve for Tension: Find Magnitude of Tension in Connecting Cord

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The discussion focuses on calculating the tension in a cord connecting two masses, one on an incline and the other on a horizontal surface, with given parameters. A free body diagram (FBD) was created for both masses, leading to the derivation of an equation that incorporates forces acting on each mass. The derived equation, F + m1a - m2g*sin(theta) = m2a, was questioned regarding its accuracy in representing the system. Ultimately, the correct magnitude of tension calculated is 12.2 N, despite disputes over the derivation process. The discussion highlights the importance of correctly applying Newton's laws to solve for tension in connected systems.
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A 1.2 kg mass, m2, on a 30.1° incline is connected to a 5.4 kg mass, m1, on a horizontal surface. The surfaces and the pulley are frictionless. If F = 20.8 N, what is the magnitude of the tension in the connecting cord?

I created a FBD for both masses
M2
X: F+T-mg*sin(theta)=m2a
Y: N-mg*cos(theta)=0

M1
X: F=m1a
Y: N-mg=0

I derived this equation

F+m1a-m2g*sin(theta)=m2a

Is this equation on the right path?
 
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If F is pulling m2 up the incline, then T acting on m2 will have the opposite sign, and T (between m1 and m2) will be acting on m1.
 
Well I was able to solve this, but there was a lot of dispute as to how to derive the equation.

I'm not sure what was wrong with my derviation, but the answer is 12.2 N.
 
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