Solve for Tension: Find Magnitude of Tension in Connecting Cord

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SUMMARY

The discussion centers on calculating the magnitude of tension in a connecting cord between two masses, m1 (5.4 kg) on a horizontal surface and m2 (1.2 kg) on a 30.1° incline, with an applied force F of 20.8 N. The user derived the equation F + m1a - m2g*sin(theta) = m2a to find the tension, ultimately concluding that the tension is 12.2 N. The frictionless nature of the surfaces and pulley is critical to the solution, and the user faced challenges in the derivation process, indicating a need for clarity in the application of Newton's laws.

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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?
 
Last edited:
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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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