How Do You Calculate Tension in a Frictionless Pulley System?

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To calculate the tension in a frictionless pulley system, it's essential to apply Newton's second law to each mass involved. The tension (Ft) can be determined by analyzing the forces acting on each mass, including gravitational force and the angles of inclination. A common approach involves setting up equations for each mass, ensuring to account for the relationship between tension and acceleration. It's important to relate the string tensions and accelerations correctly according to the conventions used. Properly applying these principles will lead to the correct calculation of tension in the system.
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1. Homework Statement
Calculate the tension in the cable connecting the two masses. Assume all surfaces are frictionless.

http://tinypic.com/r/20jg36s/7

2. Homework Equations



3. The Attempt at a Solution
I tried to begin the solution but came out with a negative acceleration (-2m/s^2)
For the 5 kg mass:
Ft-Fg2sin60=ma
Ft-(5)(9.8)sin60=5a
Ft-49sin60=5a
I wasn't sure how to get the equation for the 6 kg mass...
1. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 
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Why would the equation for the 6 kg mass be more difficult than that of the 5 kg one? The same principles apply. Just make sure you relate the string tensions and accelerations properly according to your conventions and you should be able to solve it.
 
But I'm on the right path here?
 
Get Fg1 * sin(60 degrees) and Fg2 * sin(70 degrees) and then determine the magnitude and direction of the tension force.
 
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