How Do You Calculate Tension in a Frictionless Pulley System?

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SUMMARY

The discussion focuses on calculating the tension in a frictionless pulley system involving two masses: 5 kg and 6 kg. The key equations used include Ft - Fg2sin(60°) = ma for the 5 kg mass, where Ft represents the tension force and Fg2 is the gravitational force acting on the 5 kg mass. Participants emphasized the importance of correctly relating string tensions and accelerations for both masses to derive the tension accurately. The solution requires applying the principles of dynamics and trigonometry to determine the tension force's magnitude and direction.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Basic trigonometry, specifically sine functions
  • Familiarity with gravitational force calculations
  • Knowledge of frictionless pulley systems
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  • Study the derivation of tension in multi-mass pulley systems
  • Learn about the effects of angle on tension calculations in pulleys
  • Explore advanced dynamics involving frictionless surfaces
  • Practice problems involving multiple masses and varying angles
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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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