How Is Acceleration Calculated in a Frictionless Pulley System?

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SUMMARY

The acceleration of a frictionless pulley system with masses m1 = 5.00 kg and m2 = 8.00 kg can be calculated using Newton's second law. The net force acting on the system is determined by the difference in weights of the two masses. The formula for acceleration (a) is derived as a = (m2 - m1) * g / (m1 + m2), where g is the acceleration due to gravity (9.81 m/s²). Substituting the values yields an acceleration of approximately 2.45 m/s².

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The system shown in the figure is accelerating. Asume that there is no friction anywhere in the system and that the mass of the string can be neglected. The values of the masses are:

m1=5.00 kg
m2=8.00 kg

Determine the acceleration of the system.

Figure and work done so far shown here:
http://img104.imageshack.us/img104/6218/pulleyproblemop3.th.png

Where do I go from here? How do I solve for the acceleration?
 
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