What is the tension in the suspended cord when masses are released?

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SUMMARY

The tension in the suspended cord (C) when two masses are released is determined to be T(C) = 2T, where T is the tension in each rope connected to the masses. For Mass 1 (1.2 kg) and Mass 2 (3.2 kg), the calculated tension in each rope is 17 N, resulting in a total tension of 34 N in cord C. The acceleration of the system is calculated to be approximately 4.45 m/s². The mass of the pulley and cords is negligible, simplifying the analysis of forces acting on the system.

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Ltcellis
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Homework Statement



Suppose the pulley is suspended by a cord C

Determine the tension in this cord after the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.

GIANCOLI.ch04.p54.jpg


Mass 1 : 1.2kg
Mass 2 : 3.2kg
Pulley and String mass is negligible

Homework Equations



T-m1g = -m1a
T-m2g = m2a
Tension of pulley = T(C) -mg - 2T = ma(?)

The Attempt at a Solution



So I solved for the tensions in both ropes. Since they're equal I got T=17N
For acceleraton I got 4.4545455m/s. I'm just not too sure on the equation on the Tension of Cord C. Would it be the equation I mentioned above? When I use that I get an answer around 96. Is that right?
 
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No, it's much simpler than that. Since the pulley is massless, the sum of the forces on it must add to zero. (Note further that there is no mg term acting on the pulley.)
 
So it's just T(C) = 2T?

because I was thinking mg was referring to the total weight.
 
Ltcellis said:
So it's just T(C) = 2T?
Yep, that's all it is.
because I was thinking mg was referring to the total weight.
You are analyzing the pulley, so mg can only refer to the weight of the pulley, which is zero.
 
Thanks a bunch
 

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