Tension Problem: Two boxes with two ropes

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The problem involves two masses, Ma and Mb, connected by a heavy rope, with Ma suspended from a massless rope attached to a helicopter accelerating upwards. The tensions in the ropes are labeled as T1 for the top rope, T2.1 for the downward tension on Ma, and T2.2 for the upward tension on Mb. The equations derived show that T1 equals the total mass times the sum of acceleration and gravitational force, while T2.1 and T2.2 are derived similarly based on the forces acting on each mass. The solution checks out, as it aligns with the expected results when considering a massless rope scenario. The discussion confirms the correctness of the calculations and the approach taken.
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Hi,
here's a problem I did earlier today. I think I got it right, but I'd appreciate it if somebody could check. Also, is there a different way to solve this problem?


Homework Statement


Two masses Ma and Mb are connected through a heavy rope with mass Mr. The top mass Ma is hanging from a from a massless rope that is that is attached to a helicopter that moves upwards with acceleration a. Find the tension in the top rope as well as the tensions in the bottom (heavy) rope.

I labeled the tension of the top rope T1, the tension of the heavy rope pulling downward on Ma T2.1, and the tension pulling upward on Mb T2.2.


Homework Equations


For mass A: Fnet = Ma * a
--> T1 - T2.1 - Ma * g = Ma * a
--> T1 - T2.1 = Ma * a + Ma * g

For mass B: Fnet = Mb * a
--> T2.2 - Mb * g = Mb * a
--> T2.2 = Mb * a + Mb * g
This already gives us the tension from the heavy rope pulling upwards on the second mass.

For the entire system, without the top rope:
Fnet = (Ma + Mb + Mr) * a
--> T1 - (Ma + Mb + Mr) * g = (Ma + Mb + Mr) * a
--> T1 = (Ma + Mb + Mr) * (a + g)

I plugged this into the earlier equation with T1 and T2.1:

(Ma + Mb + Mr) * (a + g) - T2.1 = Ma * (a + g)
--> T2.1 = (Mb + Mr) * (a + g)

So we have:
T1 = (Ma + Mb + mr) * (a + g)
T2.1 = (Mb + Mr) * (a + g)
T2.2 = Mb * (a + g)

The Attempt at a Solution



See above.

Is this correct?
 
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That looks good.
You can check your answer in limiting case. When mass of the rope goes to zero, your answer gives the same result as massless rope.
 
Cool, thanks.
 
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