Newtonian Mechanics/Forces Question

[MyNameIsNicholas]

These buckets are being suspended. The cords have no mass and each bucket is 3.5 kg.

a.) Find the tension in the upper cord (T₁) and the lower cord (T₂)
b.) If the apparatus is pulled upwards from the top of the upper cord, what are the new tensions of each cord?

I understand the first part. The force diagrams consist of:
(Upper Bucket): T₁ upwards, T₂ downwards, and F_g downwards
(Lower Bucket): T₂ upwards and F_g downwards

However, when the apparatus accelerates upwards, the tensions in both cords increases. This makes sense physically but in the force diagram isn't force applied (causing acceleration) going upwards? And if that were the case, then force applied would counter-intuitively decrease the tension within the cords. Can someone graciously clear this up for me?

 

[Dr. Courtney]

Newton's second law applies to each bucket independently.

 

[Student100]

These buckets are being suspended. The cords have no mass and each bucket is 3.5 kg.

a.) Find the tension in the upper cord (T₁) and the lower cord (T₂)
b.) If the apparatus is pulled upwards from the top of the upper cord, what are the new tensions of each cord?

I understand the first part. The force diagrams consist of:
(Upper Bucket): T₁ upwards, T₂ downwards, and F_g downwards
(Lower Bucket): T₂ upwards and F_g downwards

However, when the apparatus accelerates upwards, the tensions in both cords increases. This makes sense physically but in the force diagram isn't force applied (causing acceleration) going upwards? And if that were the case, then force applied would counter-intuitively decrease the tension within the cords. Can someone graciously clear this up for me?

I'm not sure why you would believe that's the case, but look at $\sum F = ma$. Solve for the tension, and you'll see why hopefully. You may be confusing systems in equilibrium and accelerating systems while doing the FD.

Edit, trying to think of a good way to explain what I think is catching you up, but anyway, what's actually accelerating the system upward? The reactionary tension of course! The force that's pulling the system upward itself isn't applied to the buckets, its mediated by the tension in the rope.

Not sure if that helps or not.

 

[MyNameIsNicholas]

I think I understand! The F_A isn't actually an applied force. Well it is, but in terms of this problem it isn't. It's actually just addition upward tensional force on the upper cord F_T1! This would, obviously, increase F_T1 and in turn increase F_T2. Thanks for the help and sorry for not using the proper format of my question. Merci.

 

[MyNameIsNicholas]

I think I understand! The F_A isn't actually an applied force. Well it is, but in terms of this problem it isn't. It's actually just addition upward tensional force on the upper cord F_T1! This would, obviously, increase F_T1 and in turn increase F_T2. Thanks for the help and sorry for not using the proper format of my question. Merci.

Edit: Ignore those files. I was going to ask a follow-up question but upon creating those images and thinking about the question, it clicked!