# 5 blocks suspended from ceiling -- What are the tensions?

• Ocata
In summary, the five blocks suspended from the ceiling by a string of negligible mass are subject to tensions due to the force of gravity.
Ocata

## Homework Statement

5 blocks connected by strings of negligible masses are suspended from a ceiling by a string of negligible mass. The strings and masses in order from bottom to top are M1, S1, M2, S2, M3, S3, M4, S4, M5, S5

M1 = 2kg
M2 = 1kg
M3 = 1kg
M4 = 2kg
M5 = 10kg

What are the tensions on S1, S2, S3, S4 and S5?

F=ma

## The Attempt at a Solution

Net Force is 0 because the system isn't accelerating.

T_1 = (m_1)a = 2kg(g) = 19.6N
T_2 = (m_1)a + (m_2)a = 2kg+1kg(g) = 29.4N
T_3 = (m_1)a + (m_2)a + (m_3)a = 2kg+1kg(g) + 1kg(g) = 39.2N
T_4 = (m_1)a + (m_2)a + (m_3)a + (m_4)a = 2kg + 1kg(g) + 1kg(g) + 2kg(g) = 58.8N
T_5 = (m_1)a + (m_2)a + (m_3)a + (m_4)a + (m_5)a = 2kg + 1kg(g) + 1kg(g) + 2kg(g) + 10kg(g) = 156N

Supposing this is correct, if we treat all the blocks as one system, the force vector upward from M_5 pointing toward the ceiling and the force vector downward from M_1 pointing toward the ground would both be 156N, yes?

Ocata said:
Supposing this is correct, if we treat all the blocks as one system, the force vector upward from M_5 pointing toward the ceiling and the force vector downward from M_1 pointing toward the ground would both be 156N, yes?
Well, in an extended-mass system (as opposed to a point-mass system), where does the force vector of gravity act?

Ocata
Ocata said:
...

Supposing this is correct, if we treat all the blocks as one system, the force vector upward from M_5 pointing toward the ceiling and the force vector downward from M_1 pointing toward the ground would both be 156N, yes?
You have a system hanging from the ceiling. There is no M1 or M5 .

The ceiling exerts a force upward on the system. The system exerts a force downward on the ceiling .

Ocata
SammyS said:
You have a system hanging from the ceiling. There is no M1 or M5 .

The ceiling exerts a force upward on the system. The system exerts a force downward on the ceiling .
Oh, I think I see. Considering the system as a whole, the force of 156N points downwards from the bottom of the system and the force of 156N upwards is from the force of the ceiling on the top string, yes?

By the way, I am guessing the values for the individual tension are correct?

Additionally, I am interested is specifying the tension values and uploaded a diagram of this problem and would like to know if the tension values (T) at each connection point is correct.

#### Attachments

• Tension c.JPG
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Ocata said:
Additionally, I am interested is specifying the tension values and uploaded a diagram of this problem and would like to know if the tension values (T) at each connection point is correct.
Yes, your tension values are correct.

The image is virtually impossible to read. -- very "washed-out" appearance.

Ocata
Thank you SammyS,

I'll definitely make the contrast darker when I scan next time, thanks.

Regards

## 1. What is the tension of the 5 blocks suspended from the ceiling?

The tension of the 5 blocks suspended from the ceiling is the force pulling on each block in order to keep it suspended. This tension is equal to the weight of each block, as well as the force of gravity acting on each block.

## 2. How do you calculate the tension of each block?

To calculate the tension of each block, you would need to know the weight of each block and the angle at which it is suspended from the ceiling. Using trigonometry, you can then calculate the horizontal and vertical components of the tension and combine them to find the total tension.

## 3. Can the tension of the blocks change?

Yes, the tension of the blocks can change if any external forces are applied to them. For example, if someone were to push or pull on one of the blocks, the tension of that block would change.

## 4. What happens if one of the blocks is heavier than the others?

If one of the blocks is heavier than the others, the tension of that block will be greater in order to support its weight. The other blocks will have less tension as they are supporting less weight. However, the total tension of all the blocks will still be equal to the weight of each block plus the force of gravity acting on it.

## 5. How does the length of the string affect the tension of the blocks?

The length of the string does not directly affect the tension of the blocks. However, if the length of the string is too short, it may not be able to support the weight of the blocks and could break, changing the tension of the remaining blocks. Additionally, a longer string may allow for a greater angle of suspension, which could change the tension calculations.

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