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

1. Jun 23, 2015

### Ocata

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

F=ma

3. 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?

2. Jun 23, 2015

### insightful

Well, in an extended-mass system (as opposed to a point-mass system), where does the force vector of gravity act?

3. Jun 23, 2015

### SammyS

Staff Emeritus
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 .

4. Jun 24, 2015

### Ocata

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?

5. Jun 24, 2015

### Ocata

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.

#### Attached Files:

• ###### Tension c.JPG
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6. Jun 24, 2015

### SammyS

Staff Emeritus
Yes, your tension values are correct.

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

7. Jun 24, 2015

### Ocata

Thank you SammyS,

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

Regards