# Problem about tension

1. Jun 12, 2016

### arpon

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

A body is connected at the middle with two different ropes as in the figure. The maximum force that rope A can resist is 60 N, and for rope B its 50 N. What will happen if someone apply a downward force at the loose end of rope B, a) gradually b) very fast

2. Relevant equations

3. The attempt at a solution
My opinion is: if the force is greater than 50N, rope B will tear for both cases. Nothing will happen to rope A.

2. Jun 12, 2016

### PeroK

Assuming the diagram represents a vertical configuration, the mass of the body is relevant.

3. Jun 12, 2016

### Let'sthink

When the applied force is is gradual the tensions in both the strings have to be identical and equal to the applied force, if we neglect the mass of the body, as the body remains at rest in a permanent fashion. So as F increase it will reach 50 N first and then become 60 N so lower rope will break first. I am not able to think about the sudden application of force.

Last edited: Jun 12, 2016
4. Jun 12, 2016

### Let'sthink

I think in second case also the lower rope will break first. if weight of the body cannot be neglected, then when you apply force even if suddenly the two tensions have to be equal but the lower rope may have less tension at any instant as in the beginning lower rope has zero tension and the tension is upper rope is equal to the weight of the body. So it is possible that at some instance above is 60 N and the lower one is below 50 N, in that case the upper rope will break.

5. Jun 12, 2016

### arpon

The mass was not given in the problem.

6. Jun 12, 2016

### PeroK

If the mass is 7kg, say, then the upper rope will break without any additional force being applied.

If it's 5kg, then the upper rope will break when the applied force reaches about 12N.

7. Jun 12, 2016

### arpon

Then I guess the mass is negligible.

8. Jun 12, 2016

### PeroK

Then you essentially have two ropes joined together and the lesser rope will always break first.

What about the case where the mass is 5kg and you apply a force of,say, 100N instantaneously?

How is the force transmitted to the upper rope?

9. Jun 12, 2016

### arpon

Won't rope B break?

10. Jun 12, 2016

### PeroK

That's what you have to work out. You need a free body diagram.

11. Jun 12, 2016

### arpon

I am confused about how the force will be transmitted.

12. Jun 12, 2016

### Vibhor

Hi arpon ,

In part b) , when the downward force is applied very fast , will the acceleration of the mass/body be large or small ?

13. Jun 12, 2016

### arpon

Will the mass be accelarated? Won't the rope break if the force exceeds the limit of 50N?

14. Jun 12, 2016

### Vibhor

Won't a large sudden force try to accelerate the bottom rope ? Isn't rope connected to the mass ? Won't the string and rope have same acceleration till the time they are connected ?

This is what we are trying to find .

15. Jun 12, 2016

### PeroK

It's perhaps not a good question. My thinking is:

1) the maximum tension in A is the tension in B plus $mg$. If $mg$ is less than 10N then B must break first.

2) If $mg$ is greater than 10N then under a gradual increase in force, A must break first. But, under an instantaneous force it's not so clear what happens. If you assume that the system is rigid and the tension travels almost infinitely fast, then A will break.

Edit: Corrected A and B.

Last edited: Jun 12, 2016
16. Jun 12, 2016

### arpon

I think the maximum tension in B is the tension in A minus $mg$.

17. Jun 12, 2016

### PeroK

Yes, I got A and B mixed up!