# Can a tension constraint lead to the wrong results?

• Physics freak
In summary: Then when we take into account how much faster they are actually accelerating, it becomes clear that they are actually in free fall.
Physics freak
Homework Statement
Find the constraint relation between a1,a2,a3
Relevant Equations
All pulleys are massless.Now for pulley 2 the upward tension T+T so the downward is 2T. And for pulley 1 since upward tension is T the downward ones must be T/2 and T/2 . Now the highlighted string is uniform so constant tension throughout ,but its coming out to be separately T/2 and 2T. Which is only possible when tension is 0, so is it really so or there's some mistake in my approach. The question just asked to find constraint relation between a1,a2,a3. I was trying to use tension constraint here and thus got struck.

Physics freak said:
Which is only possible when tension is 0,
Quite so.
What does that tell you about the accelerations of the masses? What about the pulleys?

haruspex said:
Quite so.
What does that tell you about the accelerations of the masses? what about the pulleys?
Nothing, but we normally use Σ t.a for such questions.

Physics freak said:
Nothing
No, it tells you a great deal about the accelerations of the masses. If all tensions are zero, what forces act on them?

haruspex said:
No, it tells you a great deal about the accelerations of the masses. If all tensions are zero, what forces act on them?

Gravity?

Physics freak said:
Gravity?
Right. So what are their accelerations?

Edit: if you now find the constraint relations between the five accelerations (three masses, two pulleys) you can figure out the accelerations of the pulleys. Then you may come to understand how it can be that the three masses are in free fall,

Edit 2: the original question is flawed. There are in all five accelerations that involve the strings, three masses and two pulleys. Two strings means two constraint relations. You can use one to eliminate one pulley acceleration, but you are left with the other pulley acceleration. So you cannot find an equation relating only the accelerations of the three masses.

Last edited:
I'm worried that you are still stuck on this. Please respond.

haruspex said:
I'm worried that you are still stuck on this. Please respond.
Hello. I never saw the edit till today. So basically in question, the tension is 0 and all masses and pulleys have acceleration g

Physics freak said:
Hello. I never saw the edit till today. So basically in question, the tension is 0 and all masses and pulleys have acceleration g
Right. The puzzle is, how is this possible? To understand it, I recommend figuring out the accelerations of the pulleys.

haruspex said:
Right. The puzzle is, how is this possible? To understand it, I recommend figuring out the accelerations of the pulleys.
The pulleys must also have acceleration g

Physics freak said:
The pulleys must also have acceleration g
No. The strings have fixed lengths.

haruspex said:
No. The strings have fixed lengths.
So they can reach equilibrium if the masses are same

Physics freak said:
So they can reach equilibrium if the masses are same
I mean the pulleys which are not fixed

Physics freak said:
So they can reach equilibrium if the masses are same
I don't know what you mean.
If the masses are all descending at g but the string lengths are constant then it is evident from the diagram that some pulley or pulleys must be accelerating upwards.
To get a full understanding it helps to calculate those accelerations, which you can do by writing equations which represent the constancy of the string lengths.

haruspex said:
I don't know what you mean.
If the masses are all descending at g but the string lengths are constant then it is evident from the diagram that some pulley or pulleys must be accelerating upwards.
To get a full understanding it helps to calculate those accelerations, which you can do by writing equations which represent the constancy of the string lengths.
But why are the pulleys also not accelearting with g

Physics freak said:
But why are the pulleys also not accelearting with g
Consider the upper string. It connects to the centre of a pulley at one end, a mass at the other end, and supports a pulley in the middle. If the mass and both pulleys were descending at g then the string would be lengthening at 4g. That is not allowed.

haruspex said:
Consider the upper string. It connects to the centre of a pulley at one end, a mass at the other end, and supports a pulley in the middle. If the mass and both pulleys were descending at g then the string would be lengthening at 4g. That is not allowed.
Oh finally i get it. Thanks a lot for help

Physics freak said:
Oh finally i get it. Thanks a lot for help
Ok, but I still think it helps to finish the calculation.

Let the downward accelerations of the pulleys be a1, a2.
For the upper string to have constant length we have a1+2a2+g=0.
For the lower string, the lengths of the leftmost and central sections are accelerating at g-a1, while for the rightmost it is g-a2.
So 2(g-a1)+(g-a2)=0.
From these we get a1=7g/3, a2=-5g/3 (i.e. upwards).

I think what makes it appear impossible at first that the masses are in free fall is that the pulleys have to accelerate so much faster than g.

Physics freak

## 1. Can a tension constraint cause a simulation to fail?

No, a tension constraint itself cannot cause a simulation to fail. However, if the tension constraint is not properly defined or implemented, it may lead to incorrect results in the simulation.

## 2. How does a tension constraint affect the accuracy of a simulation?

A tension constraint can affect the accuracy of a simulation if it is not accurately modeled or if the material properties of the constraint are not properly defined. In these cases, the results of the simulation may not accurately reflect the real-world behavior of the system.

## 3. Can a tension constraint be used with any type of material?

No, a tension constraint may not be suitable for all types of materials. It is important to consider the material properties and behavior when implementing a tension constraint in a simulation.

## 4. What are some potential issues to watch out for when using a tension constraint?

Some potential issues when using a tension constraint include incorrect implementation, unrealistic material properties, and limitations in the simulation software. It is important to thoroughly test and validate the tension constraint to ensure accurate results.

## 5. How can a tension constraint be improved for more accurate results?

A tension constraint can be improved by accurately modeling the material properties, properly defining the constraint in the simulation, and validating the results against real-world data. Additionally, using more advanced simulation techniques and software can also improve the accuracy of the results.

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