Infinite Acceleration on a mass-less string

[Samit Chak]

In a lecture I heard that if we suspend two objects of different masses (and the system is accelerating) on both sides of a pulley of no resistance with a mass-less string then the tension on both sides of the string is same - this is fine till now.
To explain that the tension is same, it was said that if we take a very small piece of the string and see the two opposite forces acting on them - they must be equal. If these forces are not equal then there will be Infinite Acceleration.
1. What is this Infinite Acceleration in this context (the system is already accelerating)? What will happen if there is infinite acceleration? Does this mean the string will rupture?
2. Why Mass-Less string is important here?

 

[.Scott]

In a lecture I heard that if we suspend two objects of different masses (and the system is accelerating) on both sides of a pulley of no resistance with a mass-less string then the tension on both sides of the string is same - this is fine till now.
To explain that the tension is same, it was said that if we take a very small piece of the string and see the two opposite forces acting on them - they must be equal. If these forces are not equal then there will be Infinite Acceleration.
1. What is this Infinite Acceleration in this context (the system is already accelerating)? What will happen if there is infinite acceleration? Does this mean the string will rupture?
2. Why Mass-Less string is important here?

Presumably that "infinite acceleration" will be short-lived as the string positions itself to equal out the forces on its ends.
It's really a bad analysis because, given that much detail, the model could actually demonstrate that a mechanical wave is moving through the string at light (Einstein) or infinite (Newton) speed - and that it is those mechanical waves that are transmitting the force. So we would really need to assume that the string is both massless and tends to dampen mechanical waves.

The point behind massless in these types of discussions is simply to avoid dealing with the mass of the string when it is unrelated to the point being made. In this case, if the string had mass, then it would have inertia and the tension across the string would not be exactly equal for all points on the string.

 

[haruspex]

In a lecture I heard that if we suspend two objects of different masses (and the system is accelerating) on both sides of a pulley of no resistance with a mass-less string then the tension on both sides of the string is same - this is fine till now.
To explain that the tension is same, it was said that if we take a very small piece of the string and see the two opposite forces acting on them - they must be equal. If these forces are not equal then there will be Infinite Acceleration.
1. What is this Infinite Acceleration in this context (the system is already accelerating)? What will happen if there is infinite acceleration? Does this mean the string will rupture?
2. Why Mass-Less string is important here?

The infinite acceleration refers to the pulley. Since the pulley is considered to have no inertia and no frictional torque, any difference in the tension would lead to a nonzero net torque and hence to an infinite angular acceleration.
If we allow the string to have mass but keep the pulley itself still devoid of inertia (a particularly unrealistic combination) then a difference in tension would arise just in accelerating the section of string that wraps around the pulley.

 

[.Scott]

.

 

[haruspex]

No. When the masses are unequal, the entire system is accelerating. The lighter pulley is accelerating upwards and the heavier one is accelerating downward. Under these conditions, a massive string would have different tensions at different segments - even if the pulley was frictionless.

I don't understand what part of what I wrote you disagree with. We seem to be saying the same.

 

[.Scott]

I don't understand what part of what I wrote you disagree with. We seem to be saying the same.

You're right. I misread your post.