About propagation of force through a string

Here is what I was thinking:

Case (1):If a small force not enough to break the string is applied, all parts of the system receive this force at some instant because of the tension and Newton's third law. But eventually the force is felt at $$A$$.

i.e: a force applied on a small part of the string causes an instantaneous acceleration on the small part which puts a force on the adjacent part above it.The adjacent part applies the same force so that the part which experienced the force first does not move.

This goes as a chain reaction and eventually the force is propagated to the top at point $$A$$.

Since the part $$AB$$ has to support the block,it also experiences a force of $$9.8N$$.

So if a force is applied to the string and gradually increased, a part in $$AB$$ is more likely to break.

=> Is everything in the above case(1) that I have said, correct?

Case(2): Now a very large impulsive force is applied to the system which is enough to break the string.

$$BC$$ will definitely break. But the question is, will $$AB$$ also break?

I think that a force just infinitesimally smaller than the force required to break the string would propagate onto the string $$AB$$ just before $$BC$$ breaks.

However since the string $$AB$$ also experiences the weight of the block, which is non zero, the string must break as well.

So both parts $$AB$$ and $$BC$$ will break.

=> Is this right?

Edit: what is the condition for both AB and BC to break?

• A similar question has already been answered at physics.stackexchange.com/q/291991 Apr 15, 2020 at 15:29
• According to what I said, both strings must snap when a sudden jerk is applied. Why is my explanation/reasoning wrong? Apr 15, 2020 at 15:42
• Also why does the string break at the middle when it does? Shouldn't it break at the point where the force is applied since the string is uniform? Apr 15, 2020 at 16:12
• physics.stackexchange.com/questions/525659/… Apr 15, 2020 at 21:31

Case 1

Your logic is right, except when you say

... a force applied on a small part of the string causes an instantaneous acceleration on the small part which puts a force on the adjacent part above it.

An ideal string will not extend and there will not be any acceleration, it will rather just propagate the tension across it.

Case 2

In the limit that one pulls the string with a force whose temporal profile can be represented as a Dirac's delta (i.e. infinite force for an infinitesimal amount of time), only the bottom string will break, as there will not be any transferred impulse to the brick B, which, therefore, stands still.

Indeed, even if the integral of a Dirac's delta is finite, the integral of a truncated delta (truncated at the breaking load of the fiber) is zero, as it is the integral of a finite function over an infinitesimal interval.

In real life it is not so easy to predict where the wire will snap, one has to consider the propagation of stresses inside the structure and the presence of defects ...

• So unless the force infinite and for am infinitesimal force, only BC string will break, otherwise AB? Why in real life does it break at BC when a large force is applied? Apr 15, 2020 at 17:42
• That is not what I meant. I wanted to say that in the limit of an infinite force for an infinitesimal time, only the BC string will break. In general, there will be a regime where there will be a transition from breaking the bottom string to breaking the top one. Anyhow my feeling is that it is unrealistic that both string will break at the same time. Apr 15, 2020 at 17:58
• When will both strings break, in an ideal situation? Apr 15, 2020 at 18:52
• @MichaelFaraday I think it will never happen if the fibers are the same Apr 16, 2020 at 10:01
• I don't understand why. When the string BC breaks, it would have propagated force just less than needed to break the string. And when this force reaches the string AB, it adds up with the weight of the block to break string AB. What is wrong with this? Apr 16, 2020 at 10:26

to propagate the sudden force you apply at C the block has to move, its inertia is greater, than the breaking point of the lower part of the string. all strings have a weakest point, so the string may break at any point between C and B

• I didn't understand what you meant by 'its inertia is greater than the breaking point of the string'. Inertia of the block is it's mass. How does the mass effect this situation? I thought the mass only adds more load to the string AB. Isn't that right? Apr 15, 2020 at 17:25