Infinite acceleration on a string?

[PhysicsKid0123]

I'm trying to figure out what it says in my book. Here is the link of the picture. http://i941.photobucket.com/albums/...oads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg Could someone explain the part where it says "Otherwise, there would be a net tension force acting on the sections, and they would consequently suffer an infinite acceleration." Why does it necessarily have to be infinite? The only reason why I see it should be infinite is if the string is inextensible (unbreakable and maximally stretched) and if it so happened to not be straight it must have some infinite force so to not make it straight. Is my logic correct?http://[URL=http://s941.photobucket.com/user/markangela/media/Mobile%20Uploads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg.html][PLAIN]http://i941.photobucket.com/albums/ad259/markangela/Mobile%20Uploads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg

 

[mfb]

The mass of the string is assumed to be negligible. If you put that into F=ma, a finite force leads to an extremely large ("infinite" in the limit) acceleration.

 

[PhysicsKid0123]

The mass of the string is assumed to be negligible. If you put that into F=ma, a finite force leads to an extremely large ("infinite" in the limit) acceleration.

What do you mean exactly by "put that into F=ma." You are saying that if there were to be some sort of force or tension then a approaches "infinity" as m approaches "zero" in some sense?

 

[mfb]

If tension would be different in different parts of the string, then there would be a force acting on a section of string.

A force acting on an object with a very small mass will lead to a very large acceleration (as F=m*a).
A force acting on an object with a very very small mass will lead to a very very large acceleration.
A force acting on an object with zero mass will lead to an "infinite" acceleration. (note the " ", because this does not exist in reality).

 

[PhysicsKid0123]

If tension would be different in different parts of the string, then there would be a force acting on a section of string.

A force acting on an object with a very small mass will lead to a very large acceleration (as F=m*a).
A force acting on an object with a very very small mass will lead to a very very large acceleration.
A force acting on an object with zero mass will lead to an "infinite" acceleration. (note the " ", because this does not exist in reality).

Okay I think I see now. So the author's use of infinite accel. is ambiguous.