Tension in a chopped up string

[quietrain]

if a string of length L has tension T,

when we chop it up into 3 equal pieces (of length L/3) , then tension experience by each string individually is still T...

why? shouldn't it be T/3?

issn't this analogous to a string pulling 3 blocks (each connected by a horizontal string and has mass m) horizontally together ? which means T = 3ma

so for the same acceleration, the first block has tension T, 2nd block has tension 2/3T and the third block has tension 1/3 T .

so what gives ?

thanks for the help!

 

[Doc Al]

If you treat the string as massless (the usual assumption), then any segment of the string must have a net force of zero. Thus T1 = T2 (since T1-T2 = ma = 0), and the tension is the same throughout. But if the string has mass, then the tension will vary along the length according to T1-T2 = ma.

If you are pulling a massive string with nothing attached to its far end, then you are right. The tension will varying from a max of T at the end you pull to zero at the far end. But usually strings are treated as massless and they usually have things (other masses) tied to their ends.

 

[quietrain]

ok, if the string L has 3 sections with different mass densities, why when we apply a tension to one end and fix the other, all 3 sections have the same tension?

shouldn't it be that the tension vary in accordance with the mass?

 

[Doc Al]

ok, if the string L has 3 sections with different mass densities, why when we apply a tension to one end and fix the other, all 3 sections have the same tension?

What's the acceleration of the string? If one end is fixed, I suspect the acceleration is zero, thus the tension will be the same throughout. (Since T1-T2 = ma = 0.)

 

[quietrain]

oh i see... so if the acceleration is the factor that we consider... thanks