# Tension in a chopped up string

1. Nov 13, 2009

### 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!

2. Nov 13, 2009

### Staff: Mentor

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.

3. Nov 13, 2009

### 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?

4. Nov 13, 2009

### Staff: Mentor

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.)

5. Nov 14, 2009

### quietrain

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