Tension in a chopped up string

In summary, when treating a string as massless, the tension will be the same throughout. If the string has mass however, the tension will vary according to T1-T2 = ma.
  • #1
quietrain
655
2
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!
 
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  • #2
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
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
quietrain said:
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.)
 
  • #5
oh i see... so if the acceleration is the factor that we consider... thanks
 

FAQ: Tension in a chopped up string

What is tension in a chopped up string?

Tension is the amount of force or pull exerted on a string when it is stretched or pulled. In a chopped up string, tension refers to the force applied to the individual segments or pieces of the string.

How does tension affect the behavior of a chopped up string?

Tension plays a crucial role in determining the behavior of a chopped up string. The higher the tension, the stiffer the string will be, resulting in faster vibrations and a higher pitch. Lower tension will result in a looser string, slower vibrations, and a lower pitch.

What factors can influence the tension in a chopped up string?

Several factors can affect the tension in a chopped up string, including the material and thickness of the string, the level of stretching or pulling force applied, and the length and number of segments in the chopped up string.

How can tension be measured in a chopped up string?

Tension can be measured using a device called a tension meter, which measures the amount of force or pull applied to the string. It can also be estimated by measuring the frequency or pitch of the string's vibration, as higher tension will result in a higher frequency and vice versa.

What are some real-world applications of studying tension in chopped up strings?

Understanding tension in chopped up strings has many practical applications, such as in the design and construction of musical instruments, suspension bridges, and even in medical procedures like surgery and orthopedic treatments. It is also essential in fields like acoustics, engineering, and physics.

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