Must the tension in a string be uniform?

In summary, the tension in a massless string is constant due to another assumption, that is the string is massless. When the string has mass, the tension may not be constant.
  • #1
jeremy22511
29
0

Homework Statement



Must the tension in a string be uniform? If so, why is that? Thanks!

Homework Equations





The Attempt at a Solution

 
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  • #2
I believe that when a string has no mass at every point of it the net force is equal to zero from the equation F=ma(when m=0 ,F=0).For example imagine a pulley and a string holding two masses.The force from the first mass to the string is T and from the second T'.the net force on the string is T-T'=ma because m=0 we have T=T'.
 
  • #3
i hope i helped
 
  • #4
jeremy22511 said:

Homework Statement



Must the tension in a string be uniform? If so, why is that? Thanks!

Homework Equations


The Attempt at a Solution


The tension in a string is typically assumed to be constant due to another assumption...i.e. the string is massless (or negligible). If the string has mass then the tension may not be constant.

CS
 
  • #5
But is there an explanation for that? Why is the tension in the string constant if it is massless? And how come it is not when the string has mass?
Thanks!~

J.
 
  • #6
Take a section of the rope; suppose the tension pulling it to the left is T1, the tension pulling it to the right is T2, and T1 doesn't equal T2. The section will have an infinite acceleration since it has a mass of 0. This is clearly impossible, so T1 has to equal T2.
 
  • #7
jeremy22511 said:
But is there an explanation for that? Why is the tension in the string constant if it is massless? And how come it is not when the string has mass?
Thanks!~

J.

Take an infinitely small element of a massless string. Call its length dx. Since the element's mass is zero there is no gravitational force acting on the element. The two forces acting are T1 (up) and T2 (down). Since the net force must be zero due to the zero mass of the element (F = ma), T1 must equal T2.

Drawing a FBD of the problem we find that:

T1 - T2 = ma

Since it is massless, m = 0 and thus ma = 0

Hence, T1 - T2 = 0 which gives T1 = T2.

CS
 
  • #8
Thanks everyone!
J.
 

1. Why is it important for the tension in a string to be uniform?

Uniform tension in a string is important because it ensures that the string will vibrate at a consistent frequency, which is essential for accurate measurements and experiments.

2. What happens if the tension in a string is not uniform?

If the tension in a string is not uniform, the string will vibrate at different frequencies, making it difficult to obtain accurate results. Additionally, uneven tension can cause the string to break or produce unwanted overtones.

3. How can you ensure uniform tension in a string?

To ensure uniform tension in a string, it is important to use a high-quality string that is properly installed and tightened. It may also be necessary to adjust the tension periodically to maintain uniformity.

4. Can the tension in a string ever be too uniform?

In theory, the tension in a string can be too uniform, resulting in a lack of vibrations and a flat, dull sound. However, this is typically not a concern for most scientific experiments and can be adjusted by slightly loosening the string.

5. Are there any factors that can affect the uniformity of tension in a string?

Yes, there are several factors that can affect the uniformity of tension in a string, such as temperature, humidity, and the material and thickness of the string. These factors should be taken into consideration when conducting experiments involving strings.

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