What is the relationship between diameter and mass per length in a steel wire?

In summary, the conversation discusses the calculation of tension in a steel wire using the equation v = sqrt(T / (m / L)). The density of steel is given as 7.86 g / cm^3, which is equivalent to 7860 kg / m^3. However, the mass per unit length is needed for the equation, not the mass per volume. This means that the given density cannot be used directly and must be converted to mass per length. The conversation mentions a potential misunderstanding of this concept and prompts the consideration of a steel wire with a larger diameter, which would have a greater mass per length due to the same density.
  • #1
nesan
75
0

Homework Statement



http://puu.sh/frpk5/eae7bce2e3.png

Homework Equations



v = sqrt(T / (m / L));

The Attempt at a Solution



7.86 g / cm^3 = 7860 kg / m^3

T = v^2 * m/L

T = 160 ^ 2 * 7860 which is a huge number

I have no idea where the diametre plays a part.
 
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  • #2
m/L ≠ 7860 (check the dimensions)
 
  • #3
Nathanael said:
m/L ≠ 7860 (check the dimensions)
I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?

I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.
 
  • #4
nesan said:
I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?
You were given the mass per volume, but you want to know the mass per length. You used the mass per volume where you should have used the mass per length.

nesan said:
I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.
Consider a steel wire with a larger diameter. (They are both steel, so the density is the same.) Which one will have the larger mass per length? Or will it be the same? And why?
 

1. What is a transverse wave in a string?

A transverse wave in a string is a type of wave that travels along a string or rope, causing the string to move up and down or side to side perpendicular to the direction of the wave's movement.

2. How is a transverse wave in a string created?

A transverse wave in a string is created by a disturbance or vibration at one end of the string, which then travels along the string to the other end, carrying energy with it.

3. What are the characteristics of a transverse wave in a string?

The characteristics of a transverse wave in a string include amplitude (height of the wave), wavelength (distance between two consecutive peaks or troughs), frequency (number of waves passing a given point per second), and speed (how quickly the wave travels along the string).

4. How does tension in the string affect a transverse wave?

The tension in the string affects the speed of the transverse wave. The higher the tension, the faster the wave travels. This is because a higher tension creates a stiffer string, which allows the wave to travel more quickly.

5. What are some real-world applications of a transverse wave in a string?

Transverse waves in strings are commonly used in musical instruments, such as guitars and violins, to produce different pitches and notes. They are also used in many types of telecommunications, including telephone lines and fiber optic cables, to transmit information and data.

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