Net force an an infinitesimal string

In summary, the equation dF_v = T_0 \frac{ \partial{y}}{\partial{x}} |_{x+dx} -T_0 \frac{ \partial{y}}{\partial{x}} |_{x} is a finite difference approximation commonly used in numerical methods to approximate derivatives. In order to solve it, one needs to have a function for y(x) and its derivatives.
  • #1
ehrenfest
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1

Homework Statement


The book I am using (Zwiebach on page 66) uses the expression

[tex] hello [/tex]

[tex] dF_v = T_0 \frac{ \partial{y}{\partial{x}} |_{x+dx} -T_0 \frac{ \partial{y}{\partial{x}} |_{x} [/tex]

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
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  • #2


Hello,

Thank you for sharing your question and the equation from Zwiebach's book. It would be helpful to have more context and information about the specific problem you are working on in order to provide a complete solution. However, I can offer some general guidance and suggestions.

First, it looks like you may have made a typo in the equation you shared. The "dx" in the first term should be outside of the partial derivative, so it should be written as:

dF_v = T_0 \frac{ \partial{y}}{\partial{x}} |_{x+dx} -T_0 \frac{ \partial{y}}{\partial{x}} |_{x}

This is known as the finite difference approximation and is commonly used in numerical methods to approximate derivatives.

In order to solve this equation, you will need to have a function for y(x) and its derivatives. You can then plug these values into the equation to calculate the change in the force (dF_v) at a particular point (x+dx) compared to the force at the previous point (x).

I hope this helps and good luck with your problem!
 

Related to Net force an an infinitesimal string

1. What is a net force on an infinitesimal string?

A net force on an infinitesimal string is the sum of all the forces acting on the string. This includes both external forces, such as tension or gravity, and internal forces, such as friction. The net force determines the acceleration of the string.

2. How do you calculate the net force on an infinitesimal string?

The net force on an infinitesimal string can be calculated by adding up all the individual forces acting on the string. These forces can be calculated using Newton's second law, which states that force equals mass times acceleration (F=ma). In the case of an infinitesimal string, the mass is assumed to be negligible, so the net force is simply equal to the acceleration of the string.

3. What is the significance of net force on an infinitesimal string?

The net force on an infinitesimal string is significant because it determines the motion of the string. If the net force is zero, the string will remain at rest or continue to move at a constant velocity. If the net force is non-zero, the string will accelerate in the direction of the net force.

4. How does tension affect the net force on an infinitesimal string?

Tension is one of the external forces that can contribute to the net force on an infinitesimal string. If the string is being pulled from both ends, the tension forces will cancel each other out and the net force will be zero. However, if there is an imbalance in the tension forces, there will be a net force on the string, causing it to accelerate.

5. Can the net force on an infinitesimal string be negative?

Yes, the net force on an infinitesimal string can be negative. This means that the forces acting on the string are in opposite directions and the string will experience a deceleration. A negative net force can also indicate that the string is being pulled in one direction and pushed in the opposite direction, resulting in a net force of zero but a change in the direction of motion.

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