Want help regarding my classical mechanics assignment

[Dr.Brain]

Homework Statement

I need to write a C program to simulate physics problems. My job is to write a code , in which I give the user a function F(x) = ax^n + bx^(n-1) + ... , and user inputs the coefficients a,b,c ... and my computer code should tell whether the given force F(x) is conservative or not.

Please tell me what is the condition for any f(x) to be conservative , I am good at C , but i have no idea about the condition .Please help me formulate this problem.

Thanks.

 

[learningphysics]

Look at the definition of curl as given in cartesian coordinates:

http://mathworld.wolfram.com/Curl.html

for a force to be conservative, the vector needs to be 0... ie the coefficient of $$\hat{x}$$, $$\hat{y}$$ and $$\hat{z}$$ are each equal to 0.

In your formula, there are only x's... so I presume the force is acting in the x-direction... and depends only on the x-value... in that case the force is conservative already... no matter what coefficients you give...

I think you need to incorporate y, z etc...

 

[ogb p]

I understand your need for assistance with your classical mechanics assignment. The condition for a function to be conservative is that it must satisfy the property of path independence. This means that the work done by the force in moving an object from one point to another must be the same regardless of the path taken. In mathematical terms, this can be expressed as the integral of the force over a closed path being equal to 0. In order to determine if a given function is conservative, you can use this property to check if it holds true for the given function. I suggest researching more on the concept of conservative forces and path independence to gain a better understanding of the condition. Additionally, you can also consult with your professor or peers for further clarification. Good luck with your assignment!