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mopar969
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F = a(r to the n)(r hat) Prove F is conservative. Please show steps.
mopar969 said:F = a(r to the n)(r hat) Prove F is conservative. Please show steps.
mopar969 said:I know you have to do a substitution with r hat j hat and k hat but I don't know how. Please show steps.
mopar969 said:View attachment 29049
Here is what I have done so far. Can you please show me how to finish this problem because it is due at 4 today. And thank you for all the help.
mopar969 said:The teacher wants us to show mathematically that it is conservative so the partial fractions Fx/y must equal the partial fraction of Fy/x etc. Please help me finish this problem and thank you!
mopar969 said:So I don't have to simplify the problem I can take the partial derivatives of what I have.
(I am asking because I thought that I had to get one big fraction) Also if I am allowed to take the partial fractions now I can do this for all the requirements for the force to be a conservative force. Please help me finish the problem and thank you for the help.
mopar969 said:How do I combine the square roots because the one in the numerator is to the n.
mopar969 said:can you explain how you got that.
mopar969 said:Thank you that makes sense I just wasn't seeing it as being that simple. But my next question is how do I do the partial derivative of the (x^2+y^2+z^2) to the n-1 all over 2 power. Thanks for all the help.
mopar969 said:I ended up getting the problem right and got 20 bonus points for my physics class. Thank you a lot and a lot for all the help. Thanks again Josh.
A conservative function is a type of vector function where its integral, or the total work done, is independent of the path taken. This means that if you travel from point A to point B using different paths, the work done will be the same regardless of the path chosen.
The key steps to prove that a function F is conservative are:
No, a function cannot be both conservative and non-conservative. If a function is conservative, it means that its integral is independent of the path taken, while a non-conservative function will have different values for the line integral depending on the path taken. These two properties are mutually exclusive.
Yes, it is possible for a function to have a zero curl but not be conservative. This can happen if the function is not defined on a simply connected domain. In other words, the path from point A to point B must not pass through any holes or gaps in the domain for the function to be conservative.
Conservative functions have many real-life applications, including: