Conservative Forces for Constant C

In summary, the conversation discusses finding the value of the constant c that would make the force F conservative. The suggestion is to take the derivative of the function to determine if it is conservative and further assistance is needed with determining which derivative to use and how to complete the problem.
  • #1
engineertech0
7
0

Homework Statement



For what value of the constant c is the force F=i(2x +y2)+ j(cxy) conservative?

Homework Equations


F = ma


The Attempt at a Solution


Unsure of where to start
 
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  • #2
welcome to pf!

hi engineertech0! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)

which definition (or test) of conservative force do you think will be useful here? :wink:
 
  • #3
From my understanding, taking the derivative of the function could yield the results to find if it is conservative
 
  • #4
engineertech0 said:
From my understanding, taking the derivative of the function could yield the results to find if it is conservative

yes, which derivative, how? :smile:
 
  • #5
thats where i need help. one i know where to take the derivative and how i can complete the problem
 

FAQ: Conservative Forces for Constant C

What is a conservative force?

A conservative force is a type of force that, when acting on a body, does not dissipate energy but instead conserves it. This means that the work done by the force on an object is independent of the path taken by the object.

What are some examples of conservative forces?

Examples of conservative forces include gravity, elastic forces, and electrostatic forces. In these cases, the work done by the force is the same regardless of the path taken by the object.

What is the significance of a constant C in conservative forces?

The constant C in conservative forces represents the potential energy associated with the force. It is a constant value that can be used to calculate the potential energy at any point in space.

How are conservative forces related to potential energy?

Conservative forces and potential energy are closely related. The potential energy of an object in a conservative force field is equal to the negative of the work done by the force in moving the object from a reference point to its current position.

How can conservative forces be used in real-world applications?

Conservative forces have many practical applications, such as in designing roller coasters, calculating the motion of planets in space, and determining the stability of structures. They also play a crucial role in understanding the behavior of physical systems in fields like mechanics and thermodynamics.

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