Differentiation of potential energy

In summary, the potential energy of a system of two particles separated by a distance r is given by U(r) = (A)/(r^4), and the radial force that each particle exerts on the other can be found by taking the partial derivative of U(r). This is equal to A/(3*r^3).
  • #1
zcabral
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Homework Statement



The potential energy of a system of two particles separated by a distance r is given by U(r) = (A)/(r^4), where A is a constant. Find the radial force that each particle exerts on the other. (Use A and r as appropriate in your equation.)

Homework Equations



F=-dU/dx
U is potential energy

The Attempt at a Solution



i figured out the antiderivative of U(r) is -(A)/(3*r^(3)) but it isn't the correct answer.
what else do u need to do besides the antiderivative which is equal to force. since it is 2 particles should i divide the U(r) funciton by 2?
 
Last edited:
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  • #2
you actually want the partial derivative of r
 
  • #3
ok but how do u get that? I am rather new at the whole calculus thing. wud it just b A/3r^3?
 
  • #4
Think of U(r) as A*(r^-4) then try to differentiate it...
 

What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration. It is a form of stored energy that has the potential to do work in the future.

What is the relation between potential energy and differentiation?

Differentiation of potential energy is the process of finding the rate of change of potential energy with respect to a given variable. This allows us to understand how potential energy changes as the object's position or configuration changes.

Why is differentiation of potential energy important?

Differentiation of potential energy is important because it helps us understand the behavior of systems in terms of their energy. It allows us to calculate the forces acting on an object and predict its motion.

Can potential energy be negative?

Yes, potential energy can be negative. This occurs when the object's position or configuration is such that the potential energy is less than its minimum value. For example, a ball at the bottom of a valley has negative gravitational potential energy.

How is differentiation of potential energy used in real-world applications?

Differentiation of potential energy has various applications in fields such as physics, engineering, and chemistry. It is used to analyze and optimize systems, such as in designing roller coasters or predicting the behavior of chemical reactions. It is also used in understanding the behavior of particles in quantum mechanics.

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