Calculating Potential Energy from Force for Non-Linear Systems

AI Thread Summary
To calculate potential energy from the force given by F(x) = αx - βx^3, the relationship -dV(x)/dx = F(x) is used. The limits of integration can be chosen freely, as the integration constant does not influence the force. Setting the potential energy to zero at x = 0 is acceptable and will not affect the physical outcomes. This choice simplifies calculations while maintaining the integrity of the system's physics. The discussion confirms that selecting a zero-level for potential energy is a matter of convenience.
RubroCP
Messages
14
Reaction score
4
Homework Statement
##F(x)=\alpha x-\beta x^3##
Relevant Equations
##-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x)##
If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that:
$$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$
but what about the limits of the integration?
 
Physics news on Phys.org
The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.
 
  • Like
Likes rsk and RubroCP
Orodruin said:
The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.
So can I say without loss of generality that for x = 0 the potential is also null?
 
Yes, this will not affect the physics.
 
Orodruin said:
Yes, this will not affect the physics.
Thanks!
 
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Back
Top