The discussion revolves around a problem involving the calculation of velocity related to a spring's potential energy and average force. The subject area includes concepts from mechanics, specifically elastic potential energy and forces in springs.
Some participants have provided guidance regarding the use of average force in the energy equations, while others are questioning the assumptions made about the force values and their implications for the calculations. Multiple interpretations of the problem are being explored without reaching a consensus.
The average force is specified in the problem, and there is confusion regarding its application in the energy equations. Participants are also discussing the implications of using average versus instantaneous force in the context of the spring's behavior.
The elastic potential energy stored in a spring is equal in magnitude to the work done by it when moving from its compressed distance, x, to its original uncompresed length, that is, [tex]E_p = \int Fdx[/tex], from the definition of work, where F, from Hookes Law, is [tex]F =kx[/tex]. Performing the calculus, you get the well known equation for the elastic potential energy of the spring, [tex]E_p =1/2kx^2[/tex]. Noting that [tex]F=kx[/tex] at its max compressed point, this is identically equivalent to [tex]E_p = F/2 (x)[/tex], or [tex]E_p = F_{avg} x[/tex].temaire said:So Phanthom, you're saying that [tex]E_p = F_{ave}x[/tex] is an actual formula?