Derivative of Force and Work in Respect to Time

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SUMMARY

The discussion centers on the relationship between the derivative of force with respect to time and work, specifically exploring the equation dF/dt = d^2p/dt^2. Participants debate the implications of time-dependent forces on work, concluding that dW/dt = F·v holds true for time-independent forces, while time-dependent forces complicate the relationship. The conversation highlights the distinction between work as a functional and its derivative, emphasizing that dW/dt cannot be treated as a simple derivative due to its dependence on the path taken and the nature of the force.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly Newton's laws.
  • Familiarity with the concepts of work and energy in physics.
  • Knowledge of calculus, specifically derivatives and integrals.
  • Basic understanding of vector calculus and force dynamics.
NEXT STEPS
  • Study the relationship between work and energy in classical mechanics.
  • Learn about time-dependent forces and their implications on work and energy.
  • Explore the concept of work as a functional in advanced physics texts.
  • Investigate the mathematical treatment of derivatives in the context of physical quantities.
USEFUL FOR

Students and professionals in physics, particularly those focusing on classical mechanics, as well as educators seeking to clarify the concepts of work and force dynamics.

  • #31
marlon said:
Indeed that is what i meant. Don't mind dextercioby with his useless remarks. He is just angry and not willing to see he's just regurgitating self-adapted physics...

let's not get into that...

YOU ARE RIGHT...

marlon

:smile: I'm not angry... :-p For the last couple of days,i've been laughing my a$$ out... :smile: I ain't got nobody to be angry at...If somebody proves me wrong,i'll accept it,even if it's Marlon... :-p So far,i haven't had sufficient evidence to admit i was/am/will be wrong...

Self-adapted physics u say... :-p I wish i could believe you... :-p

Daniel.
 
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  • #32
dextercioby said:
:smile: I'm not angry... :-p For the last couple of days,i've been laughing my a$$ out... :smile: I ain't got nobody to be angry at...If somebody proves me wrong,i'll accept it,even if it's Marlon... :-p So far,i haven't had sufficient evidence to admit i was/am/will be wrong...

Self-adapted physics u say... :-p I wish i could believe you... :-p

Daniel.

good for you...

marlon
 
  • #33
dextercioby said:
This is wrong,if 'W' stands for potential energy.If it stands for work,then the force should not depend on time:
\frac{dW}{dt}=\frac{d}{dt}(\vec{F}\cdot \vec{r})=\vec{F}\cdot \vec{v}=P(1)
,where P is the mechanical power.

this is just plain wrong again...

\Delta W = \int mvdv = \Delta E _{kinetic}

from this formula you need to start...

marlon
 

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