- #1
Obliv
- 52
- 1
Hello, I am trying to generalize the work equation and understand the very definition of it. From what I understand, Work is the energy required to displace an object with a force in the direction of the displacement. (also the change in kinetic energy but I'm not going to worry about that yet)
[tex] W = \int \vec{F} \cdot {d}\vec{x} [/tex] This equation makes sense to me. If I were to add bounds to the integral, would they be in 3-D if the displacement and force is in 3-D?
Otherwise
[tex] W = \int_{x_i}^{x_f} {F_x} {dx} + \int_{y_i}^{y_f} {F_y} {dy} + \int_{z_i}^{z_f} {F_z} {dz}[/tex]
This method would get the work with calculus I know of. Is it possible to make bounds in multiple dimensions? If so, how would one solve them? Thank you!
edit: Oh one more question: This equation describes non-conservative work, right? What would describe conservative work? Just this? [tex] W = \vec{F} \cdot \vec {d} [/tex]
[tex] W = \int \vec{F} \cdot {d}\vec{x} [/tex] This equation makes sense to me. If I were to add bounds to the integral, would they be in 3-D if the displacement and force is in 3-D?
Otherwise
[tex] W = \int_{x_i}^{x_f} {F_x} {dx} + \int_{y_i}^{y_f} {F_y} {dy} + \int_{z_i}^{z_f} {F_z} {dz}[/tex]
This method would get the work with calculus I know of. Is it possible to make bounds in multiple dimensions? If so, how would one solve them? Thank you!
edit: Oh one more question: This equation describes non-conservative work, right? What would describe conservative work? Just this? [tex] W = \vec{F} \cdot \vec {d} [/tex]
Last edited: