- #1
sponsoredwalk
- 533
- 5
In deriving the gravitational potential energy term I have a question.
[tex] W \ = \ \int_{r_1}^{r_2} \overline{F}( \overline{r}) \cdot \,d \overline{r} \ = \ \int_{y_1}^{y_2}mg \,dy [/tex]
[tex] W \ = \ \int_{y_1}^{y_2}mg\,dy [/tex]
[tex] W \ = \ mgy_2 \ - \ mgy_1 [/tex]
[PLAIN]http://img696.imageshack.us/img696/2303/workvk.jpg
[tex] W \ = \ mgy_2 \ - \ mgy_1 \ = \ U_{grav}_2 \ - \ U_{grav}_1 [/tex]
I think I understand that y2 < y1 and that is the
reason why people write the above as:
[tex] W \ = \ mgy_1 \ - \ mgy_2 \ = \ U_{grav}_1 \ - \ U_{grav}_2 [/tex]
but is it such a crime to just be aware of the y2 < y1 and
write the equation in the more logical fashion that the straight calculation gives
you. To me it seems similar to how you rewrite the equations of constant
acceleration the standard way the calculus shows them and you mentally
set g = - 9.8 m/s²
Just like to hear some thoughts on this, thanks!
[tex] W \ = \ \int_{r_1}^{r_2} \overline{F}( \overline{r}) \cdot \,d \overline{r} \ = \ \int_{y_1}^{y_2}mg \,dy [/tex]
[tex] W \ = \ \int_{y_1}^{y_2}mg\,dy [/tex]
[tex] W \ = \ mgy_2 \ - \ mgy_1 [/tex]
[PLAIN]http://img696.imageshack.us/img696/2303/workvk.jpg
[tex] W \ = \ mgy_2 \ - \ mgy_1 \ = \ U_{grav}_2 \ - \ U_{grav}_1 [/tex]
I think I understand that y2 < y1 and that is the
reason why people write the above as:
[tex] W \ = \ mgy_1 \ - \ mgy_2 \ = \ U_{grav}_1 \ - \ U_{grav}_2 [/tex]
but is it such a crime to just be aware of the y2 < y1 and
write the equation in the more logical fashion that the straight calculation gives
you. To me it seems similar to how you rewrite the equations of constant
acceleration the standard way the calculus shows them and you mentally
set g = - 9.8 m/s²
Just like to hear some thoughts on this, thanks!
Last edited by a moderator: