- #1

sponsoredwalk

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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 y

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 y

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 y

_{2}< y_{1}and that is thereason 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 y

_{2}< y_{1}andwrite 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!

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