# Why did Feynman use a negative sign while defining the potential energy function?

Why is it ($$-U$$) and not ($$+U$$)? And how do we know it's going to help us if we take it to be negative beforehand?

• It is in general better to type out the question rather than just posting a screenshot. Regardless, some resources on the sign convention for potential energy are here physics.stackexchange.com/questions/tagged/… Commented Dec 28, 2020 at 17:00

The negative is just a convention that essentially makes the total mechanical energy $$E=K+U$$ rather than $$E=K-U$$.

• Thanks for the explanation Commented Dec 28, 2020 at 17:07
• But what problems would we face if it were K - U ? Just curious! Commented Dec 28, 2020 at 17:17
• Probably knowledge of definite integral and boundary conditions will help in understanding the fact of Negative signs. Commented Dec 28, 2020 at 17:51

Potential energy function sign depends on exact potential form definition. Usual convention is to use such sign of potential energy, so that field accomplished work by moving a particle from higher potential energy area to lower potential energy area, should be positive. So for example gravitational potential energy near Earth surface is defined as : $$E = \pmb+mgh$$,

So that work done by gravity field is $$W = E_2 - E_1 = mg\,(h_2 - h_1) \gt 0$$

Now if two masses are separated apart by huge distances, then gravitational potential takes universal form of :

$$U = \pmb- \frac {\alpha}{r}$$

So, for example Earth done work by attracting moon closer from distance $$r_2$$ to $$r_1$$ is :

$$W = U_2 - U_1 = \alpha \left(\frac 1r_1 - \frac 1r_2\right) \gt 0$$, again positive work done by gravity.