# 我们如何从重力势能单位中恢复力量单位？

eurocoder 06/24/2018. 4 answers, 1.182 views

$$\ bigg [\ rm \ frac {J} {kg} \ bigg] = \ bigg [\ rm \ frac {kg \ cdot m ^ 2} {s ^ 2 \ cdot kg} \ bigg] = \ bigg [\ rm \ frac {m ^ 2} {s ^ 2} \ bigg]。$$

$$\ bigg [\ rm \ frac {J} {kg \ cdot m} \ bigg] = \ bigg [\ rm \ frac {kg \ cdot m} {s ^ 2 \ cdot kg} \ bigg] = \ bigg [ \ rm \ frac {m} {s ^ 2} \ bigg]。$$

$$\ bigg [\ rm N \ bigg] = \ bigg [\ rm \ frac {kg \ cdot m} {s ^ 2} \ bigg] \ neq \ bigg [\ rm \ frac {m} {s ^ 2} \ bigg]$$

Steeven 06/24/2018.

• 力等于引力势的负梯度 ”但是

• 力等于引力势能的负梯度 ”：

$$F = - \ nabla U = - \ frac {dU} {dx}$$

John Rennie 06/24/2018.

$$F = ma$$

my2cts 06/24/2018.

abu_bua 06/24/2018.

gravitational force由下式给出

$$\ mathbf {F} = - m \ cdot \ nabla G _ {\ text {pot}}$$

$$\ Bigg [\ cfrac {kg \ cdot m} {s ^ 2} \ Bigg] = \ Bigg [kg \ cdot \ cfrac {J} {kg \ cdot m} \ Bigg] = \ Bigg [kg \ cdot \ cfrac {kg \ cdot \ frac {m ^ 2} {s ^ 2}} {kg \ cdot m} \ Bigg]$$

$$\ Bigg [\ cfrac {kg \ cdot m} {s ^ 2} \ Bigg] = \ Bigg [\ cfrac {kg \ cdot m} {s ^ 2} \ Bigg]$$

$$\ mathbf F = - \ nabla U \ quad。$$

btw:将万有引力视为经典力量是错误的 - >参见Einstein's Relativity Theory