# Newton should have rediscovered the law of lever!

1. Sep 11, 2004

### sexwish

say i have a closed system of two weights in evacuated space on some distance between them. at the beginning they start the mutual attraction without initial push. conservation of impulse requires:
d(p_1+p_2)=0
d(d(m_1x_1+m_2x_2)/dt)=0
if x_1=D_1 and x_2=-D_2 then you get the law of lever as condition for equilibrium in the system:
m_1/m_2=D_2/D_1
but
d(p_1+p_2)=(F_1+F_2)dt=0 so you get Newton III as condition for equilibrium.
however, the law of lever is m_1/m_2=D_2/D_1=F_1/F_2 so Newton respects the law of lever only partially.