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Key Equations

Difference of potential energy ΔUAB=UBUA=WABΔUAB=UBUA=WAB
Potential energy with respect to zero of
potential energy at r0r0
ΔU=U(r)U(r0)ΔU=U(r)U(r0)
Gravitational potential energy near Earth’s surface U(y)=mgy+const.U(y)=mgy+const.
Potential energy for an ideal spring U(x)=12kx2+const.U(x)=12kx2+const.
Work done by conservative force over a closed path Wclosed path=Fcons·dr=0Wclosed path=Fcons·dr=0
Condition for conservative force in two dimensions (dFxdy)=(dFydx)(dFxdy)=(dFydx)
Conservative force is the negative derivative of potential energy Fl=dUdlFl=dUdl
Conservation of energy with no
non-conservative forces
0=Wnc,AB=Δ(K+U)AB=ΔEAB.0=Wnc,AB=Δ(K+U)AB=ΔEAB.
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