University Physics Volume 1

# Key Equations

### Key Equations

 Difference of potential energy $ΔUAB=UB−UA=−WABΔUAB=UB−UA=−WAB$ Potential energy with respect to zero ofpotential energy at $r→0r→0$ $ΔU=U(r→)−U(r→0)ΔU=U(r→)−U(r→0)$ 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 $Wclosed path=∫F→cons·dr→=0Wclosed path=∫F→cons·dr→=0$ 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 nonon-conservative forces $0=Wnc,AB=Δ(K+U)AB=ΔEAB.0=Wnc,AB=Δ(K+U)AB=ΔEAB.$