y ∠U=U-U1=-W=-F.d mg 2. The potential energy of gravity For the ball-Earth system, We take upward direction to be y positive direction △=((2)-U()-(mg)dhy=mg(y2-y1) J(2=U(D+mg(2-yi), dependent on U(y) The physically important quantity is AU, not U(2)orU) If We set U(=0)=0(the reference zero point of U is at O) We have u()=mgy (129) Ch 12 Energy II: Potential energy
Ch.12 Energy II: Potential energy 2. The potential energy of gravity For the ball-Earth system, we take upward direction to be y positive direction ( ) ( ) ( ) ( ) 2 1 2 1 2 1 U U y U y m g dy m g y y y y = − = − − = − The physically important quantity is , ΔU not or . ( ) 2 U y ( ) 1 U y U(y1 = 0) = 0 U( y) = mgy (12-9) If We set We have (the reference zero point of U is at O) y2 y1 y ΔU =U −U = −W = − F ds f i mg ( ) ( ) ( ) 2 1 2 1 U y =U y +mg y − y , dependent on ( ) 1 U y
3. The potential energy of spring force Fig11-13 When the spring is in its relaxed state. and we can declare the Relaxed length potential energy of the system to be zero(u0=0D U(x-0=- Fdx=-nr7 kx)dx →U(x)=k (12-8) The reference zero point of potential is at x=0. Ch 12 Energy II: Potential energy
Ch.12 Energy II: Potential energy 3. The potential energy of spring force 0 u0 = − = − = − − x U(x) Fdx ( kx)dx 0 0 2 2 1 U (x) = kx o x Relaxed length Fig 11-13 When the spring is in its relaxed state, and we can declare the potential energy of the system to be zero ( ) (12-8) The reference zero point of potential is at x=0. 2 1