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Gravitational Potential Energy U_grav, 1

$U_(grav, 1) = K_2 + U_(grav, 2) - W_(other) - K_1$

$(K_1)"Initial Kinetic Energy"$

$(U_(grav, 2))"Final Gravity Energy"$

$(W_(other))"Work by Other Force"$

$(K_2)"Final Kinetic Energy"$

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Reference

University Physics 12th Edition, Chapter 7, Equation #7.7