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Work
W=Fd\cos\theta
Kinetic Energy
KE=\frac12mv^2
Potential Energy (Gravitational)
PE=mgh
Potential Energy (Elastic)
PE_{sprig}=\frac12kx^2
Work-Energy Theorem
W_{net}=\Delta KE
Conservation of Energy
KE_{i}+PE_{i}=KE_{f}+PE_{f}
For problems with Friction
W_{net}=W_{applied}-W_{friction}=\Delta KE