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Conservation of Energy

Formula sheet

Every equation used in the labs and derivations, in one printable page.

Energy

U=mghU = mgh

Gravitational potential energy

K=12mv2K = \tfrac{1}{2}mv^2

Kinetic energy

E=K+UE = K + U

Mechanical energy

K+U=constantK + U = \text{constant}

Conservation of mechanical energy

Free fall (from rest)

v2=u2+2aSv^2 = u^2 + 2aS

Equation of motion

v=2gxv = \sqrt{2gx}

Speed after falling x

t=2hgt = \sqrt{\dfrac{2h}{g}}

Time to fall a height h

K=mgx,U=mg(h−x)K = mgx,\quad U = mg(h-x)

Energies at distance x

Simple pendulum

U=mgL(1−cos⁡θ)U = mgL(1-\cos\theta)

Potential energy at angle θ

v=2gL(1−cos⁡θ0)v = \sqrt{2gL(1-\cos\theta_0)}

Speed at the lowest point

T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}}

Time period (small angles)