Work, Energy and Power — Formula Sheet

A · B = AB cos θ

K = 1/2 mv^2

W = F d cos θ

Kf − Ki = W

W = ∫xi to xf F(x) dx

ΔW ≈ Σ F(x)Δx

F(x) = −dV/dx

V(h) = mgh

K_i + V(x_i) = K_f + V(x_f)

V(x) = kx^2/2

F_s = −kx

For constant force, the theorem follows from the kinematic relation v^2 - u^2 = 2as.

Work

W = Fd cos θ

Work done by a constant force is W = F · d = Fd cos θ.

If force changes with position, the work done is W = ∫ F(x) dx from initial to final position.