Work, Energy and Power

The dot product of two vectors

The dot product of two vectors A and B is A · B = AB cos θ. It gives a scalar, not a vector. It is useful because work depends on the component of for

Work done by a constant force

Work done by a constant force is W = F · d = Fd cos θ. Work depends on force, displacement, and the angle between them. No work is done when displacem

The change in kinetic energy

The change in kinetic energy of a particle is equal to the work done on it by the net force. For constant force, K_f − K_i = W. For variable force, th

Kinetic energy is K = 1/2

Kinetic energy is K = 1/2 mv^2. It depends on mass and the square of speed, so speed changes affect kinetic energy strongly.

If force changes with position

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