Motion under several forces

If several forces act on a body, their vector sum – the net (resultant) force – gives the acceleration: m·a = F₁ + F₂ + … . To solve a problem we draw all forces on the body, choose axes (usually one along the acceleration) and project the equation on each axis. On a horizontal surface with a pulling force F and sliding friction Fₛ = μN, a = (F – μmg)/m. On an inclined plane (angle α) the weight splits: mg sinα along the plane and mg cosα perpendicular to it, so N = mg cosα and for sliding down a = g(sinα – μcosα). The body stays at rest if tanα ≤ μ. For loads m₁ and m₂ (m₂ > m₁) on a string over a fixed pulley (massless string and pulley, no friction): a = g(m₂ – m₁)/(m₁ + m₂) and the tension is T = 2m₁m₂g/(m₁ + m₂). During the motion the weight of each load (the force on the string) equals T: although their masses differ, the two loads have the same weight.