Resultant Forces

The resultant force on an object is the single force that has the same effect as all the forces acting on it together. It is the vector sum of the forces, and by Newton's second law it equals mass × acceleration: F₁ + F₂ + ... = ma.To use this, choose a positive direction, add the forces in that direction and subtract those in the opposite direction. The result divided by the mass gives the acceleration.For a rocket rising vertically, the resultant force is the thrust T minus the weight mg, so T - mg = ma.For a person of mass m in a lift accelerating upwards, the support force R from the floor is greater than the weight, R - mg = ma, so the person feels heavier. When the lift accelerates downwards, R is less than mg and they feel lighter.For two masses m₁ and m₂ hanging on either side of a light pulley, with m₁ greater than m₂, both masses have the same acceleration: (m₁ - m₂)g = (m₁ + m₂)a. The tension can then be found by applying F = ma to one mass on its own.