Solving problems in mechanics

Pick the body (or system) and draw a free-body diagram showing every force acting on it, and only those forces.

Choose axes, usually along and perpendicular to the direction of acceleration, and write the second law separately for each axis.

For connected bodies, the string condition gives the same magnitude of acceleration for both bodies and, for a light string, the same tension at both ends.

Treating connected bodies as one system gives the common acceleration quickly, because internal tensions cancel; a separate free-body diagram is then needed to find the tension.

For two masses m₁ > m₂ hanging over a light frictionless pulley, a = (m₁ − m₂)g/(m₁ + m₂) and T = 2m₁m₂g/(m₁ + m₂).

With friction on connected bodies, first check whether the driving force exceeds limiting static friction; if not, the system stays at rest and friction equals the driving force.

When a force is applied at an angle to a floor, its vertical component changes the normal reaction and therefore the friction.