Common forces in mechanics

Gravity acts at a distance; all other everyday mechanical forces are contact forces that arise where bodies touch.

The normal reaction is the component of a contact force perpendicular to the surfaces in contact; it adjusts to whatever value prevents the bodies from passing into each other.

Tension is the pull transmitted by a string. For a light (massless) inextensible string over a frictionless pulley, the tension is the same all along it.

A spring exerts a restoring force F = −kx for small extension or compression x, where k is the spring constant; the negative sign shows it opposes the deformation.

In a lift accelerating upward at a, a person's apparent weight (the normal force from the floor or the scale reading) is m(g + a); accelerating downward it is m(g − a).

A lift moving up but slowing down has downward acceleration, so the scale reads less than mg. The direction of acceleration matters, not the direction of motion.

In free fall (a = g downward) the scale reads zero; the body appears weightless though gravity still acts on it.