Gravity and Newton's Second Law

For a constant-mass body in an inertial reference frame, Newton's second law is ΣF = ma. Force and acceleration are vectors. In a chosen direction, add all forces with their signs before dividing by mass. A force of one newton accelerates one kilogram at one metre per second squared.

Weight is the gravitational force W = mg; it is not mass. A stationary supported object can have nonzero weight and zero acceleration because its support force balances gravity. See NASA's discussion of Newton's laws.

Worked example: take upward as positive. A 10 kg body accelerates upward at 2 m/s². With g = 9.80665 m/s² and no other forces, the required support force satisfies R − mg = ma, giving R = 118.0665 N. Its weight is 98.0665 N; the net upward force is 20 N.

The conventional standard acceleration is gₙ = 9.80665 m/s². It is a defined reference, not a measurement of gravity at every sea-level location. Actual local gravity depends on position and local mass distribution. Precision work requires a suitable local value. NIST lists the standard value; NIST also explains gravity measurement.

Fluid-static example: for a stationary liquid of constant density, the pressure increase at depth h is Δp = ρgh. At 2 m depth in a liquid with an assumed density of 1000 kg/m³, standard gravity gives Δp = 19,613.3 Pa. Add the pressure at the surface to obtain absolute pressure. Use the hydrostatic pressure calculator to enter a different density, depth, surface pressure or gravity.

With downward positive, constant g, zero initial velocity and no air resistance, v = gt and s = ½gt². The table is calculated using standard gravity; values are rounded to three decimals. It describes ideal motion before impact, not a prediction including aerodynamic drag. NASA explains these free-fall assumptions.

At 2 seconds the unrounded values are 19.6133 m/s and 19.6133 m. Equal numerical values here do not make velocity and distance the same quantity: their units differ.

Stopping distance, deformation and contact time are needed to estimate impact forces. These free-fall equations alone do not determine peak impact load, fall-arrest performance or structural safety.

When converting mass into a static beam load, first calculate its weight in newtons. The rectangular beam calculator accepts concentrated and distributed forces, not kilograms. Its static elastic model does not include impact amplification.

Gravity head is one part of the reservoir pump-duty calculation. That calculation also includes pressure differences and flow losses.