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In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it (Newton's second law): = =, where F is the net force acting on the body, m is the mass of the body, and a is the center-of-mass acceleration.
In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. [49] If the total external force is not zero, then the center of mass changes velocity as though it were a point body of mass . This follows from the fact that the internal forces ...
Then the attraction force vector onto a sample mass can be expressed as: = Here is the frictionless, free-fall acceleration sustained by the sampling mass under the attraction of the gravitational source. It is a vector oriented toward the field source, of magnitude measured in acceleration units.
This allowed a description of the motions of light and mass that was consistent with all available observations. In general relativity, the gravitational force is a fictitious force resulting from the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime.
Thus the kilogram-force is defined as precisely 9.80665 newtons. In reality, gravitational acceleration (symbol: g) varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also Gravimetry. Engineers and scientists understand the distinctions between mass, force, and weight.
The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s −2.The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s −2. A newton is thus equal to ...
If a g-force (acceleration) is vertically upward and is applied by the ground (which is accelerating through space-time) or applied by the floor of an elevator to a standing person, most of the body experiences compressive stress which at any height, if multiplied by the area, is the related mechanical force, which is the product of the g-force ...
This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit [11] —the use of Newton's second law, F = m ⋅ a, requires another factor, g c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s 2).