According to Newton's
law of gravitational attraction, any two particles or bodies have a mutual
attractive or gravitational force acting between them. In the case of a
particle located at or near the surface of the earth, however, the only
gravitational force having sizable magnitude is that between the
earth and the particle. Consequently, this force, termed the weight, will be
the only gravitational force considered in our study of mechanics.
From Law of gravitation,
we can develop an approximate expression for finding the weight of a particle
having a mass m1 = m. If we assume the earth to be a nonrotating sphere of
constant density and having a mass of m2 = Me, then if r is the distance between the earth’s
centre and the poarticle we have
Letting g = GMe/r2,
yields
W = mg
By comparison with F = ma, we term g the
acceleration due to gravity. Since it depnds on r, it can be seen that the
weight of a body is not an absolute quantity. However, for most engineering calculations, g is
determined at sealevel amd at a latitude of 45o, which is considered
as “standard location.”
