Page 153 - Standard Handbook Of Petroleum & Natural Gas Engineering

138 General Engineering and Science

produced by a couple is calculated by multiplying the magnitude of one of the two
forces times the perpendicular distance between them. Moment is a vector quantity,
and its sense of direction is considered to be outwardly perpendicular to the plane of
counterclockwise rotation of the couple. The moment of a single force about some
point A is the magnitude of the force times the perpendicular distance between A
and the line of action of the force.
Velocity. A measure of the instantaneous rate of change of position in space with
respect to time. Velocity is a vector quantity.
Acceleration. A measure of the instantaneous rate of change in velocity with respect
to time. Acceleration is a vector quantity.
Gravitational acceleration. Every body falling in a vacuum at a given position above
and near the surface of the earth will have the same acceleration, g. While this
acceleration varies slightly over the earth’s surface due to local variations in its shape
and density, it is sufficiently accurate for most engineering calculations to assume
that g = 32.2 ft/s2 or 9.81 m/sp at the surface of the earth.
Weight. A measure of the force exerted on a body of mass M by the gravitational
attraction of the earth. The magnitude of this force is
W=Mg
where W is the weight of the body. Strictly speaking, weight is a vector quantity since
it is a force acting in the direction of the gravitational acceleration.

General Laws

The foregoing defined quantities interact according to the following fundamental
laws, which are based upon empirical evidence.
Conservation of mass. The mass of a system of particles remains unchanged during
the course of ordinary physical events.
Parallelogram law for the addition of forces. Two forces, F, and F,, acting on a particle
may be replaced by a single force, R, called their resultant. If the two forces are
represented as the adjacent sides of a parallelogram, the diagonal of the parallelogram
will represent the resultant (Figure 2-1).
Principle of transmissibility. A force acting at a point on a body can be replaced by a
second force acting at a different point on the body without changing the state of
equilibrium or motion of the body as long as the second force has the same magnitude
and line of action as the first.

Newton’s Laws of Motion

1. A particle at rest will remain at rest, and a particle in motion will remain in
motion along a straight line with no acceleration unless acted upon by an
unbalanced system of forces.

FI
Figure 2-1. Parallelogram law for addition of forces.