Page 154 - Standard Handbook Of Petroleum & Natural Gas Engineering

Basic Mechanics (Statics and Dynamics) 139

2. If an unbalanced system of forces acts upon a particle, it will accelerate in the
direction of the resultant force at a rate proportional to the magnitude of the
resultant force. This law expresses the relationship between force, mass, and
acceleration and may be written as

F=Ma (2-2)
where F is the resultant force, M is the mass of the particle, and a is the
acceleration of the particle.
3. Contact forces between two bodies have the same magnitude, the same line of
action, and opposite direction.

Gmuitution. Two particles in space are attracted toward each other by a force that
is proportional to the product of their masses and inversely proportional to the square
of the distance between them. Mathematically this may be stated as

where I F 1 is the magnitude of the force of gravitational attraction, G is the universal
gravitational constant (6.673 x 10-"m3/kg - s2 or 3.44 x 10.' ft4/lb - s4), m, and m2
are the masses of particles 1 and 2, and r is the distance between the two particles.

Systems of Units
Two systems of units are in common usage in mechanics. The first, the SI system.
is an absolute system based on the fundamental quantities of space, time, and mass.
All other quantities, including force, are derived. In the SI system the basic unit of
mass is the kilogram (kg), the basic unit of length (space) is the meter (m), and the
basic unit of time is the second (s). The derived unit of force is the Newton (N),
which is defined as the force required to accelerate a mass of 1 kg at a rate of 1 m/s'.
The US. customary or English system of units is a gravitational system based upon
the quantities of space, time, and force (weight). All other quantities including mass
are derived. The basic unit of length (space) is the foot (ft), the basic unit of time is
the second (s), and the basic unit of force is the pound (Ib). The derived unit of mass
is the slug, which is the unit of mass that will be accelerated by a force of one pound
at a rate of 1 ft/s2. To apply the slug in practice, as in Equation 2-2, the weight in
pounds mass must first be divided by g = 32.2 ft/s2, thus generating a working mass in
units of lb - s2/ft, or slugs.
Statics

If there are no unbalanced forces acting on a particle, the particle is said to be in
static equilibrium, and Newton's second law reduces to

Thus, solving a problem in particle statics reduces to finding the unknown force
or forces such that the resultant force will be zero. To facilitate this process it is useful
to draw a diagram showing the particle of interest and all the forces acting upon it.
This is called afree-body diagram. Next a coordinate system (usually Cartesian) is
superimposed on the free-body diagram, and the forces are decomposed into their