Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 44

Lithosphere

Ocean

Mid-ocean
ridge

F

Plate

- F

Fig. 3.12 A shear couple acts at the junction between lithosphere and asthenosphere.

sum, or resultant, of all these forces must equal the
observed change of momentum of a substance, or

distance moved, x . Mechanical or flow work of

this kind comes in units of force times unit distance, or
Nm, of dimensions ML 2 T 2 . A single unit of work done
is termed a Joule, J. All objects, moving or stationary, may
be said to be capable of doing mechanical work: they all
possess energy . This energy must also have units ML 2 T 2 .
A moving object or portion of substance has the energy
proportional to its mass, m , times velocity squared, u 2 .
This is called kinetic energy (i.e. energy of movement) and
may be shown (Cookie 5) equal to 0.5 m u 2 . A stationary
object or piece of substance has the energy of its weight
force, m g , times distance, h , from the center of gravity to
which it is being attracted. This is what Rankine originally
called potential energy (i.e., energy of position), m g h . It is
usual to define h with respect to some convenient refer-
ence level.
Energy may clearly be released at variable rate, either
very slowly as during motion of a great lithospheric plate,
or spectacularly rapidly as in an explosive volcanic erup-
tion. The time rate of liberation of energy, in J s 1 , is
termed power . It has dimensions ML 2 T 3 and specified
units called Watts, W. In terms of work, power is the rate
at which work is done.
The interrelated concepts of force, energy, work, and
power are perhaps easiest grasped by reference to fluid
flowing down a sloping channel under the influence of
gravity (Fig. 3.11). Fluid movement is created by gravity
and the resulting applied force is opposed by the reactive
friction force of the channel bed and banks. The flowing
fluid has kinetic energy of motion that is provided by the
fall in elevation of its surface as a loss of potential energy,
though some of the latter is lost in friction. The available
power of the river is the time rate of change of this poten-
tial energy to kinetic energy minus the frictional losses.
The energy of flow is available to do mechanical work, arti-
ficially in turning a water wheel or naturally in sediment
transport. See Section 3.12 for energy conservation in
moving fluid.

x , or F ·

m a . In a steady flow of material, however fast or
slow, or in a substance at rest,

F

0 and for that very
important case the arrayed forces must balance out to
zero. Major progress in physical dynamics may be made in
such cases.

F

3.3.6 Signs and orientations of forces

As a vector quantity, force acts in the same direction as the
acceleration that produces it. Complications arise in turbu-
lent flows where the direction of the force is constantly
changing in time and space. In slowly deforming or static
solid rock or ice (Sections 3.13-3.15), we can more easily
speak of the orientation of forces with respect to the dis-
tortion they produce: compressive forces tending to push
adjacent portions of rock together (which is what is
happening under a surface load) or extensional forces
doing the opposite. Across any plane, force vectors point-
ing toward each other are designated compressional and
positive and those pointing away from each other, exten-
sional and negative. Forces acting on a plane can also have
any orientation. The two end members are normal and
shear force orientations, the former normal to the plane
in question and the latter parallel. As a vector, force may
have any orientation and can always be resolved into
components.

3.3.7 Energy, mechanical work done, and power

Energy, work done, and power are interrelated scalar
quantities. When a mass of substance is displaced from one
position to another during flow or deformation, mechani-
cal work must have been done to achieve the displacement.
This must be equal to the force required, F , times the