Download Force and Stress I

Force and Stress I
Fundamental Quantities & Units of Rocks
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Mass: Dimension: [M]
Length: Dimension: [L]
Time: Dimension: [T]
Unit: g or kg
Unit: cm or m
Unit: s
Velocity, v = distance/time = dx/dt
Change in distance per time)
v =[L/T] or [LT-1] units: m/s or cm/s
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Acceleration (due to gravity): g = velocity/time
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Acceleration is change in velocity per time (dv/dt).
g = [LT-1 ]/[T] = LT-2, units: m s -2
Force:
F = mass . acceleration
 F = mg F = [M][LT-2]
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units: newton: N = kg m s-2
Newton’s 1st Law
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Law 1. An object continues in its initial state of
rest or motion with uniform velocity unless it is
acted on by an unbalanced, or net external, force.
 The net force acting on an object, also called
the resultant force, is the vector sum of all the
forces acting on it.
Mathematically, Law 1 is expressed as Fnet = S F
where Fnet represents the net force, and SF
represents the vector sum of all of the forces acting
on a given object.
Newton’s
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nd
2
Law
The acceleration of an object is inversely
proportional to its mass and directly
proportional to the net force acting on it.
Mathematically, Law 2 can be expressed as:
a = Fnet/m
or
Fnet = ma
where a = acceleration and m = the mass of the object
upon which the force is acting.
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Physicists define mass as an intrinsic property of an
object that is a measure of its resistance to
acceleration while acceleration is simply the
change in velocity over a change in time (i.e.
a=Dv/Dt)
Force
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A property or action that changes or
tends to change the state of rest or
velocity or direction of an object in a
straight line
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In the absence of force, a body moves at
constant velocity, or it stays at rest
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Force is a vector quantity; i.e., has
magnitude, direction
Units of Force
Two of the more common units of force are the dyne (d) and
newton (N)
 The units of a newton are kgm/s2 while those for a dyne are
gcm/s2
 A newton is the force required to impart an acceleration of
one meter per second per second to a body of one kilogram
mass
 A dyne is the force required to accelerate one gram of mass
at one centimeter per second per second
F = (mass)(acceleration) or
F = ma or F = mg F = [M][ LT-2]
newton: N = kg m s –2
dyne: gr cm s -2 1 N = 105 dyne
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Natural Forces
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Gravitational force
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Thermally-induced forces
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Acts over large distances and is always attractive
 Ocean tides are due to attraction between Moon & Earth
e.g., due to convection cells in the mantle.
Produce horizontal forces (move the plates)
The other three forces act only over short ranges (atomic
scales). May be attractive or repulsive
 Electromagnetic force
 Interaction between charged particles (electrons)
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Nuclear or strong force
 Holds the nucleus of an atom together.
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Weak force
 Is responsible for radioactivity
Body Forces
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Any part of material experiences two types of
forces:
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surface & body
Body Force: Results from action of a field at
every point within the body
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Is always present
Could be due to gravity or inertia
 e.g., gravity, magnetic, centrifugal
Its magnitude is proportional to the mass of the body
Surface Forces
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Act on a specific surface area in a body
 Are proportional to the magnitude of the area
 Reflect pull or push of the atoms on one side of
a surface against the atoms on the other side
e.g., force of a cue stick that hits a pool ball
 force of the jaws of a vice
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Body forces give rise to spatial variations or
gradients on surface forces
Stress is Great!
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Forces applied on a body do either or both of the
following:
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Change the velocity of the body
Result in a shape change of the body
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A given force applied by a sharp object (e.g.,
needle) has a different effect than a similar force
applied by a dull object (e.g., peg). Why?
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We need another measure called stress which
reflect these effects
Traction
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Traction is force per unit area
It is the intensity of the force, i.e., how concentrated the force is
s = lim dF/dA when dA → 0
A force acting on a small area such as the tip of a sharp nail or
base of high heel shoe, has a greater intensity than a flat-headed
nail or a snow shoe!
s = [MLT-2] / [L2]=[ML -1T-2]
In the mks system of the SI system:
s = kg m-1 s-2 pascal (Pa) = N/m2
1 bar (non-SI) = 105 Pa ~ 1 atmosphere = 0.1 MPa
1 kb = 1000 bar = 108 Pa = 100 Mpa
1Gpa = 109 Pa = 1000 Mpa = 10 kb
1 Mpa is equivalent to 1 N/mm2
P at core-mantle boundary is ~ 136 Gpa (at 2900 km)
P at the center of Earth (6371 km) is 364 Gpa
Ten common units geologists use to describe stress
equivalent to 1 megapascal (MPa)
Units
MPa Equivalent
megapascal (Mpa)
1
gigapascal (Gpa)
0.001
pascal (Pa) = N/m2
1,000,000
kg/cm2
10.197
d/cm2
100,000,000.000
bar (b)
10
kilobar (kb)
0.010
pounds per square inch (psi)
145.030
atmosphere (atm) ~ bar
9.869
Types of Stress
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Tension: Stress acts _|_ to and away from a plane
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Compression: stress acts _|_ to and toward a plane
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pulls the rock apart
forms special fractures called joint
may lead to increase in volume
squeezes rocks
may decrease volume
Shear: acts parallel to a surface
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leads to change in shape