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Force and Stress I. Fundamental Quantities & Units of Rocks. Mass: Dimension: [M] Unit: g or kg Length: Dimension: [L] Unit: cm or m Time: Dimension: [T] Unit: s Velocity , v = distance/time = d x/ d t Change in distance per time)

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fundamental quantities units of rocks
Fundamental Quantities & Units of Rocks
  • Mass: Dimension: [M] Unit: g or kg
  • Length: Dimension: [L] Unit: cm or m
  • Time: Dimension: [T] 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

Acceleration (due to gravity): g = velocity/time

  • 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]
  • units: newton: N = kg m s-2
newton s 1 st law
Newton’s 1st Law
  • 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 2 nd law
Newton’s 2nd 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.

  • 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
Force
  • 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
  • In the absence of force, a body moves at constant velocity, or it stays at rest
  • Force is a vector quantity; i.e., has magnitude, direction
units of force
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

natural forces
Natural Forces
  • Gravitational force
    • Acts over large distances and is always attractive
      • Ocean tides are due to attraction between Moon & Earth
  • Thermally-induced forces
    • 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)
    • Nuclear or strong force
      • Holds the nucleus of an atom together.
    • Weak force
      • Is responsible for radioactivity
body forces
Body Forces
  • Any part of material experiences two types of forces:
    • surface & body
  • Body Force: Results from action of a field at every point within the body
    • 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
Surface Forces
  • 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
  • Body forces give rise to spatial variations or gradients on surface forces
stress is great
Stress is Great!
  • Forces applied on a body do either or both of the following:
    • Change the velocity of the body
    • Result in a shape change of the body
  • 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?
  • We need another measure called stress which reflect these effects
traction
Traction
  • 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-2pascal(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
types of stress
Types of Stress
  • Tension: Stress acts _|_ to and away from a plane
    • pulls the rock apart
    • forms special fractures called joint
    • may lead to increase in volume
  • Compression: stress acts _|_ to and toward a plane
    • squeezes rocks
    • may decrease volume
  • Shear: acts parallel to a surface
    • leads to change in shape