Force and Stress I

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Force and Stress I
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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 MLT-2
• units newton N kg m s-2

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Newtons 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.

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Newtons 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.
  aDv/Dt)

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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

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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

• 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

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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

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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

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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

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Stress

• Stress 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 / L2ML -1T-2
• In the mks system of the SI system
• s kg m-1 s-2 pascal (Pa) newton/m2
• 1 bar (non-SI) 105 Pa 1 atmosphere
• 1 kb 1000 bar 108 Pa 100 Mpa
• 1Gpa 109 Pa 1000 Mpa 10 kb
• P at core-mantle boundary is 136 Gpa (at 2900
  km)
• P at the center of Earth (6371 km) is 364 Gpa

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Ten common units geologists use to describe
stress equivalent to 1 megapascal (MPa)
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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