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Force and Stress I

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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Force and Stress I

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  1. Force and Stress I

  2. 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

  3. 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.

  4. 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)

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Ten common units geologists use to describe stressequivalent to 1 megapascal (MPa)

  13. 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

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