ForceForce• An example of Force is weight

• Force = mass x acceleration• Force of gravity F = mg• In SI units, mass m is kilograms• An example of acceleration is g, the

gravitational acceleration.• IN SI units g = 9.81 meters/second2

• 1 kilogram meters/sec2 is one Newton

Mass Wasting and HillslopesMass Wasting and Hillslopes

Steep slopeGd > F

Gentle slopeGd< F

Gp

Gp

Gp

ModerateslopeGd=F

2. Gd = FBoulder on vergeof moving

1. Friction force uphill F is greater than downhill component of gravity.

Gd. Boulder isstable

3. Gd > F . Bouldermoves downslope

F

F

F

Gd

Gd

Gd

WW

W

• Gravity overcomes Friction

START HERE

Mass x gravity = mg = weight “w” Mass x gravity = mg = weight “w”

Downhill force (white) = mass x gravity x sine of angle

Component of weight along slope (red) Component of weight along slope (red) FFdd = mg sine (= mg sine ())

Shear ForceShear Force = FFdd = = w sine (w sine (αα))

wh

dip

shear force not shear stress

The downhill force, parallel to the incline,Is called the shear force. It is the force that tries to slide the rock down the slope.

FrictionFriction and and Normal ForceNormal Force• Friction Force uphill (yellow)Friction Force uphill (yellow) is proportional to

Normal Force (green)Normal Force (green)• Normal ForceNormal Force is perpendicular to the slope. It is

the component of weight pressing the rock into the slope.

• Increased water pressure Increased water pressure between the surfaces lifts the rock, and it will slip at a lower dip angle.

wh

dip

StressStress

• The Force per unit area is called stress

• Stress has the same units as Pressure

• The term stress is used for solids e.g. rock, pressure for fluids (liquid e.g. water, gas e.g. air)

• SI units are Pascals = Newtons/meters2

Stress Sign Conventions• The “standards”• The original sign convention is from Physics and Engineering

– For Normal Stress: Divergence lengthens a solid in that direction and is

therefore positive

– For Shear: Follow the right–hand-rule

Look at the x-face, up is positive shear, positive shearturns the elementCounter-clockwiseAll of these conventions vary All positive stresses, both normal and shear

Stress Sign Conventions• From your text p47 bottom left”

– “The only ingredient left in our description is a sign convention. In physics and engineering, tensile stress is considered positive, and compressive stress negative. In geology, however, it is customary to make compression positive and tension negative, ….”

• Even shear has variable sign conventions• You must be fluent in both conventions, just as you

must be fluent in both English and SI units. We will start with the engineering convention.

Problem 1 (worked example)

Engineering Convention, tension stress is positive, here positive x-shear is UP

The angle is measured from the x-axis x to the normal axis n. If this direction is clockwise, the angle is negative, as shown.

The angle is identical to the angle between the vertical axis and the fracture.

Problem 2

Engineering Convention, tension stress is positive

Problem 3

Engineering Convention, tension stress is positive

Problem 4

Engineering Convention, tension stress is positive

Problem 5 for LAB/HOMEWORK

Engineering Convention, tension stress is positive

Problem 6 for LAB/HOMEWORK

Engineering Convention, tension stress is positive

Problem 7 for LAB/HOMEWORK

Engineering Convention, tension stress is positive

Problem 8 for LAB/HOMEWORK

Engineering Convention, tension stress is positive

End of part 1Stress Elements

Part 2Correctly determining the angle

Homework question 1

Homework question 2

Next TimeStress Transformation Equations

• Next time I will show you the derivation of the Stress Transformation Equations.

• These will lead us to a graphical method, the Mohr’s Circle