C. Material behaviors under applied force

(Ohio competencies 6 and 7, 9 and 11)

1. Material behavior depends upon conditions of both the material and the environment. For example, gravity is an important force in Geology, and is responsible for environmental problems of various sorts. Consider the effect of gravity on unconsolidated material:

• Slide: describe/interpret/share exercise:
• slide or photo of rockslide, for example, Turtle Mtn, Alberta
• Have students write a description of the scene and then write an interpretation. Then have them discuss in pairs or as a class. This type of exercise is very effective with all sorts of photos of geological results. Gets the students thinking about processes.
• Demo: sand pile on plate or desk and toy bulldozer:
• Oversteepen the slope of the sand pile and then shake slightly to cause a landslide.
• The angle of repose/slope stability is compromised during construction of, for example, a road.
• Slide or photo of the Gros Ventre, WY, landslide (river undercut)

2. Forces in geology: gravity is also important when we look at Earth materials. It is responsible for the force of the overburden (weight of overlying rocks) within the crust of the Earth, and students can calculate the force due to gravity at different depths in the crust via F = mg, where mass is calculated using average rock density and the volume of rock above a designated depth (height x area); g, the acceleration due to gravity = 980 cm/sec2 at Earth’s surface.

Example problem: What is the force on the base of a continent 30 km thick, with an area of 3 x 107 km2, and an average density of 2.85 gm/cm3? (This is also good for making students consider the importance of compatible units.)

• F = p g H A, where p = density, H = thickness of continent, and A = area
• F = (2.85 gm/cm3)(980 cm/sec2)(3 x 106 cm)(3 x 1017 cm2)
• F = 2.51 x 1027 dynes = 2.51 x 1022 Newtons

3. However, in Geology, we are interested in the response of materials to an imposed force, and so a more interesting quantity is that of stress which is the force acting on an area.

1. Stress is that which tends to deform a body. Permanent deformation occurs if the material strength is exceeded.
2. Stress on a plane = force/area, or s = F/A
3. Stress units: psi; kg/cm2; Pascal

Pascal: a stress of one Pa is created by the force of 1 Newton acting on an area of one square meter.

• 1 Pa = 1 N/m2 = 10 dyne/cm2
• KPa = 1000 Pa (or, 103 Pa); MPa = 106 Pa; GPa = 109 Pa

Example problem: What is the stress on the base of the continent above?

• s = F/A
• s = 2.51 x 1027 dynes / 3 x 1017 cm2 = 8.37 x 109 dynes/cm2
• s = 2.51 x 1022 N / 3 x 1013 m2 = 8.4 x 108 N/m2

Shoe problem: In this problem, students measure the area of their shoe (they can get creative: use a string to measure perimeter then make equivalent square; or divide into basic geometric shapes); then consider same force (weight) acting on the area of a high heeled dancing shoe; ice skate or roller blade; or compare golf shoe or track/soccer cleats on concrete versus on the ground.

The Difference between force and stress, or don’t step on my foot when you are dancing with me!
K.Fryer, June 2001

Calculate the stress exerted by your foot onto the ground when you are standing still:

1. When wearing sneakers, and
2. When wearing (high-heeled) dancing shoes or, ice skates, or roller-blades, or compare golf shoes (or track cleats) standing on concrete versus standing on the golf course.

Data:

• area of bottom of sneaker
• area of high heels, skate blade or roller blade, or cleat contact area

This problem is also good practice in converting units!

Please show all work done in making calculations.

4. Deformation of Earth materials arises from the imposition of force to create stress, acting on the material; forces which deform the crust arise from tectonic movements, particularly acting at the boundaries of tectonic plates. But how the material responds to the stress is more than a function of the amount of stress; rather, we must again consider the environmental conditions of the material.

Demo: pull on silly putty slowly (ductile behavior), and then quickly (brittle behavior)

Activity: give students chilled tootsie rolls (they can feel the candy becoming more ductile as warms up in mouth)

1. Ductile versus brittle behavior
(See Project Primary, 1997, for more background.)
• Demo: silly putty vs. pencil to demonstrate ductile versus brittle behavior.
• Demo: store energy in rubber band, then exceed strength; will break and return to original size.
2. Brittle behavior of crust => earthquakes: It is the ability of rocks to store energy and then suddenly break that leads to earthquakes.

5. energy and earthquakes (Ohio competencies 8 and 9)

Demo: tell students to shut eyes. Break a pencil. Ask them what happened, and then how they know => sound waves

1. Earthquake energy is also transmitted by waves: compressional and shear, through Earth’s interior: our window into Earth’s interior
2. Studying earthquake waves is another example that can be used in the study of waves in Physics classes. There are good exercises on how waves are transmitted (slinky model for compressional waves, and “whip-like” motion for shear waves). Dominoes can be used to model the density/velocity relationship for waves traveling through Earth, as in Leong, The Domino Effect, 1994.