# Vectors and slope stability

**This activity was selected for the On the Cutting Edge Exemplary Teaching Collection**

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This page first made public: Jul 26, 2006

#### Summary

This homework or in-class activity is designed to teach students with little or no experience with vectors, free-body diagrams, or the like to apply vectors to slope stability problems.

Students first learn the basic properties of vectors, vector addition, resolving forces, etc. They then apply these techniques to establish in a simplified way how geologists can determine if a slope is stable, how much loading a slope can withstand to become unstable, and other principles of slope stability determination.

This activity is used in an introductory geohazards course with no pre-requisites. It can be completed in one to two hours.

## Learning Goals

- graphically add vectors
- resolve vectors into perpendicular components
- represent forces as vectors
- determine if a slope is stable or unstable based on the forces acting on it
- articulate why a steeper slope is less stable than a shallow slope
- determine, from the mass on a slope and the angle of the slope, how large the downslope force is
- determine how much weight can be added to a slope before it becomes unstable.

## Context for Use

It can be done in an evening but often students require some additional assistance from a tutor or someone who has seen vectors before.

## Teaching Notes and Tips

Note that pounds are used as the force units so that students do not need to convert between units of weight and force, as would have to be done if the metric system was used. I found this reduced student errors.

## Teaching Materials

This assignment has two parts. The first is a general introduction to vectors, graphical manipulation of vectors and vector addition. The second part of the homework asks students to look at vector diagrams to see if a house is stable on slopes of differing angles. A final question asks students to find the maximum weight for a house on a given slope with known friction.

## Assessment

## Contact the Author

## Controlled Vocabulary Terms

**Subject**: Geoscience:Geology, Environmental Science:Natural Hazards:Mass Wasting

**Resource Type**: Activities:Problem Set, Classroom Activity, Lab Activity

**Inquiry Level**: Step-By-Step Instruction

**Special Interest**: 2YC:Geo2YC, Quantitative, Geo2YC- OLD DO NOT USE, Hazards

**Grade Level**: College Lower (13-14)

**Quantitative Skills**: Vectors and Matrices, Problem Solving

**Ready for Use**: Ready to Use:Tested, Ready to Use

**Theme**: Teach the Earth:Incorporating Societal Issues:Hazards, Teach the Earth:Course Topics:Environmental Science, Teach the Earth:Teaching Environments:Two-Year Colleges

**Quantitative Skills Activity Type**: Classroom Activity, Lab Activity, Problem Set

**Science Background Required**: Broadly accessible

**Topics**: Human Dimensions/Resources, Earth surface

**Solid Earth Processes**: Weathering/Erosion