Crevasse Rescue and Trigonometry

Grade Level: 9-12

Summary

This resource will provide background information on ice in polar regions and researcher safety, and introduce physics and mathematical concepts of forces and trigonometry by relating them to the real-world crevasse rescue component of anchor-building. Hands-on components include building a snow anchor (if possible) and a physical exercise to support understanding of the relationship between angles and force decomposition.

Materials and Preparation

  • Weights that can be tied to a rope (between 10-20 lbs is best)
  • Ropes
  • Pencil
  • Paper

Learning Objectives

Objective #1
Develop/strengthen an introductory understanding of decomposing forces into vertical and horizontal components
Objective #2
Use trigonometry to determine forces in a cartesian plane
Objective #3
Design an effective anchor system for a crevasse rescue scenario

Opening Activity

Start with a physical example of how weight and angles interact by having students lift weights with ropes and change the rope direction from vertical to nearly horizontal. Prompt students to think about all of the pieces of this puzzle including weight, gravity, pulling force, and angle.

You can also use a video to introduce your students to crevasse rescue and travel (some suggestions are linked in the resources).


Activity Overview

Introduce students to concept of crevasse rescue

A crevasse is a crack that forms in a glacier. These pose a significant safety risk for polar researchers. Rescuing a victim of a crevasse fall is challenging as it requires going against gravity to get a person up and out of the crevasse. This work also needs to be done quickly due to the threat of hypothermia.

Through the use of PreCalculus and physics, we can learn about how to set up a rope system that is more effective for crevasse rescue! NOTE: we are going to simplify this system for the moment by disregarding friction.

An important early step in building the rope system is to create an anchor and a backup anchor. We need to figure out how to orient these in respect to each other.


Reflection

Students refer back to their original prediction for the safest anchor configuration and see if it is supported by their calculations. If not, they reflect on what they should have thought about (relating to the demo) if they were to make their predictions over again.


Supporting Documents

Using Mathematics and Computational Thinking

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions.

Additional video ideas:

How to travel safely on a glacier (6 min):
https://www.youtube.com/watch?v=sS9Rg_3EItc

Glacier movement, crevasse formation and how to avoid a crevasse fall (5 min):
https://www.youtube.com/watch?v=sS9Rg_3EItc

If students are interested in exploring more about crevasse rescue on their own, they might look at this video series:
https://youtube.com/playlist?list=PL4iId69UI0BLmgZfv2h3TY2BWlwEmQZwG&feature=shared

Standards:

Science Practice 2
Developing and using models
Science Practice 3
Planning and carrying out investigations
Science Practice 5
Using mathematics and computational thinking
Crosscutting Concept 2
Cause and effect: mechanism and explanation
Crosscutting Concept 3
Scale, proportion, and quantity
PS 2
Motion and stability: forces and integrations

Polar Literacy Principles:

2A
Ice is dynamic and comes in many shapes and sizes—big, small, floating in water or layered on land, thin or thick, solid or porous soft.

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