Runaway Runway Surveyors

By Bartley Richardson •

Grade Level	11th and 12th
Subject Area	Physics (Mechanical Physics)
Duration	70 minutes (one class period)
Setting	Classroom
Background Knowledge	It is recommended that studnets have some experience with vector addition (even if it is only a few simple homework problems), significant digits, right-triangle trigonometric rules (Pythagorean Theorem and SOH-CAH-TOA), and rearranging algebraic equations to solve for a desired variable.
Author	Bartley Richardson

Summary
This lab experiment utilizes two methods to reinforce the concept of vector addition. In the first activity, students use surveying equipment to find the straight-line distance between two points where a direct line-of-sight between the points does not exist. They also use the equipment to find the angle between the distance vector and the horizontal. In the second activity, students apply vector addition to forces acting on a bolt. The objective is to find the total force acting on the bolt and the angle at which this force acts.

Objectives
Students will be able to 1. Accurately measure distances and angles (to proper significant digits). 2. Maintain proper significant digits throughout the calculations. 3. Create an accurate diagram of their measurements. 4. Apply right triangle trigonometric rules to calculate the hypotenuse of the triangle and a given interior angle. 5. Use the Law of Sines and Law of Cosines to calculate the hypotenuse of a triangle and a given interior angle. 6. Identify sources of error in the lab and explain their significance. 7. Use a total station or theodolite to measure distances and angles. 8. Calculate the percent error of a given calculation. 9. Apply the principle of vector addition to a real-world engineering problem involving forces. 10. Accurately and effectively report their results in scientific language. 11. Identify when vector addition is necessary and what steps need to be taken before the vectors can be added.

Mateirals Required
•Vectors for Everyday Life Packet (1 per student) o Step-by-step instructions o Worksheets / data tables • Total station or theodolite (1 total) • 100 ft. tape measure (4 total) • Ruler or other straight-edge (1 per student) • Data sheet (if real data cannot be measured or otherwise obtained) • Grading rubric

Ohio Standards

Science

* Science and Technology

o Benchmark A - Predict how human choices today will determine the quality and quantity of life on Earth.

Mathematics

* Number, Number Sense and Operations

o Benchmark B - Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices.

* Measurement

o Benchmark A - Explain differences among accuracy, precision and error, and describe how each of those can affect solutions in measurement situations.

* Geometry and Spatial Sense

o Benchmark A - Use trigonometric relationships to verify and determine solutions in problem situations.

* Patterns, Functions and Algebra

o Benchmark D - Apply algebraic methods to represent and generalize problem situations involving vectors and matrices.

Technology

* Technology and Society Interaction

o Benchmark A - Interpret and practice responsible citizenship relative to technology.
o Benchmark C - Interpret and evaluate the influence of technology throughout history, and predict its impact on the future.

Documents

Lesson Plan