Course Overview

Introduction to Physics 2207

Physics 2207 at Cornell University is designed to introduce students to fundamental principles of physics with an emphasis on calculus-based modeling. The course is structured to support students from diverse academic backgrounds, including pre-health, chemistry, and architecture, and aims to build both content knowledge and problem-solving skills.

Course Objectives

Learning Goals

• Content Knowledge: Define fundamental physics principles, quantities, and relationships using words, diagrams, and mathematical symbols.

• Quantitative Reasoning: Generate, evaluate, and apply mathematical models to describe physical phenomena in both familiar and novel contexts.

• Drawing Connections: Describe the interdisciplinary nature of science and connect physics to biology, chemistry, and everyday life.

• Flexible Problem Solving: Use a small set of tools to solve a wide variety of problems, including those with no single correct procedure.

Mathematics in Physics

Role of Mathematics

Mathematics in physics is used not just for calculation, but as a language to model the world. Physical quantities are represented by symbols, which include units and often a sign. Equations in physics describe relationships between quantities and model physical situations.

• Physical Quantities: Variables such as m (mass), v (velocity), and T (temperature) are always accompanied by units.

• Equations as Models: For example, describes the relationship between acceleration, force, and mass.

• Subscripts and Formatting: Subscripts carry important information, e.g., .

Representing Motion

Position and Motion Maps

To model motion, we first define position as the location of an object relative to a reference point. Motion maps record the position of an object at regular intervals, such as each second, to visualize its movement over time.

• Position: Measured relative to a reference point (e.g., "1 mile from home").

• Motion Map: A diagram showing the position of an object at each time interval.

Physical Quantities and Indexes

Defining Physical Quantities

Physical quantities characterize features of a system that remain constant during specific changes. An example is density, which is defined as the ratio of mass to volume and can be thought of as a "compactness index."

• Density:

• Index: A single value that characterizes a system, determined by a consistent procedure.

Fastness Index Activity

Students are asked to develop an index representing each car's "fastness," using information such as oil drips per second. The activity encourages defining a quantitative measure for speed and comparing different cases.

• Fastness Index: Quantifies the speed of each car based on consistent criteria.

• Comparison: Identifying which car is fastest or slowest based on the index.

Modeling Motion in Real-World Contexts

Predator-Prey Models

Physics principles are applied to biological systems, such as predator-prey interactions. For example, the strategies and tactics of prey capture by lions can be analyzed using models of motion and velocity.

• Application: Modeling the motion of predators and prey to understand behavior and escape mechanisms.

Active Learning and Collaboration

Learning Philosophy

Active learning is emphasized, with students encouraged to practice applying concepts, reflect on connections, and work collaboratively. Collective intelligence is highlighted as a means for groups to solve problems that individuals cannot solve alone.

• Practice: Repetition helps build proficiency.

• Reflection: Applying ideas to new situations enhances understanding.

• Collaboration: Working with peers and instructors supports learning.

Course Components and Grading

Assessment Structure

The course includes a variety of assessment components, such as lectures, co-op sessions, quizzes, labs, exam practice, and exams. Participation is valued, and drops are allowed to accommodate student needs.

Summary and Next Steps

Upcoming Topics

Future lectures will focus on defining quantitative indexes for motion, analyzing position and velocity over time, and applying these concepts to real-world biological systems such as predator-prey behavior.

Additional info:

• Some content was inferred to provide academic context and completeness, especially regarding the mathematical modeling and physical quantities.

• Images were included only when directly relevant to the explanation of motion maps, predator-prey modeling, and collective intelligence.