Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Francesca Wise, Gauge Mccain, Sophomore Jacob Bealefeld
Lead Presenter's Name
Gauge Mccain
Lead Presenter's College
DB College of Arts and Sciences
Faculty Mentor Name
Dr. Jorge Gonzalez
Abstract
The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known as terminal velocity. By analyzing the mathematical model and its solution, the project illustrates how ordinary differential equations can accurately represent real physical systems. The results provide insight into how factors such as mass and drag coefficient influence the motion of objects in air, with applications to real-world situations such as skydiving, falling objects, and vehicle dynamics.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Aerodynamics and Fluid Mechanics Commons, Fluid Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons
Motion With Air Resistance
The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known as terminal velocity. By analyzing the mathematical model and its solution, the project illustrates how ordinary differential equations can accurately represent real physical systems. The results provide insight into how factors such as mass and drag coefficient influence the motion of objects in air, with applications to real-world situations such as skydiving, falling objects, and vehicle dynamics.