2021 Live Review 8 | AP Physics C: Mechanics | Understanding Resistive Forces

The script opens with a discussion on the importance of considering air resistance in physics problems, using the example of terminal velocity when skydiving. It introduces the session as part of the AP Daily Live Review for AP Physics C Mechanics, highlighting that it's the last session. The logistics are reviewed, mentioning that the session is recorded and will be available on the AP Classroom and College Board's AP YouTube channel. The presenter encourages subscribing for review materials and provides a URL for additional resources and feedback. The main focus of the session is to explore resistive forces, learn to express and solve differential equations based on free body diagrams, and understand the functional and graphical representations of speed, acceleration, and position under resistive forces.

This paragraph delves into the specifics of solving physics problems involving resistive forces by starting with free body diagrams. It uses an example of an object falling under gravity and air resistance, illustrating how to draw the forces acting on the object. The paragraph explains how to translate Newton's second law into a differential equation, emphasizing the importance of correctly identifying forces and their directions. It also discusses the process of finding terminal velocity by setting acceleration to zero in the differential equation and solving for velocity. The presenter encourages practicing with old exam questions and using scoring rubrics to understand how to earn points.

The focus shifts to integrating the previously derived differential equation to find the relationship between velocity and time. The paragraph explains the process of separating variables and integrating with respect to time, highlighting the importance of setting up the integral correctly to earn points. It provides a general form of the integrated equation and discusses the significance of the integration constant. The presenter then solves the differential equation, deriving an expression for velocity as a function of time, and emphasizes the importance of understanding the functional form of the solution, even if the actual integration is time-consuming.

This section discusses the importance of graphing the functions derived from the differential equations to visualize the behavior of the system over time. It provides a detailed explanation of how to graph velocity as a function of time, starting from rest and approaching terminal velocity. The paragraph also touches on the concept of acceleration as a function of time, showing how it starts at a maximum and asymptotically approaches zero as terminal velocity is reached. The presenter uses multiple-choice questions to illustrate common mistakes and emphasizes the importance of understanding the underlying physics to solve problems correctly.

The script moves on to apply the concepts of resistive forces to scenarios such as skiing down a hill. It starts by drawing a free body diagram for a skier and writing the differential equation for motion under the influence of gravity, friction, and air resistance. The paragraph explains how to find terminal velocity in such scenarios and how to solve the differential equation to find the velocity function. It also discusses the process of graphing acceleration and the importance of understanding the initial conditions and the behavior of the system as it approaches terminal velocity.

This paragraph explores the effects of resistive forces on horizontal motion, such as a car moving on a flat surface. It discusses the initial conditions, the differential equation for motion, and the process of finding the initial acceleration. The paragraph explains how to derive an equation for velocity as a function of time and how to integrate this equation to find the displacement. It also touches on the concept of maximum displacement and how the object will eventually come to rest due to the resistive force.

The focus is on solving for displacement when an object is subjected to a resistive force that is proportional to its velocity. The paragraph explains how to find the maximum displacement an object can travel before coming to rest. It provides a detailed explanation of the process of integration to solve for displacement and discusses the functional form of the displacement function. The presenter also compares different scenarios, such as an object initially at rest with an applied force, and outlines the steps to solve for velocity, displacement, and terminal velocity.

In the final paragraph, the presenter wraps up the AP Physics review session by summarizing the key lessons learned. They emphasize the importance of drawing free body diagrams, using them to express Newton's law as a differential equation, and understanding terminal velocity. The paragraph also discusses the significance of the graphical forms of the solutions and encourages students to practice with free response questions and their scoring rubrics. The presenter thanks the students for joining the session and invites them to provide feedback for future improvements.