Derivation of velocity equation with Air Resistance

The derivation of the equation for the velocity of an object experiencing air resistance was long and tricky.  I've prepared a PDF of it with notes about the steps.  You can find it here.

https://drive.google.com/file/d/0B54jRZBDezIHSnB6UHFaWkRXMlE/view?usp=sharing

There is a minor mistake in the middle of the second page.  Twice I write dt instead of u, in the denominator of the right hand side of the equation.  This is in the section that I've labeled "now collect terms and integrate."

Flying Pigs

Take measurements of the pig's mass, and of the radius, period and the angle of the string's deflection from vertical as it flies in circles.  Calculate the tension in the string in two different ways.  (1.  based on the weight, 2. based on the net force.)
Do the 2 methods come within 5% of each other?  If not, what went wrong?

Answer the 3 minilab questions in your google doc lab file.
https://docs.google.com/document/d/1yVSiC_mXguFtIBFf3f9qZG8buX92i011d1_tuNPzDiw/edit?usp=sharing

Unit 3 - Forces

Major Topics

• Newton's Laws
• Weight vs. Mass vs. Inertia
• N3L forces vs. Balanced Forces
• Solving problems in 1 and 2 dimensions (inclined planes...)
• Tension and Atwood Machines
• Friction
• Circular Motion and Centripetal Force
• Springs in series and parallel (Hook's Law)
• Velocity dependent forces (air resistance...)

Homework:  Three Large Assignments  11/3, 11/16, 11/25
Labs:  No major labs.  2 mini labs (Flying Pigs, Springs)
Test:  Probably 12/2

Please read about Newton's Third Law at the following link http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law

Lab 2 - Projectile Motion

AP Lab 2 – Projectile Motion.

Your Task:

First derive an equation for the range of a projectile based on the launch angle and the initial velocity.

Then determine the initial velocity produced by a projectile launcher by gathering data about the launch angle and range, graphing them, transforming the graph to make it linear and then interpreting the slope of the graph.  While not easy, this is your task.  A final part of the task is to qualitatively describe how air resistance affected your results and based on that how do you get the greatest range when there is air resistance.  

1. Derive an equation for  R(θ, v)
2. Find  a way to manipulate your axes so that a graph with axes based on θ and R should produce a linear graph, the slope of which will allow you to determine v0.
3. Collect enough good data, that you can determine v0 within a tolerable range.
4. Graph and analyze your data, looking for v0 and a description of the effects of air resistance.

As before copy the questions from the link below to your lab document and answer the questions.

https://docs.google.com/document/d/1JzXZZQAA-xAqU-zDM0WbjdqM6kjIlm_hUAkllqm9K-A/edit?usp=sharing

Kinematics in 2D

Motion in 2D - Chapters 3 and 4

Topics

• Adding Vectors
• Breaking Vectors in Components
• Solving Kinematics Problems in 2D
• Special emphasis on 
• Projectiles
• Circles and 
• Describing motion from a moving frame of Reference

Homework due10/4, 10/6 and 10/13

Unit Test 10/16

Lab due date TBD

Rheostat Lab

Introduction to vectors in 2D.

Purpose:  Practice two methods for adding vectors and demonstrate their equivalence.

After you have completed your data collection and calculations, follow this link to the questions for minilabs.

https://docs.google.com/document/d/1yVSiC_mXguFtIBFf3f9qZG8buX92i011d1_tuNPzDiw/edit?usp=sharing

Paste the questions and answers into your lab document.  Be sure to name this lab in your lab document.

Non Uniform Acceleration and Integration MiniLab

Follow this link to the questions for minilabs.

https://docs.google.com/document/d/1yVSiC_mXguFtIBFf3f9qZG8buX92i011d1_tuNPzDiw/edit?usp=sharing

Paste the questions and answers into your lab document.