Mr. Rogers' AP Physics C: Mechanics (With IB Physics Topics) Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Gravity   Circular Motion Statics Rotation  

Chapter 13: Universal Gravitation

AP Physics C Newtonian Mechanics:

F. Oscillations and gravitation 9%, cumulative 82%
    4. Newton's law of gravity 
    5.Orbits of planets and satellites
        a. Circular 
        b. General 

Practice Test Study Guide

Objectives
Essential Question: Do force fields really exist and are they similar to the force fields on Star Trek or Star Wars?
  1. The Flat Earth Model of Gravity
  2. Mathematically define gravity field.
  3. Draw a ray diagram of a constant gravity field.
  4. State the meaning of the space between rays in a force field diagram.
  5. State the two assumptions implicit in modeling the Earth's gravity field as constant.
  • The Earth is flat
  • The Earth's surface is infinitely large
  1. Calculate terminal velocity for a falling object with air resistance and compare it to a falling object without air resistance. (see page 162)
  2. Explain where air resistance comes from and why it should not be called air friction.

 

Activities

Lesson 1

Key Concept: Falling in Uniform Gravity Fields

Purpose: Introduce the concept of force fields using the most common force field gravity. Show how a velocity dependent force like air resistance interacts with a constant gravity field.

Interactive Discussion: Star Wars vs. real life

In Class Problem Solving:  

  1. Derive an expression for calculating terminal velocity.

 
Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Analysis of Low velocity Air Resistance for a streamlined and non-streamlined object
Purpose Determine if air resistance is directly proportional to velocity for a streamlined and non streamlined object/
Overview Air resistance is often modeled as being directly proportional to velocity when included in mathematical models using Newton's second Law. 
Data, Calculations Perform regression analysis on the the data for each object using Minitab and plot the residuals.
Questions, Conclusions Was a linear relationship between air resistance and velocity appropriate?

How did the streamlined object differ from the non streamlined one.
Resources/Materials: Wind Tunnel and associated equipment.

 

Essential Question: What causes non uniform force fields?

Gravity Fields Around Planets

Section 13.1, 14.2

  1. Correctly use the universal gravitational force equation.

  • yields an action reaction pair

  • r = distance between centers of mass

  • G = universal gravitational constant

  • the equation does not work inside a planet

  • force is directly proportional to mass

  • force is inversely proportional to r squared

  1. Draw a ray diagram of the gravity field around a planet (see red lines in figure at right). Note tat the spacing of the lines is directly proportional to the g-field strength, if the drawing id made to scale.

  2. Calculate the gravity field strength (acceleration due to gravity) using the universal gravitational force equation.

  3. Note that the gravity field above a planet's surface acts as though it came from a point source located at the planet's center of mass.

  4. Explain why the equation for gravity force vs. distance from a planet (a point source of gravity) is only valid above the planet's surface.

Homefun: Read 13.1 to 13.3; Problems 1, 3, 11, 23 p. 412 - 413  Serway

 

Lesson 2

Key Concept: Non-Uniform Gravity Fields

Purpose: Introduce the concept of force fields and show how it can be used in problem solving.

Interactive Discussion: Objectives

Demo 1: Demonstrate the inverse square law with a flashlight.

Video Clip: Show a video clip of Armageddon when the asteroid is split in half and travels around the Earth. Estimate the tidal forces casued by the asteroid as it travels within 300 miles of Earth's surface. (teams of 2)

In Class Problem Solving:

  1. Calculate g for planet Earth.
  2. Calculate g for Zorg.

Resources/Materials: Flashlight

 

 
Essential Question: How can the force of gravity be calculated inside a planet?

The Ultimate Transportation System -- a Tunnel Through the Center of a Planet.

  1. Define scaling factor.
  2. Derive an expression for the gravity field vs. radius inside a planet, using the following:
  • the gravity field inside a hollow planet is zero
  • if  an object's center of mass (CM) is at a distance r from the planet's CM, only mass in the sphere of radius r will create a net gravitational force.
  • the gravitational force is calculated using the universal gravity equation using the above sphere
  • mass scales with the cube of the scaling factor.
  1. Using the displacement equation for simple harmonic motion as show below, derive the velocity and acceleration equations for simple harmonic motion.

x = (xmax)cos (wt)

  1. Derive the time it would take to fall through a tunnel bored through the center of the Earth.
  2. Plot a graph of g-field vs, distance from the center of a planet.

Homefun:  Serway

Lesson 3

Key Concept: Gravity Field Inside a Planet

Purpose: Introduce scaling factors and show how scaling factors in combination with simple harmonic motion and the universal gravitational equation can be used to analyze the g-field inside a planet.

Interactive Discussion:
  1. Describe the gravity field inside a hollow planet.
  2. Describe the ultimate transportation system.

In Class Problem Solving:

  1. Derive an equation for the gravity field inside a planet.
  2. Give the displacement vs. time equation for simple harmonic motion, derive the velocity and acceleration vs. time equations.
  3. Calculate the time required to fall completely through a tunnel from one side of Earth to the other.
 
Essential Question: How is gravitational Potential energy calculated when the g-field is not constant?
 

Gravitational Potential Energy From a Planet

  1. Note that that by convention the gravitational potential energy is considered to be zero at a distance of infinity from a planet.
  2. Using the definition of gravitational potential energy, derive an expression for gravitational potential energy vs. distance from the center of a planet, above the planet's surface. (Note blue dashed lines at right are constant potential energy lines.)
  3. Explain why the equation for potential energy vs. distance from a planet (a point source of gravity) is only valid above the planet's surface.
 

Homefun: Read 13.4 to 13.6,  Problems 27 p. 415 Serway

Metacognition Problem Solving Principle 13.1: When deriving a gravitational potential energy equation, remember it will come from an analysis of the work done to move an object, in other words, a gravity force expression times a displacement.

For example:

U =  - (force expression) (displacement)

    = - ([G(m2m1)] / r2) (r)

    = - m1[G(m2) /r]

 

Lesson 4

Key Concept: Potential Energy Around a Planet

Purpose: Relate gravitational potential energy to gravity force.

Interactive Discussion: How are gravity field lines related to constant potential energy lines?

In Class Problem Solving:

  1. Derive an expression for potential energy vs distance from the center of a planet.
Essential Question: How can a spacecraft escape from a planet's gravity?

Gravity and Orbits

  1. Circular Orbit: Calculate the velocity or radius (depending on what is given) for circular orbits by combining circular motion equations with the universal gravity equation.

v = [(GMe) / re]^0.5

  1. Elliptical Orbit (speed lowered at P): Describe what happens to a satellite in circular orbit if it's tangential velocity is decreased.
  2. Eliptical Orbit (speed increased at P): Describe what happens to a satellite in circular orbit if it's tangential velocity is increased.
  3. Escape from Orbit: Calculate escape speed from the surface of a planet. (p. 407)

v = [(2GMe) / re]^0.5

  1. State the two critical speeds for orbits.
  2. Calculate the height of a geosynchronous orbit.

 

Homefun: Read 13.4 to 13.7,  Questions 1-10 p. 411 - 412; Problems 41 Serway

 

Lesson 3

Key Concept: Orbiting and Escaping from a Planet

Purpose: Derive the key equations associated with orbits.

Interactive Discussion: Objective s

Video Clip: Show a video clip of the Space Shuttle taking off from the surface of the asteroid in Armageddon. Calculate the escape velocity needed. How fast would the ship have to be moving to take off? Work in groups of two
 
Mr
 

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