FrictionNow add friction…

Why does friction occur?What are the properties of friction?• Draw a graph of friction vs.

applied force

At what angle does an object begin to slide down a ramp?

Directions and extreme values

Ch5

DragDragTerminal VelocityCalculusGraphs

Ch5

Ch5Uniform Circular MotionProportional Reasoning from PicturesRotational Dynamics• Ferris wheel FBDs• Apparent forces• 3rd Law

The Banked CurveConsider a car going around a curve…• Flat, without friction• Flat, with friction• Banked, without friction• Banked, with friction• Max and Min speeds

Ch5

Ch13Newtonian GravityOrbits as free fallWeightlessness • Apparent• Fictitious force• Non-inertial framesNewton’s Universal Law of Gravity• Drawing• Equation• WordsCalculate g – the Gravitational Field!Geostationary satellites

QUALITATIVE

QUAN

TITATIVE

Physical Situation

Mathematical (Formal) Solution

Representation Interpretation

• Visual Representaton

• Symbolic Notation

• Select Physical Principles/Approach

• Build Relationships• Solve

• Check Limiting Cases

• Check Reasonableness

• Insert Numbers

(Experience)

(Ideas) • Check Dimensions

• Conceptual and Narrative Representation

• Solution Statement

Problem Solving Model: RevisitedCO

NCR

ETE

CONCR

ETE

ABSTRA

CT

QUALITATIVE

QUAN

TITATIVE

Physical Situation

Mathematical (Formal) Solution

Representation Interpretation

• Motion Graphs: origin, signs, units

• Symbolic Notation

• General Equations: Kinematics Toolbox

• Apply Specifics to Build Relationships • Solve

• Check Limiting Cases

• Check Reasonableness

• Insert Numbers

(Experience)

(Ideas) • Check Dimensions

• Assumptions and Approximations: frictionless, constant a, etc.

• Solution Statement

Problem Solving Model: KinematicsCO

NCR

ETE

CONCR

ETE

ABSTRA

CT

QUALITATIVE

QUAN

TITATIVE

Physical Situation

Mathematical (Formal) Solution

Representation Interpretation

• Simply Free Body Diagrams, Vector Drawings, Coordinate Systems, Signs, Axes

• Symbolic Notation

• Newton’s Laws for each direction, for each Object

• Build Relationships• Solve

• Check Limiting Cases

• Check Reasonableness

• Insert Numbers

(Experience)

(Ideas) • Check Dimensions

• Friction, Constant Forces, What to Ignore

• Solution Statement

Problem Solving Model: Newtonian ForcesCO

NCR

ETE

CONCR

ETE

ABSTRA

CT