Transcript Chapter 5 - galileo.harvard.edu

Chapter 5
Using Newton’s Laws with Friction,
Circular Motion and Drag Forces
Introduction: Our approach
• Additions to our understanding on each side
of ∑F = ma
• On the ∑F side:Friction
– static and kinetic
• On the ma side: Circular motion
– uniform motion
– highway curves, banked and not
– non-uniform motion
• More on the ∑F side: Drag force
– terminal velocity
Friction
• Kinds (“rolling” later)
– kinetic (sliding)
– static
• Complex phenomena
• Example EXERCISE
• Problem solving using Newton’s Laws
– location of additions to problem solving (see)
– framing the problem (esp. with static friction)
Uniform Circular Motion
• Acceleration
– direction EXERCISE
– representation (aR and atan)
– uniform (=?)
– aR = v2/R
– atan = 0
• Exercises, examples
• Problem solving using Newton’s Laws
– location of additions to problem solving (see)
Highway Curves; Banked & Not
• Relation to both sides of Newton’s 2nd Law
• When is there sliding on unbanked curves?
• What is the friction force on vehicles going on
banked curves?
• Resource:
http://www.mhhe.com/physsci/physical/giam
battista/banked_curve/banked_curve.html
Non-uniform Circular Motion
• Components of acceleration
– meaning
– total acceleration (?)
– magnitude of acceleration (?)
• Relation to Cartesian coordinate
representation
Drag Force
• At “low” and “high” speeds; velocity
dependence (?)
• Example, low speeds (e.g. boat in water)
• Terminal velocity
– key? (a = 0)
• Example: In slow case, derive the expression
for the terminal velocity?
– Graph (roughly) the x,v,a motion graphs (?)
• Modeling, if time available
the end
friction exercise
• in groups, get whiteboards, pens, erasers
• Question: At what angle does a wood block
slide down a wood incline? (See table 5-1.)
– include other variables as needed
• Question: At this angle, describe the motion
of the wood block down the wood incline?
back
Using Newton’s Laws
The Physical situation
Choose/identify objects and forces
Create simple FBDs
Choose inertial coordinate systems
Implement Newton’s Laws
Mathematical representation
Problem
Solution
back
Using Newton’s Laws
The Physical situation
Choose/identify objects and forces
Create simple FBDs
Choose inertial coordinate systems
Implement Newton’s Laws
Mathematical representation
Problem
Solution
back