Download Chapter 4 - galileo.harvard.edu

Chapter 4
The Classical Mechanics Explanation
of Motion (Dynamics): Newton’s
Laws of Motion
Introduction: Our approach
•
•
•
•
•
•
•
Inertia
Force
Nature of Interaction
Mass
Force & acceleration
Problem solving using Newton’s Laws
Lab investigation
Inertia
• The revolutionary idea of inertia: constant
velocity motion is the new “natural motion”
• Newton’s First Law of Motion
• Examples, Activities
– Inertial reference frames
– Comment on “non-accelerating”
• Newton’s First Law as a test of inertial frames
• “Inertia” as a name for the validity of the First
Law
Force
• Refining our use of “force” (class activity)
• A vector quantity (What does that mean?)
• As the explanation of changes in motion
– kinematics of simple collision
– implications
• Simple free body diagrams to represent forces
on an object
– Exercises
– Tutorial
– Contact and non-contact forces
– Precision in the use of the simple FBD
The Nature of Interaction
• Force – the assumed form of interaction
• Forces among objects come in pairs, equal and
opposite
• Precise implementation of Newton’s Third Law
– Implications and examples
– Using simple FBDs for systems of objects
– Tutorials
– Examples: Weight and normal force
– Coins stack/Drop tower physics
– The Third Law as a test of inertial frames
Mass
• Mass as a measure of the amount of inertia
– When there is a non-zero net force on the object
– In contrast to “the quantity of matter”
– In contrast to weight
– Comment: Will go deeper in terms of energy
(E=mc2), later in PH 212
From Force to Acceleration
• Review: The revolutionary idea of force
tracking with acceleration, but how
quantitatively?
• Newton’s Second Law, features to note:
– net force on object
– mass of object
– acceleration of object
– vector equation
• The “Newtonian Project”
Problem Solving
using Newton’s Laws
•
•
•
•
General approach and a new diagram (see)
Sequence of learning (start)
Exercise (graphic)
Examples/Practice
– Jeopardy problems: 1
– Suggested problems
2
3
• Comment: Why Newton needed to invent
calculus
Lab investigation
of net force question
• Net force and Newton’s 1st Law (demo)
• Question: Net force and Newton’s 2nd Law
– Preparation assignment
– Lab resources (for next class)
the end
Using Newton’s Laws
The Physical situation
Mathematical representation
Problem
Solution
Using Newton’s Laws
The Physical situation
Mathematical representation
Problem
Solution
Using Newton’s Laws
The Physical situation
Choose/identify objects and forces
Mathematical representation
Problem
Solution
Using Newton’s Laws
The Physical situation
Choose/identify objects and forces
Create simple FBDs
Mathematical representation
Problem
Solution
Using Newton’s Laws
The Physical situation
Choose/identify objects and forces
Create simple FBDs
Choose inertial coordinate systems
Mathematical representation
Problem
Solution
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
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
1
return
2
Choose/identify objects and forces
3
4
Create simple FBDs
5
Choose inertial coordinate systems
7
6
Implement Newton’s Laws
9
8
Mathematical representation
Problem
Solution
10
Jeopardy problem 1
Describe in words a problem for which the
following equation is a representation of the
physical situation. Also draw a simple FBD that
is consistent with the equation (specify the
direction of the axis):
+24.2 N – FBG = (4.2 kg)(3.0 m/s2)
next
return
Jeopardy problem 2
Describe in words a problem for which the
following equation is a representation of the
physical situation. Also draw a simple FBD that
is consistent with the equation (specify the
direction of the axis) (note - f denotes friction):
+1.0 N – fAT = (1.2 kg)(-1.3 m/s2)
next
return
Jeopardy problem 3
Describe in words a problem for which the
following equation is a representation of the
physical situation. Also draw a simple FBD that
is consistent with the equation (specify the
direction of the axis) (note - f denotes friction):
+1.0 N cos(12O)– fAT = (1.2 kg)(1.3 m/s2)
return