chapter 4 the classical mechanics explanation of motion (dynamics): newton’s laws of motion

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 2 3 – Suggested problems

• 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 LawsThe Physical situation

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Create simple FBDs

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Create simple FBDs

Choose inertial coordinate systems

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Create simple FBDs

Choose inertial coordinate systems

Implement Newton’s Laws

Mathematical representation

SolutionProblem

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Create simple FBDs

Choose inertial coordinate systems

Implement Newton’s Laws

Mathematical representation

SolutionProblem

back

Using Newton’s LawsThe Physical situation

Choose/identify objects and forces

Create simple FBDs

Choose inertial coordinate systems

Implement Newton’s Laws

Mathematical representation

SolutionProblem

return

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3 4

5

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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