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PHY3221-01
Intermediate Mechanics
System of forces
Syllabus
Credit Hours 3
Semester Spring 2009
Course Ref# 03716
Instructor Dr. W. Roberts
Room KEN605
(850) 644-2223
wroberts @ fsu.edu
Classroom HCB310
Time 10:10 - 11:00AM
M W F
Office Hours 11:15AM - 1:15PM
M W
Tutorial Sess. 5:00 - 6:30 PM
Tuesday
Textbooks
Other references may be found on page 628 of the text by Thornton and Marion, and on page 595 of the text by Symon.
  • S. T Thornton and J. B. Marion, Classical Dynamics of Particles and Systems, Fifth Edition , Brooks/Cole-Thomson Learning, California, 2004.
  • K. R. Symon, Mechanics. Some material for the course, as well as some of the homework problems, will be taken from the text by Symon.
  • E. Butkov, Mathematical Physics.
  • G. Arfken, Mathematical Methods For Physicists.
Grades
Homework 30%
2 Midterms 30% each
Fri, 2/6/2009
Fri, 3/20/2009
Closed book
No calculators
1 Cheat sheet
No make-ups
Final Exam 40%
Mon, 4/27/2009
5:30 - 7:30PM
Room HCB310
Closed book
No calculators
1 Cheat sheet
No make-ups

Intermediate Mechanics is aimed mainly at physics majors, for whom this course is the first ‘serious’ mechanics course. As such, the material covered in this course will be assumed knowledge for many of your future physics courses, some of which will develop the ideas that you have met here further. Students are therefore expected to demonstrate a thorough understanding of the concepts that they encounter in this course.

In this course, we will be attempting to analyze mechanical systems (as opposed to memorising them), beginning with systems consisting of a single particle. To do this, we will use certain tools. Among these tools, several branches of mathematics, including arithmetic, algebra, trigonometry, and calculus, are indispensable. You are therefore expected to be comfortable with each of these areas in order to use them to solve physics problems.

Definition

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  • Mechanics - the study of the motion of material bodies
  1. Kinematics - the description of possible motion of material bodies (e.g. a in terms of v and x)
  2. Dynamics - the study of the laws of motion which determine which of the potential motions will actually take place in any given case. Forces are introduced and described as a sum total.
  3. Statics - study of (system of) forces, described by components, that act on body at rest
  • Electrostatics - Electric and magnetic forces exerted by electric charges and currents upon another
  • Gravitation - Gravitational forces on another

Vectors

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  • Coordinate systems
    • Cartesian
    • Cylindrical
    • Spherical
  • Vectors
  • Dot Product (Scalar)
  • Cross Product
  • Gradient
    • Divergence
    • Curl

Newtonian Mechanics

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  1. Inertia
    Decribes total force only, not its components, which is inconvenient in Statics where all
  2. Rate of Change of Momentum
    What Newton discovered was not that F = ma, but that F is most easily described this way
  3. Action-Reaction
    Fails to hold for electromagnetic forces when the interacting bodies are far apart, rapidly accelerated, or propagated from another body with finite velocity

Problem Solving

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The main Equations of Motion - These all have constant acceleration

Examples of Elementary Physics Problems and Equations Associated with them

  • Particle in a Straight Line
Kinematics example
  • Projectile Motion
Dynamics example
  • Pulley
Dynamics example
  • Block on an Incline
Statics example, introduces friction, which is nonconservative and inelastic
  • Centripetal Motion
  • Moon's Orbit about Earth
Gravitation example
The fact that g is proportional to m, instead of something else like q, is totally a coincidence. This is a big mystery in physics, thats why Gravitation has its own little subdivision in physics and other forces don't

Motion of Particle in 1-Dimension

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Forces in 1st dimension go by

  • Momentum and Energy Theorems
From Newtons 2nd Law
where
  • Force dependent on time
Given an applied force F(t) dependent only on time t, not displacement and not velocity
Damping forces F(v) are dependent only on velocity v, not time and not displacement
Conservative forces F(x) are dependent only on displacement x, not time and not velocity
  • Conditions for being conservative:
  • Falling Objects
Equation for the vertical motion of a falling object
Force of a falling body
where

Motion of Particle in n-Dimensions

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2 Dimensional forces go by F(x, y) and 3 Dimensional forces go by F(x, y, z)

  • Momentum and Energy Theorems
From Newtons 2nd Law
where
  • Conservative forces in 3D
  • Conservation of energy and the work-energy theorem
  • Planar kinematics
  • Three-dimensional kinematics
  • Conservation laws: linear momentum, angular momentum, energy

System of Particles

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  • Central forces, center-of-mass coordinates
  • Properties of central forces, specific examples
  • Inverse-square central force, Kepler’s laws, classification of orbits
  • Systems of particles
  • Specific examples, variable mass systems

Rigid Body

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is a special kind of system of particle

Damping coefficient

The Harmonic Oscillator Equation

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It's the equation of a particle with linear restoring force and friction proportional to velocity

1 Dimension

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Solve for the equation. Try

  • Damped
  • Undamped

is the natural frequency of undamped oscillator

  • Critically damped
  • Damped Energy balance in damped oscillating systems
  • Linear and nonlinear oscillating systems
  • Forced oscillator, transient and driven response
  • Mechanical resonance, phase and amplitude response
  • Principle of superposition

N Dimensions

[edit]

Gravitation

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  • Classical gravitation
Gravitational force
Gravitation intensity/field
  • At Earth's surface
where h is the height from the earth's surface
  • Center of gravity
  • Gravitational fields and potentials
  • Fields from general mass distributions