Physics 2211, Spring 2002

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Physics 2211 Lecture 8Todays Agenda

• Newtons Laws (Particle Dynamics)
• How and why do objects move?

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Dynamics

• Isaac Newton (1643 - 1727) published Principia
  Mathematica in 1687. In this work, he proposed
  three laws of motion
• Law 1 An object subject to no external forces
  is at rest or moves with a constant
  velocity if viewed from an inertial reference
  frame.

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Newtons First Law

• An object subject to no external forces is at
  rest or moves with a constant velocity if viewed
  from an inertial reference frame.
• If no forces act, there is no acceleration.
• The following statements can be thought of as the
  definition of inertial reference frames.
• An IRF is a reference frame that is not
  accelerating (or rotating) with respect to the
  fixed stars.
• If one IRF exists, infinitely many exist since
  they are related by any arbitrary constant
  velocity vector!

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Is Atlanta a good IRF?

• Is Atlanta accelerating?
• YES!

• Atlanta is on the Earth.
• The Earth is rotating.

• What is the acceleration (centripetal) of Atlanta?

• T 1 day 8.64 x 104 sec,
• R RE 6.4 x 106 meters .
• Plug this in aatl 0.034 m/s2 ( 1/300 g)
• Close enough to zero that we will ignore it.
• Atlanta is a pretty good IRF.

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Newtons Second Law

• The constant of proportionality is called mass,
  denoted m.
• This is the definition of mass.
• The mass of an object is a constant property of
  thatobject and is independent of external
  influences.

• Force has units of M x L / T2 kg m/s2 N
  (Newton)

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Newtons Second Law

• What is a force?
• A Force is a push or a pull.
• A Force has magnitude direction (vector).
• Adding forces is just like adding vectors.

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Newtons Second Law

• Again, we can treat the three dimensions
  independently!

• Suppose we know m and FX , we can solve for aX
  and apply the things we learned about kinematics
  over the last few weeks. For example, if aX is
  constant

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Example Pushing a Box on Ice.

• A skater is pushing a heavy box (mass m 100 kg)
  across a sheet of ice (horizontal
  frictionless). She applies a force of 50 N in
  the x-direction. If the box starts at rest,
  what is its speed v after being pushed a distance
  d 10 m ?

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Example Pushing a Box on Ice.

• A skater is pushing a heavy box (mass m 100 kg)
  across a sheet of ice (horizontal
  frictionless). She applies a force of 50 N in
  the x-direction. If the box starts at rest,
  what is its speed v after being pushed a distance
  d 10 m ?

v
F
a
m
x
d
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Example Pushing a Box on Ice.

• Start with F ma.
• a F / m.
• Recall that v2 - v02 2a(x - x0 )
• So v2 2Fd / m

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Example Pushing a Box on Ice.

• Plug in F 50 N, d 10 m, m 100 kg Find v
  3.2 m/s.

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ExampleForce and acceleration

• A force F acting on a mass m1 results in an
  acceleration a1.The same force acting on a
  different mass m2 results in an acceleration a2
  2a1.

m1
m2
F
a1
F
a2 2a1

• If m1 and m2 are glued together and the same
  force F acts on this combination, what is the
  resulting acceleration?

m1
m2
F
a ?
(a) 2/3 a1 (b) 3/2 a1 (c) 3/4
a1
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ExampleForce and acceleration

• Since a2 2a1 for the same applied force, m2
  (1/2)m1 !
• m1 m2 3m1 /2

• So a (2/3)F / m1

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Forces

• We will consider two kinds of forces
• Empirical (contact) forces
• This is the most familiar kind.
• I push on the desk.
• The ground pushes on the chair...
• Fundamental (action-at-a-distance) forces
• Gravity
• Electric Magnetic (Electromagnetic)

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Overview of Physics
Laws of Motion Newtons Laws

• Observables
• Fundamental (M,L,T,Q)
• Derived

• Forces/Fields
• Fundamental
• Gravitational
• Electromagnetic
• Strong
• Empirical (Contact)

electroweak
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Empirical (Contact) Forces(examples)

• Linear Restoring Force
• Friction Force
• Fluid Force

Characterized by variable, experimentally determin
ed constants k, m, b, etc.
These forces are all electromagnetic in origin.
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Contact forces

• Objects in contact exert forces.

This is not a universal convention
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Gravitational Force(only fundamental force well
study this semester)
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Gravitation Force(Courtesy of Newton)

• Newton found that amoon / g 0.000278
• and noticed that RE2 / R2 0.000273

• This inspired him to propose the Universal Law
  of Gravitation

where G 6.67 x 10 -11 m3 kg-1 s-2
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Gravitation Force
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Gravitation Force

• Near the Earths surface
• R12 RE
• Wont change much if we stay near the Earth's
  surface.
• i.e. since RE gtgt h, RE h RE.

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Gravitation Force

• Near the Earths surface...

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Example gravity problem

• What is the force of gravity exerted by the earth
  on a typical physics student?

• Typical student mass m 55kg
• g 9.8 m/s2.
• Fg mg (55 kg)x(9.8 m/s2 )
• Fg 539 N

• The force that gravity exerts on any object is
  called its weight
• W 539 N ( 121 lbs.)

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Newtons Third Law

• For every action there is an equal and opposite
  reaction.
• We have already seen this in the case of gravity

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Newton's Third Law
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Example of Fuzzy Thinking
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Example of Good Thinking

• Consider only forces on the box!

• Free Body Diagram (next time).

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ExampleNewtons 3rd Law

• Two blocks are stacked on the ground. How many
  action-reaction pairs of forces are present in
  this system?

(a) 2 (b) 3 (c) 4
a
b
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ExampleNewtons 3rd Law
(c) 4
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Recap of todays lecture

• Newtons Three Laws (Text 4-1 to
  4-4)
• Law 1 An object subject to no external forces
  is at rest or moves with a constant velocity if
  viewed from an inertial reference frame.
• Law 2 For any object,
• Law 3 Forces occur in pairs
• For next time Read Chapter 4.5 - 4.7 in Tipler.