Physics 2211: Lecture 8 Todays Agenda

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Physics 2211 Lecture 8Todays Agenda

• Newtons three laws
• How and why do objects move?
• Dynamics

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(No Transcript)
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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.
• Law 2 For any object,
• Law 3 Forces occur in pairs
• (For every action there is an equal
  and opposite reaction.)

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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 centripetal acceleration of Atlanta?
• T 1 day 8.64 x 104 sec,
• R RE 6.4 x 106 meters .
• Plug this in aatl .034 m/s2 ( 1/300 g)
• Close enough to 0 that we will ignore it.
• Atlanta is a pretty good IRF.

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Newtons Second Law

• For any object,
  .
• The acceleration of an object is proportional
  to the net force acting on it.
• 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 like adding vectors.

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Newtons Second Law...

• Components of
• FX maX
• FY maY
• FZ maZ
• 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). He applies a force of 50 N in the
  i direction. If the box starts at rest, what is
  its speed v after being pushed a distance d 10
  m ?

v 0
F
m
a
i
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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). He applies a force of 50 N in the
  i direction. If the box starts at rest, what is
  its speed v after being pushed a distance d 10
  m ?

v
F
m
a
i
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

v
F
m
a
i
d
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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.

v
F
m
a
i
d
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Lecture 8, Act 1Force 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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Forces

• We will consider two kinds of forces
• Contact force
• This is the most familiar kind.
• I push on the desk.
• The ground pushes on the chair...
• Action at a distance
• Gravity
• Electric Magnetic

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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

electroweak
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Empirical 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.
• Convention means the force
  acting on a due to b.
• So means the force on the
  head due to the thumb.

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Action at a distance

• Gravity

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Gravitation(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

R
RE
where G 6.67 x 10 -11 m3 kg-1 s-2
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Gravity...

• The magnitude of the gravitational force
  exerted on an object having mass m1 by another
  object having mass m2 a distance R12 away is
• The direction of is attractive, and lies
  along the line connecting the centers of the
  masses.

m1
m2
R12
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Gravity...

• 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.

m
h
M
RE
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Gravity...

• Near the Earths surface...

???
g

• So mg ma
• a g

All objects accelerate with acceleration g,
regardless of their mass!
Where
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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

Fg

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

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Newtons Third Law

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

m1
m2
R12
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Newton's Third Law...

• is true for contact forces
  as well

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Example of Bad Thinking

• Since , why isnt
  and a 0 ?

a ??
ice
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Example of Good Thinking

• Consider only the box as the system!
• Fon box mabox
• Free Body Diagram (next time).

abox
ice
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Lecture 8, Act 2Newtons 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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Recap of todays lecture

• Newtons 3 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.