Physics%20of%20Technology%20PHYS%201800

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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

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PHYSICS OF TECHNOLOGY Spring 2009 Assignment
Sheet
Homework Handout
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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

Introduction and Review
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Dennisons Laws of Motion

1. Stuff happens (or not).
2. The bigger they are the harder they fall.
3. You get what you give.

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Newtons Laws in Review

• 1st Law a special case of the 2nd Law for
  statics, with a0 or Fnet0
• An objects velocity remains unchanged, unless a
  force acts on the object.
• 2nd Law (and 1st Law)How motion of a object is
  effected by a force.
• The acceleration of an object is directly
  proportional to the magnitude of the imposed
  force and inversely proportional to the mass of
  the object. The acceleration is the same
  direction as that of the imposed force.
• 3rd Law Forces come from interactions with other
  objects.
• For every action (force), there is an equal but
  opposite reaction (force).

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Newtons First Law of Motion
An object remains at rest, or in uniform motion
in a straight line, unless it is compelled to
change by an externally imposed force.
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Newtons Second Law of Motion
The acceleration of an object is directly
proportional to the magnitude of the imposed
force and inversely proportional to the mass of
the object. The acceleration is the same
direction as that of the imposed force.
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Newtons Second Law of Motion

• Note that a force is proportional to an
  objects acceleration, not its velocity.
• Precise definitions of some commonly used
  terms
• The mass of an object is a quantity that tells
  us how much resistance the object has to a change
  in its motion.
• This resistance to a change in motion is called
  inertia.

Force has dimensions of (MLT-2)
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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

Mass Weight
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Mass and Weight

• What exactly is mass?
• Is there a difference between mass and weight?
• If something is weightless in space, does it
  still have mass?

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Mass, Weight, and Inertia

• A much larger force is required to produce the
  same acceleration for the larger mass.
• Inertia is an objects resistance to a change
  in its motion.
• Mass is a measure of an objects inertia.
• The units of mass are kilograms (kg).

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Mass, Weight, and Inertia

• An objects weight is the gravitational force
  acting on the object.
• Weight is a force, measured in units of newtons
  (N).
• In the absence of gravity, an object has no
  weight but still has the same mass.

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Mass Standard
How do we determine what the magnitude of a
gravitational force (weight) is?

• The International Prototype Kilogram (IPK) is
  the kilogram.
• It sits next to an inch-based ruler for scale.
  The IPK is made of a platinum-iridium alloy and
  is stored in a vault at the BIPM in Sèvres,
  France.

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Mass, Weight, and Inertia

• Objects of different mass experience the same
  gravitational acceleration on Earth g
  9.8 m/s2
• By Newtons 2nd Law, F ma, the weight is W
  mg.
• Different gravitational forces (weights) act on
  falling objects of different masses, but the
  objects have the same acceleration.

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Weight

• Example A body of mass 100 kg on the moon weighs

W m . g
100 x 9.8 / 6
163 N
(Compared with 980 N on Earth)
Note In English (imperial) system, weight (W) is
measured in lbs (pounds) which is also a force.
1 lbs 4.45 N
so, W 163 N
36.6 lbs only!
A mass of 1 kg therefore weighs 2.2 lbs near
Earths surface (or 9.8 N).
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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

A closer Look at Forces
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A Closer Look at the Table

• The forces acting on the book are W
  (gravitational force from Earth) and N (normal
  force from table).
• Normal force refers to the perpendicular force
  a surface exerts on an object.

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Third-Law Action/Reaction Pair
An uncompressed spring and the same spring
supporting a book. The compressed spring exerts
an upward force on the book.
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Compression on an Atomic Scale
Bonds between atoms in a compressed solid can be
treated as compressed springs. Ultimately the
forces come from electrostatic interactions
between electrons and protons (and a little
quantum mechanics).
Fspring-k ?x
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Third-Law Action/Reaction Pair

• The car pushes against the road, and the road, in
  turn, pushes against the car.

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• What is friction?
• A resistive force opposing motion.
• So far we have assumed many examples with no
  friction but friction is a very important force
  in our lives
• No surface is perfectly smooth when viewed at the
  atomic level!
• Frictional forces arise between two surfaces in
  contact because they tend to dig into each other.

Two objects in contact supported by a few high
spots or prominences.
contact points
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• What is friction?
• Friction is known to be independent of surface
  area counter intuitive!
• Reasoning If reduce area, the number of contact
  points reduces. This causes the pressure to
  increase at these points, which in turn flattens
  them more and results in an increase in contact
  area.
• Overall effect total contact area about the
  same!
• There are no simple laws of friction, as it is
  affected by several factors, eg
• Surface quality (roughness)
• Type of material
• Presence of lubricants
• Lubricants act to separate the two surfaces and
  allow them to float greatly reducing the
  friction.

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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

Introduction and Review
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Free Body Diagrams

• Fancy Science Vector analysis of complex force
  problems is facilitated by use of a free body
  diagram.
• Common Sense A picture is worth a 100 words. (A
  scale picture is worth an A!)
• Key is to
• Isolate a single body and draw all the forces
  acting on it.
• Add up all the arrows (vectors).
• Whats left is the net force.
• Net force (and masses) ? a.
• A plus initial conditions? motion!

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Does a sky diver continue to accelerate?

• Air resistance R is a force directed upward, that
  opposes the gravitational force W
• R increases as the sky divers velocity increases
• When R has increased to the magnitude of W, the
  net force is zero so the acceleration is zero
• The velocity is then at its maximum value, the
  terminal velocity

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Example Sea Lion splash!
Fk
N
Fk
mg sin?
F
mg cos?
?
Free body diagram
Wmg
W m g

• Resolve the weight force into two components
  parallel and perpendicular to ramp.

Result - Down slope force F m g sin ?
- Normal force N m g cos ?
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Net force down slope
Fnet F - Fk
m a
but friction, Fk µk N
µk mg cos?
Thus Fnet m g sin? µk m g cos? m a
a g (sin? - µk cos?)
For ? 23º, µk 0.26, g 9.81 m/s2, then
a 9.81 (sin 23º - 0.26 x cos23º)
a 1.5 m/s2 (note a is independent of mass)
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Physics of TechnologyPHYS 1800

• Lecture 8
• Mass Weight
• Motion with Friction

More Complex Problems in Statics and Dynamics
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Newton Provided Both the Ideas and the Methods
Harts list of most influential people in the
history of the world Newton (2) Einstein
(10) Galileo Galilei (12) Aristole
(13) Copernicus (19) Kepler (75) (even
though they got the wrong answer on the test)
Simmons list of most influential scientists in
the history of the world Newton (1) (and 2
and 6 and 40) Einstein (2) Galileo Galilei
(7) Copernicus (9) Kepler (10) Tyco Brahe (22)
Aristole (an honorable mentioned)
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How does this trajectory happen?
Key - resolve motion into its HORIZONTAL and
VERTICAL components.
VH constant
VG (due to gravity)
VTOTAL
But we know VG increases with time due to gravity
acceleration!
VH (constant)
At any instant the total velocity is vector sum
of VH and VG
Uniform increase in VG with time
Resultant TRAJECTORY STEEPENS with increasing
time.
As NO horizontal acceleration the ball
moves equal distances horizontally in equal time
(assuming NO air resistance).
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Physics of Technology

• Next Lab/Demo Forces
• Thursday 130-245
• ESLC 53
• Ch 3
• Next Class Wednesday 1030-1120
• BUS 318 room
• Read Ch 4