PHYS 1443-001, Summer I 2005

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PHYS 1443 Section 001Lecture 3
Thursday June 2, 2005 Dr. Andrew Brandt

• One Dimensional Motion
• Acceleration
• Motion under constant acceleration
• Free Fall
• Vectors

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Announcements

• Homework 9/12 of you have signed up, need to
  include contact info
• First homework assignment has been given on Ch.
  2, due Monday, June 6 at 2pm
• Second HW to be assigned today on Ch. 3 will be
  due Tuesday, June 7 at 6pm
• Remember! Homework counts 20 of your grade
• First test on Ch 1-3 Weds June 8 at 8 am sharp
• Physics Clinic in basement 010 1200-600 pm,
  M-Th
• You should have read Ch 12 and started HW

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One Dimensional Motion

• Lets start with the simplest case acceleration
  is a constant (aa0)
• Using definitions of average acceleration and
  velocity, we can derive equations of motion
  (description of motion, velocity and position as
  a function of time)

(If tft and ti0)
For constant acceleration, average velocity is a
simple numeric average
(If tft and ti0)
Resulting Equation of Motion becomes
often use o instead of i for initial
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One Dimensional Motion contd
Average velocity
Solving for t
Since
Substituting t in the above equation,
Resulting in
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Kinetic Equations of Motion in a Straight Line
Under Constant Acceleration
Velocity as a function of time
Displacement as a function of velocity and time
Displacement as a function of time, velocity, and
acceleration
Velocity as a function of displacement and
acceleration
You may use different forms of Kinetic equations,
depending on the information given to you for a
specific problem!!
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Example 2.11
Suppose you want to design an air-bag system that
can protect the driver in a head-on collision at
a speed 100km/s (60miles/hr). Estimate how fast
the air-bag must inflate to effectively protect
the driver. Assume the car crumples upon impact
over a distance of about 1m. How does the use of
a seat belt help the driver?
How long does it take for the car to come to a
full stop?
As long as it takes for it to crumple.
The initial speed of the car is
We also know that
and
I would have used Formula 2!
Using the kinematic formula
The acceleration is
Thus the time for air-bag to deploy is
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Free Fall

• Free fall is a motion under the influence of
  gravity only
• The gravitational acceleration is g9.80m/s2
  (direction?) on the surface of the earth, with
  minor variations as a function of altitude
• This is constant acceleration so all the
  kinematic formula we have just learned can be
  used to address free fall problems
• Gravitational acceleration is inversely
  proportional to the distance between the object
  and the center of the earth
• The direction of gravitational acceleration is
  ALWAYS toward the center of the earth, which we
  normally call (-y) where up and down direction
  are indicated as the variable y
• Thus the correct denotation of gravitational
  acceleration on the surface of the earth is
  g-9.80m/s2

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Solving Problems (p.28)

• Read problem carefully
• Draw a diagram (choose coordinate system)
• Write down known and unknown quantities
• Think!
• Calculate (substitute numbers at end)
• Is answer reasonable?
• Check units

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Example for Using 1D Kinematic Equations on a
Falling object

• Stone was thrown straight upward at t0 with
  20.0m/s initial velocity on the roof of a 50.0m
  high building,

g-9.80m/s2
What is the acceleration in this motion?
(a) Find the time the stone reaches the maximum
height.
What is so special about the maximum height?
V0
Solve for t
(b) Find the maximum height.
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Example of a Falling Object II
(c) Find the time for the stone to return to its
original height.
motion is symmetric
(d) Find the velocity of the stone when it
reaches its original height.
(e) Find the velocity and position of the stone
at t5.00s.
Velocity
Position
bonus examples!
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Coordinate Systems (Start Ch. 3)

• Makes it easy to express locations or positions
• Two commonly used systems, depending on
  convenience
• Cartesian (Rectangular) Coordinate System
• Coordinates are expressed in (x,y)
• Polar Coordinate System
• Coordinates are expressed in (r,q)
• Vectors become a lot easier to express and compute

How are Cartesian and Polar coordinates related?
(x1,y1)(r,q)
O (0,0)
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Example
Cartesian Coordinate of a point in the xy plane
are (x,y) (-3.50,-2.50)m. Find the polar
coordinates of this point.
r
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Vector and Scalar
Vector quantities have both magnitude (size) and
direction
Force, gravitational pull, momentum
Normally denoted in BOLD letters, F, or a letter
with arrow on top
Their sizes or magnitudes are denoted with normal
letters, F, or absolute values
Scalar quantities have magnitude only Can be
completely specified with a value and its unit
Energy, heat, mass, weight
Normally denoted in normal letters, E
Both have units!!!
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Properties of Vectors
magnitudes

• Two vectors are the same if their
  and their
• are the same, no matter
  where they are on a coordinate system.

directions
Which ones are the same vectors?
ABED
Why arent the others?
C The same magnitude but opposite direction
C-AA negative vector
F The same direction but different magnitude
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Vector Operations

• Addition
• Triangular Method One can add vectors by
  connecting the head of one vector to the tail of
  the other (head-to-tail)
• Parallelogram method Connect the tails of the
  two vectors and extend
• Addition is commutative Changing order of
  operation does not affect the results ABBA,
  ABCDEECABD

OR

• Subtraction
• The same as adding a negative vectorA - B A
  (-B)

Since subtraction is the equivalent to adding a
negative vector, subtraction is also
commutative!!!

• Multiplication by a scalar is increasing the
  magnitude A, B2A

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Vector Components

• Coordinate systems are useful for resolving
  vectors into their components (lengths along
  coordinate axes)
• This makes vector algebra easier
• Dont forget about direction of vectors

Components
(,)
(Ax,Ay)
Magnitude
(-,)
(-,-)
(,-)
Example on board
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Example of Vector Addition
A car travels 20.0km due north followed by 35.0km
in a direction 60.0o west of north. Find the
magnitude and direction of resultant displacement.