Lecture 2: Physics 103

1
Lecture 2 Physics 103

• Measurement
• Problem solving
• Kinematics

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Physics 103

• Consult the course web site, especially the
  planner

http//tycho.physics.wisc.edu/courses/phys103/fall
08

• Should be
• Reading chapter before class
• Doing pre-flights - one for today on physics
• There are pre-flights for every lecture
• Going to discussion section and lab
• Pre-lab questions for your first lab this week
• Homework, due Wednesday at 5PM, 80 credit if
  late by less than 1 week
• Try practice exams when exam time comes

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Significant Figures

• There is uncertainty in every measurement, this
  uncertainty carries over through the calculations
• Use rules for significant figures to approximate
  the uncertainty in results of calculations
• A significant figure is one that is reliably
  known
• All non-zero digits are significant
• Zeros are significant when
• between other non-zero digits
• After the decimal point and another significant
  figure
• can be clarified by using scientific notation
• Significant figures in a final result equals
  significant figures in the least accurate of the
  factors being combined
• Hint Keep at least one more significant figure
  in your calculation than needed until the very
  end, then round your final answer

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Significant Figure Example

• You are asked to calculate a trajectory for a
  space ship to the moon to 1 accuracy.
• If your off by more than 1 you might miss the
  moon and not have enough fuel to correct course
  and land!
• 1 is the accuracy we ask for in the homework
  questions
• Formula distance 1/2 accelerationtime2 x
  1/2at2
• Steps. Choose acceleration and calculate time.
  Confirm the ship covers the distance and arrives
  at the right place!
• x 506,000,000m, a 0.1004 m/s2, t 100400sec
• Known to 1 precision 1 part in 100 or 3
  decimal places
• Case 1 After figuring out t and a we round off
  to 1 precision x 1/2at2 1/210000020.100
  500,000,000m
• Case 2 We keep 4 significant figures to be safe
  x 1/2at2 1/210040020.1004
  506,024,032m
• In case 1 we are 1.2 off. You just killed the
  astronauts!
• Lesson to get 1 accuracy keep 4 digits and
  round at end

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Order of Magnitude Estimates

• A very good fastball pitcher can throw the ball
  100 mph. What is the ball speed in m/s?
• (5 miles is approximately 8 km)
• 4444 m/s
• 44.44 m/s
• .4444 m/s

Order of magnitude estimate A mile is of order
103 meters An hour is of order 103
seconds Therefore, the answer should be of order
102 m/s
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Problem Solving Diagrams
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Lightning Question

• Lightning was observed and thunder followed 5.0s
  later - Given speed at which light (c3.0x108
  m/s) and sound (v3.3x102 m/s) travel, can we
  calculate how far away the cloud burst was?
• 1. Yes
• 2. No

Distance x
Label all quantities
Distance of cloud burst - x Time of cloud burst
- t0 Time lightning seen - tL Time thunder
heard - tS
Write relations
Solve 3 equations but 4 unknowns. Surprise In
this case the solution is possible!
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Solution to Lightning Question
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Lightning Question
Lightning was observed and thunder followed 5.0s
later - Given speed at which light (c3.0x108
m/s) and sound (v3.3x102 m/s) travel, can we
calculate how far away the cloud burst was?
Neglecting time taken for light to travel -
since it travels so fast, what is the distance
of cloud burst from the observer? 1.
17 km 2. 1.7 km
2 significant figures
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Units, Significant Figures, Estimates

• Fundamental Units
• Length L meters
• Mass M kilograms
• Time T seconds
• Dimensional Analysis
• Both sides of an equation must have the same
  dimensions
• Can be used to verify equations, answers vd/t,
  m/s m/s
• Significant Figures
• Final significant figures determined by number
  with the least significant figures used in the
  calculation
• Keep at least one extra digit along the way and
  round at the end(4 for 1 accuracy)
• Order of magnitude estimates also useful to
  double check answers

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Problem Solving
Lightning was observed and thunder followed 5.0s
later - Given speed at which light (c3.0x108
m/s) and sound (v3.3x102 m/s) travel, can we
calculate how far away the cloud burst was?
Draw a picture Write down all the things you
know Write down relevant equations Try to
simplify if possible Check answer with
dimensional analysis and order of magnitude
estimates Round to significant figures
1.7 km
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Kinematics
Coordinate Systems

• Kinematics Lets you track position of an
  object?
• Where is it? How fast is it moving? Which
  direction? How fast is its speed changing? -
  Where will it be in future?
• We will be tracking the position of a point
• When a ball moves, it is the center of the ball
  that we describe.
• More on center of mass later in the semester.

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Position and Displacement

• Position xi -- defined in terms of a frame of
  reference (location of origin)
• Displacement Dx xf - xi (i stands for
  initial, f for final)
• Movement in one dimension label axis as x --
  horizontal (y for vertical)
• Can be positive or negative - i.e., it has
  direction
• Object can move towards right or left of position
  x0
• Units are meters

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Kinematics Distance and total distance

• Distance the magnitude or size of displacement
• Has no direction absolute value xf - xi
• I displace myself (from origin) -3 m and then 1m
• My displacement (from origin) is -2 m
• My distance (from origin) is 2 m
• Total distance I moved is could be 4 m
• Not very useful to determine where I am
• Useful for determining how many frequent flyer
  miles are awarded after a round-trip flight.

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Question ?

• An object goes from one point in space to
  another. After it arrives at its destination, its
  displacement is
• either greater than or equal to
• always equal to
• either less than or equal to
• not related to
• the distance it traveled.

Displacement can be negative, and when it is, it
is less than distance, which is the absolute
value of displacement!
The distance and displacement of an object is not
the same as the total distance it travels The
total distance is always going to be the longest
Throw a ball straight up and catch it at the same
point you released it The total distance is
twice the height, but the displacement is zero!
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Speed

• The average speed of an object is defined as the
  total distance traveled divided by the total time
  elapsed
• Average speed totally ignores any variations in
  the objects actual motion during the trip
• The total distance and the total time are all
  that count
• Units are meters/second

s
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Average Velocity

• Average velocity is the displacement divided by
  the time interval and has the same direction as
  displacement

Units are meters/second

• Velocity has direction (can be positive or
  negative when motion is in one dimension)
• Speed is not velocity car on straight highway
  vs. car on winding country road take same time
  between 2 towns
• Average velocity same
• Average speed (country rd) gt average speed
  (highway)
• Highway had traffic jam!

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Instantaneous Velocity

• Instantaneous velocity is the average velocity
  over an infinitesimal (very short) time interval.
• Instantaneous velocity applies to one point of
  time.
• Example drive slowly, then speed up to pass a
  car.
• Special Case Uniform velocity is constant
  velocity
• Instantaneous velocities are always the same
• Instantaneous velocities also equal the average
  velocity

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Average Velocity

• Position vs. time graph
• Motion is non-constant velocity
• Average velocity is the slope of blue line
  joining two points

20 m/s
13.33 m/s
20 m/s
0 m/s
-6 m/s
Average is not necessarily speed at which object
is moving at any instance!
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Instantaneous Velocity
Instantaneous velocity is slope of tangent at any
point and applies to that point in time only