Motion in One Dimension
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Reminder: Homework due
Wednesday at the beginning of
class
Sig. figs
Converting Units
Order of magnitude
2.1 Reference Frame
2.2 average Velocity
Significant Figures
Scientific notation is commonly used in
physics; it allows the number of significant
figures to be clearly shown.
Much of physics involves approximations;
these can affect the precision of a
measurement also.
Reading Significant Figures
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Nonzero Digits are always significant
Zeros between significant figures are
significant.
Examples:
409.8 s
0.058700 cm
950.0X 101 mL
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Answer
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In 409.8 s : all four digits are significant
In 0.058700 cm: the two zeros on the left
are not significant, they are used to place a
decimal point, the numbers 5,8,7 are
significant, and so are the two final zeros.
In 950.0 X 101 ml: the final zero is
significant since it comes after the decimal
point. The zero at its left is also significant
since it comes between two other significant
digits, so the results is four significant
figures.
Adding Significant Figures
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67.9 g + 0.002 g + 3.51 g =
?
Sum (or difference) can’t
be more precise than least
precise quantity
Answer: 71.4 g
When you add or subtract you
keep the decimal place of the
least precise value.
Multiplying Significant Figures
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Distance = velocity x time
Velocity = 65.4mph
Time = 4.2 hours
Distance=274.7 or 275 or 2.7x102 miles
When you multiply (or divide) you keep
the number of significant figures that are
equal to the quantity with the smallest
number of significant figures.
Importance of Units
The 165 million dollars Mars Polar
Lander
Units help you figure out equations:
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Speed in m/s
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Density in kg/m3
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Units help you
determine the correct
solution
www.nasa.gov
Units, Standards, and the SI System
Quantity Unit
Standard
Length
Meter
Length of the path traveled
by light in 1/299,792,458
second
Time
Second
Mass
Kilogram
Time required for
9,192,631,770 periods of
radiation emitted by cesium
atoms
Platinum cylinder in
International Bureau of
Weights and Measures, in
Paris
Order of Magnitude
Viruses
Mt Everest’s
Height=8850m
Order of Magnitude
Order of Magnitude
Units, Standards, and the SI System
We will be working in the SI system, in which the
basic units are kilograms, meters, and seconds.
Quantities not in the table are derived quantities,
expressed in terms of the base units.
Other systems: cgs; units
are centimeters, grams,
and seconds.
British engineering system
has force instead of mass
as one of its basic
quantities, which are feet,
pounds, and seconds.
Converting units
1.
Multiplying by 1 leaves a quantity
unchanged.
2.
“1” can be represented as
3.
Choose form for ‘1’ for which units
match.
26.2mi = 26.2mi
1609m
1mi
4
= 4.22 ´ 10 ?
Converting units
1.
2.
You're stopped by police for
speeding 30.0 km/h over the
speed limit on an Ontario highway.
What is the speed in mph?
That'll be a $180 fine, plus a $35
victim surcharge and a $5 court
fee ($220 in all) should you decide
to plead guilty and settle out of
court. (in Canadian Dollars). What
is the fine in US dollars?
Converting units
1.
2.
30.0 km/h =?
1 km = 0.6214 miles
$220 Canadian Dollars = ?
1 US dollar = 0.97 Canadian
dollar
Prefixes
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Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
Prefixes
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The prefixes can be
used with any base
units
They are multipliers of
the base unit
Examples:
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1 mm = 10-3 m
1 mg = 10-3 g
Fundamental and Derived
Quantities
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In mechanics, three fundamental or base
quantities are used
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Length
Mass
Time
Will also use derived quantities
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These are other quantities that can be
expressed as a mathematical combination of
fundamental quantities
Density
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Density is an example of a derived
quantity
It is defined as mass per unit volume
m
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V
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Units are kg/m3
Question
1 atm = 1.013 x105 Pa = 14.70 lb/in2
If you want to convert 0.46 atm to Pa you
should
A. Multiply 0.46 atm by 14.70 lb/in2
B. Multiply 0.46 atm by 1.013 x105 Pa
C. Divide 0.46 atm by 14.70 lb/in2
D. Divide 0.46 atm by 1.013 x105 Pa
Order of Magnitude: Rapid Estimating
A quick way to estimate a calculated quantity is
to round off all numbers to one significant
figure and then calculate. Your result should at
least be the right order of magnitude; this can
be expressed by rounding it off to the nearest
power of 10.
Diagrams are also very useful in making
estimations.
Order of Magnitude: Rapid Estimating
Example 1-6: Thickness of a page.
Estimate the thickness
of a page of your
textbook. (Hint: you
don’t need one of these!)
Coordinate Axis
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y
-x
o
-y
x
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In Physics we draw
a set of coordinate
axis to represent a
frame of reference.
In one dimensional
axis coordinate, the
position of an object
is given by its x or y.
Position on a line
1. Reference point (origin)
2. Distance
3. Direction
Symbol for position: x
SI units: meters, m
Displacement on a line
• Change of position is called Displacement:
xf
xi
Displacement is a vector quantity
It has magnitude and direction
Displacement
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Defined as the change in position during some time
interval
 Represented as x
SI units are meters (m) x can be positive or
negative
Different than distance – the length of a path
followed by a particle.
Displacement has both a magnitude and a direction
so it is a vector.
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Example
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Mary walks 4 meters East, 2 meters South, 4
meters West, and finally 2 meters North. The
entire motion lasted for 24 seconds. Determine
the displacement and distance Mary travelled.