Transcript Document

Motion in One Dimension
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
Measurement and Uncertainty; 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.
Measurement and Uncertainty; Significant
Figures
Conceptual Example 1-1: Significant figures.
Using a protractor, you measure an angle to be 30°.
(a) How many significant figures should you quote in
this measurement? (b) Use a calculator to find the
cosine of the angle you measured.
Prefixes
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Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
Prefixes, cont.
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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
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.
mi
26.2mi = 26.2mi
= 0.0163?
1609m
1609m
4
26.2mi = 26.2mi
= 4.22 ´ 10 ?
1mi
Question
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A.
B.
C.
D.
1 atm = 1.013 x105 Pa = 14.70 lb/in2
If you want to convert 0.46 atm to Pa
you should
Multiply 0.46 atm by 14.70 lb/in2
Multiply 0.46 atm by 1.013 x105 Pa
Divide 0.46 atm by 14.70 lb/in2
Divide 0.46 atm by 1.013 x105 Pa
Converting units
1.
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?
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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
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30.0 km/h =?
1 km = 0.6214 miles
$220 Canadian Dollars = ?
1 US dollar = 0.97 Canadian
dollar
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 1-5: Volume of a lake.
Estimate how much water
there is in a particular
lake, which is roughly
circular, about 1 km
across, and you guess it
has an average depth of
about 10 m.
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
coordinate.
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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Vectors and Scalars
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Vector quantities need both magnitude
(size or numerical value) and direction to
completely describe them
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Will use + and – signs to indicate vector
directions
Scalar quantities are completely described
by magnitude only
Average Speed
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Average speed =distance traveled/ time
elapsed
Example: if a car travels 300 kilometer (km) in
2 hours (h), its average speed is 150km/h.
Not to confuse with average velocity.
Average Velocity
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The average velocity is rate at which
the displacement occurs
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x x f  xi
vaverage 
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t
t
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The SI units are m/s
Is also the slope of the line in the
position – time graph
Average Velocity, cont
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Gives no details about the motion
Gives the result of the motion
It can be positive or negative
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It depends on the sign of the displacement
It can be interpreted graphically
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It will be the slope of the position-time
graph
Not to Confuse
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Speed is a number : a scalar
Velocity is a vector : with magnitude
and direction
Average Velocity
Example 2-1: Runner’s average velocity.
The position of a runner as a function of time is plotted as
moving along the x axis of a coordinate system. During a
3.00-s time interval, the runner’s position changes from x1
= 50.0 m to x2 = 30.5 m, as shown. What was the
runner’s average velocity?