Transcript x 10 -6 - Images

Measurement in Physics
AP Physics B
There are seven fundamental units in
the metric system. All other units are
derived from these units.
2
3
Most commonly used prefixes in Physics
Prefix
Factor
Symbol
Mega- ( mostly used for radio station frequencies)
x 106
M
Kilo- ( used for just about anything, Europe uses
the Kilometer instead of the mile on its roads)
x 103
K
Centi- ( Used significantly to express small
x 10-2
distances in optics. This is the unit MOST people in
AP forget to convert)
c
Milli- ( Used sometimes to express small
distances)
x 10-3
m
Micro- ( Used mostly in electronics to express the
value of a charge or capacitor)
x 10-6
m
Nano ( Used to express the distance between
wave crests when dealing with light and the
electromagnetic spectrum)
x 10-9
n
Tip: Use your constant sheet when you forget a prefix value
SI units for Physics
The SI stands for "System International”. There are 3
fundamental SI units for LENGTH, MASS, and
TIME. They basically breakdown like this:
SI Quantity
SI Unit
Length
Meter
Mass
Kilogram
Time
Second
Of course there are many other units to consider. Many times, however, we
express these units with prefixes attached to the front. This will, of course,
make the number either larger or smaller. The nice thing about the prefix is
that you can write a couple of numbers down and have the unit signify
something larger.
Example: 1 Kilometer – The unit itself denotes that the number is actually
larger than "1" considering fundamental units. The fundamental unit would
be 1000 meters
RULES FOR COUNTING SIGNIFICANT FIGURES
1. All nonzero digits are significant.
Ex. 123 g
3 significant figures.
25 g
2 significant figures
26.42 g 4 significant figures
2. All zeros between non zero digits are significant.
Ex. 506 L
3 significant figures
900.43 L 5 significant figures
3. Decimal numbers that begin with zero.
The zeros to the left of the first nonzero number are not significant.
Ex. 0.205 L 3 significant figures
0.0047 L 2 significant figures
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4. Decimal numbers that end in zero.
The last zero is significant.
Ex. 8.00 g
3 significant figures
35.000 g
5 significant figures
8.0 g
2 significant figures
5. Non decimal numbers that end in zero.
The zero is significant only when a written decimal is shown.
Ex. 480 g
2 significant figures
900 g
1 significant figure
90. g
2 significant figure
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PRACTICE
Determine the number of significant figures.
1. 65.42 g
2. 385 L
3. 0.14 ml
4. 709.2 m
5. 5006.12 kg
6. 400 dm
7. 260. mm
8. 0.47 cg
9. 0.0068 km
10. 7.0 cm
11. 36.00 g
12. 0.0070 kg
13. 100.6040 L
14. 340.00 cm
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Rounding Numbers

Round 40.701 the following to
4 sf
3 sf
2 sf
1 sf
Multiplying & Dividing Sig Figs
Keep the smallest number

55.65 x 8.01 =

30.95 / 5.1 =
Adding and Subtractiong Sig Figs
Stop at the least certain place value.
(last sig fig closet to the left)


8800 + 35.03 =
853.354 – 3 =
Scientific Notation
You must have the same number of sig figs in the
answer as the question.
Convert to scientific notation
5800000
23.00
0.000050
0.0035
Example
If a capacitor is labeled 2.5mF(microFarads),
how would it be labeled in just Farads?
The FARAD is the fundamental unit used when discussed capacitors!
2.5 x 10-6 F
Notice that we just add the factor on the
end and use the root unit.
The radio station XL106.7 transmits at a
frequency of 106.7 x 106 Hertz. How would it
be written in MHz (MegaHertz)?
A HERTZ is the fundamental unit used when discussed radio frequency!
106.7 MHz
Notice we simply drop the factor and add
the prefix.
Dimensional Analysis
Dimensional Analysis is simply a technique you can use to convert from one unit
to another. The main thing you have to remember is that the GIVEN UNIT MUST
CANCEL OUT.
Suppose we want to convert 65 mph to ft/s or
m/s.
miles 1hour 1 min 5280 ft  65 11 5280  95 ft

65
1 60  60 1
hour 60 min 60 sec 1mile
s
ft
95
s
1meter  95  1 
1 3.281
3.281 ft
29 m / s
Solve for the variable

Solve for x
y = mx + b
a2 2
a

Solve for x
y = kx/z

Sove for b
c2 =
Solve for the variable

Solve for h
V =π r2 h

Solve for d1
A = ½ d1 d2
Slope
y = mx + b
X
0
Y
4
1
16
Plot using the calculator
2
28
 Hit stat enter
4
52
6
76
to clear existing list hit 2nd + #4
8
100
enter (look for the work done)
 Insert x in L1 and y in L2
 Hit stat then arrow to cal then hit #4 enter
Slope
y = mx + b
Plot using the calculator
Determine
 The slope
 What is the y-intercept
 Write the equation of the line in
the form of y=mx+b
 Determine y if x = 7
 Determine x if y = 0
X
Y
0
4
1
16
2
28
4
52
6
76
8
100
Trigonometric Functions
Many concepts in
physics act at angles
or make right triangles.
Let’s review common
functions.
c2  a2  b2
Pythagorea n Theorem
opp
  tan (
)
adj
-1
Trig Review
Solve for all the
sides and
angles.
В°
llll
35
7.5 m
Trig Review
Solve for all the
sides and
angles.
В°
llll
65
13
m
Trig Review
Solve for all the
sides and
angles.
В°
20 m
llll
25
Example
A person attempts to measure the height of
a building by walking out a distance of
46.0 m from its base and shining a
flashlight beam toward its top. He finds
that when the beam is elevated at an
angle of 39 degrees with respect to the
horizontal ,as shown, the beam just
strikes the top of the building. a) Find
the height of the building and b) the
distance the flashlight beam has to
travel before it strikes the top of the
building.
What do I know?
What do I
want?
•The angle
The opposite
•The adjacent side side
Course of
action
USE
TANGENT!
Example
A truck driver moves up a straight mountain highway, as shown above.
Elevation markers at the beginning and ending points of the trip show that he
has risen vertically 0.530 km, and the mileage indicator on the truck shows
that he has traveled a total distance of 3.00 km during the ascent. Find the
angle of incline of the hill.
What do I know?
What do I
want?
•The hypotenuse
The Angle
•The opposite side
Course of
action
USE INVERSE
SINE!
AREA UNDER THE CURVE