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Physics chapter 1 1
Models, Measurements,and Vectors
Physics chapter 1 2
Physics is….
The study of nature. the study of the natures of matter and
energy. The study of the relationship between
matter and energy.
Physics chapter 1 3
Physics is based on
Experiments Observations
Physics chapter 1 4
The language of physics
The laws of physics can almost always be expressed using mathematical relationships.
So, mathematics is the language of physics.
Physics chapter 1 5
Why study physics?
A fundamental science
Technology
Scientific insight into everyday world
Physics chapter 1 6
Theories
Theories
Principles
Laws
Physics chapter 1 7
Idealized models
ModelSimplified version of a complicated physical
system
We neglect minor effects on the system to concentrate on the major effects.
Physics chapter 1 8
Units
We use the metric or SI system Base units
Meter – m – lengthKilogram – kg – massSecond – s – time
All answers must have units, or they are meaningless
Physics chapter 1 9
Prefixes
Added to units to indicate mulitples of 10 or 1/10
Kilo – 1000 or 103 – kilometer – km Nano – 10-9 – nanosecond – ns Milli – 10-3 – milligram – mg Micro – 10-6 – microsecond – ms Page 6 for more
Physics chapter 1 10
Unit analysis
Also called dimensional analysis. Units must work out. Units are treated just like algebraic
symbols in equations
Physics chapter 1 11
Example 1
vtd
km/h 100v h 2t
h 2h
km100
d
km 200d
Physics chapter 1 12
Alternative method (Example 2)
vtd
km/h 100v h 2t
2002100 d
km 200d
kmhh
km
Physics chapter 1 13
Unit Conversions
Use ratios
Carry your units through to make sure they cancel
Physics chapter 1 14
Example 3
Convert 6 ft 1 in to m.
Physics chapter 1 15
Uncertainty
More accurate measurements have less uncertainty.
We can express uncertainty in two ways:75.6 3.78 cm75.6 cm 5%
Physics chapter 1 16
Significant figures
We usually don’t write numbers with uncertainties.
Instead, we use significant figures.
Physics chapter 1 17
Significant Figures
All the digits known in a measurement, plus one that is somewhat uncertain.
All nonzero digits are significant Zeros are governed by four rules
1. Zeros between nonzero digits are significant
203 has 3 sig figs 5.0279 has 5 sig figs
Physics chapter 1 18
Significant Figures
2. Zeros in front of all nonzero digits are not significant
0.0035 has 2 sig figs 0.0008 has 1 sig fig
3. Zeros at the end of a number and after the decimal point are significant.
75.000 has 5 sig figs 0.000800 has 3 sig figs
Physics chapter 1 19
Significant Figures
4. Zeros at the end of a number but before the decimal point may or may not be significant.
If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show
all zeros are significant, use a decimal point. To show some are, use scientific notation (later) 2000 has 1 sig fig 2000. has 4 sig figs
Physics chapter 1 20
Examples 4
2.52 sig figs
2.503 sig figs
2502 sig figs
250.3 sig figs
250.04 sig figs
0.00252 sig figs
0.002503 sig figs
0.0025014 sig figs
Physics chapter 1 21
Multiplication and Division
The result should have the same number of significant figures as the least number of significant figures in any factor.
Physics chapter 1 22
Example 5
Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would record our answer as 1.6
608.12.134.1
Physics chapter 1 23
Example 6
Since 8 only has 1 sig fig, the answer should only have 1 sig fig. Record the answer as 3
25.38
26
Physics chapter 1 24
Addition and Subtraction
The result has no significant figures beyond the last decimal place where all of the original numbers had significant figures.
Physics chapter 1 25
Example 7
Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Record the answer as 1.253
25342.1
21342.0
040.1
Physics chapter 1 26
Example 8
Since 900 has its last sig fig in the hundreds column, then the result’s last sig fig must be in the hundreds column. Record the answer as 300
340
900
1240
Physics chapter 1 27
Conversion factors
Conversion factors are considered exact, and do not affect significant digits.
There are exactly 100 cm in 1 m, so don’t use the 100 to figure out how many significant digits your answer should have.
Physics chapter 1 28
Scientific Notation
Useful when writing very small or very large numbers
Also useful for indicating the number of significant figures
696,000,000 m = 6.96 x 108 m 4,000,000 km = 4 x 106 km
or 4.00 x 106 km
Physics chapter 1 29
Precision vs. Accuracy
Bathroom scale with 5 pound increments might be very accurate, but is not very precise.
Doctor’s office scale with 1/10 pound increments is very precise, but might not be very accurate.
A good measurement is both accurate and precise.
Physics chapter 1 30
Estimates and orders of magnitude Read section 1.6, including the example.
Physics chapter 1 31
Vectors
Have magnitude and direction Typed in bold with an arrow over them
A
Handwritten with an arrow over them
Physics chapter 1 32
Vectors
Two vectors with the same direction are parallel.
Two vectors with the opposite direction are antiparallel.
Two vectors with the same direction and magnitude are equal.
Physics chapter 1 33
Vector magnitude
The magnitude of a vector is a scalar (a number) and is always positive.
Write it as the vector name without the arrow or like this:
A
Physics chapter 1 34
Vector addition - geometrically
Place the tail of the second vector at the tip of the first vector.
The vector sum, or the resultant, is the vector connecting the starting point and the ending point.
Physics chapter 1 35
Example 9
Miss Becker drives 4 mi north and then 11 mi west. How far and in what direction is she from her starting point?
Physics chapter 1 36
Vector subtraction
Just flip around vector B and then add.
BABA
Physics chapter 1 37
Vector components
Any vector can be separated into component vectors that are parallel to the Cartesian (x and y) axes.
The vector sum of these components is equal to the original vector
yx AAA
Physics chapter 1 38
Finding vector components
We can find vector components using trigonometry.
A
yA
xA
y
x cosAAx sinAAy
A
AxcosA
Aysin
These equations work when q is measured CCW from the positive x-axis.
Physics chapter 1 39
Example 10
B
yB
xB
y
x
m 0.5B 50
cosBBy
B
BycosB
Bxsin
sinBBx
50cosm 0.5yB 50sinm 0.5xB
m 2.3yB m 8.3xB
Physics chapter 1 40
Vector addition – using components Each component of the resultant vector is
equal to the sum of the corresponding components of the vectors being added
... xxxx CBAR
... yyyy CBAR
Physics chapter 1 41
Finding vector magnitude and direction If given a vector in terms of its
components, we can find its magnitude and direction using trig
m 4.1
m 1.6
y
x
A
A
A
yA
xA
y
x
22yx AA A
22 m 4.1m 6.1 A
2m 52.4A
m 1.2A
Physics chapter 1 42
Finding vector direction
A
yA
xA
y
x
x
y
A
Atan
x
y
A
A1tan
m 6.1
m 4.1tan 1 41
Physics chapter 1 43
Example 11
Find the resultant vector in terms ofA) componentsB) magnitude and direction
BAR
m 4.1
m 8.4
y
x
A
A
m 83
m 3.2
.B
B
y
x
Physics chapter 1 44
Example part A)
yyy
xxx
BAR
BAR
m 6.1xR
m 4.2yR
m 2.3m 8.4 xR
m 8.3m 4.1 yR
Physics chapter 1 45
Example part B)
22yx RR R
22 m 4.2m 6.1 R
m 9.2R
Physics chapter 1 46
Example part B)
Is this right?
x
y
R
R1tan 1 2.4 mtan
1.6 m
56
Physics chapter 1 47
Tan-1 can be tricky
Angles that differ by 180° have the same tangent.
Your calculator doesn’t know which one you want.
R
56 180 236 y
x
axis- xnegative fromCCW 56
or56
56