Transcript physcis-c1-A-Physics-Toolbox

Chapter
1
A Physics Toolkit
Chapter
1
A Physics Toolkit
In this chapter you will:
Use mathematical tools to
measure and predict.
Apply accuracy and
precision when measuring.
Display and evaluate data
graphically.
Chapter
1
Table of Contents
Chapter 1: A Physics Toolkit
Section 1.1: Mathematics and Physics
Section 1.2: Measurement
Section 1.3: Graphing Data
Section
1.1
Mathematics and Physics
In this section you will:
Demonstrate scientific methods.
Use the metric system.
Evaluate answers using dimensional analysis.
Perform arithmetic operations using scientific notation.
Section
1.1
Mathematics and Physics
1.) What is Physics?
Physics is a branch of
science that involves the
study of the physical
world: The study of
energy and matter, and
how they are related.
What types of careers do
people with a background in
physics have?
Section
1.1
Mathematics and Physics
2.) Will we use a lot of math in physics?
Physics uses numerical results to make
predictions and to support theories and form
conclusions.
Section
1.1
Mathematics and Physics
Electric Current
The potential difference, or voltage, across a circuit equals the
current multiplied by the resistance in the circuit. That is, V (volts) = I
(amperes) × R (ohms). What is the resistance of a lightbulb that has
a 0.75 amperes current when plugged into a 120-volt outlet?
Section
1.1
Mathematics and Physics
Electric Current
Rewrite the equation so that the unknown value is alone on the left.
V = IR
Section
1.1
Mathematics and Physics
Electric Current
Reflexive property of equality.
IR = V
Divide both sides by I.
Section
1.1
Mathematics and Physics
Electric Current
Substitute 120 volts for V, 0.75 amperes for I.
Resistance will be measured in ohms.
Section
1.1
Mathematics and Physics
3.) What are the seven SI base units?
Section
1.1
Mathematics and Physics
4.) How is the SI regulated?
It is regulated by the International Bureau of Weights
and Measures and the National Institute of Science
and Technology (NIST).
Section
1.1
Mathematics and Physics
5.) What is an advantage of using SI Units?
An advantage is that conversions are easy because
they are all multiples of ten.
Prefix
Kilo
Hecto
Deka
Base (meter)
Deci
Centi
Milli
Multiplier
1000 x base
100 x base
10 x base
1 x base
0.1 x base
0.01 x base
0.001 x base
symbol
K
H
D
d
c
m
Section
Mathematics and Physics
1.1
Additional prefixes
.
femto
pico
nano
micro
mega
giga
tera
1 X 10-15 x base
1 x 10-12 x base
1 x10-9 x base
1 x 10-6 x base
1 x 10 6 x base
1 x 10 9 x base
1 x 10 12 x base
f
p
n
μ
M
G
T
Section
1.1
Mathematics and Physics
6.) What is dimensional analysis?
A method of problem solving that uses units
to set up problems.
For example, if you are finding a speed and
you see that your answer will be measured in
s/m or m/s2, you know you have made an
error in setting up the problem.
Section
1.1
Mathematics and Physics
7. What is a conversion factor?
A fraction used in dimensional analysis in which the
numerator and denominator have different units but
equal to each other in value. All conversion factors
have a value of one.
For example, because 1 kg = 1000 g, you can
construct the following conversion factors:
Section
1.1
Mathematics and Physics
Dimensional Analysis
Choose a conversion factor that will make the units cancel,
leaving the answer in the correct units.
For example, to convert 1.34 kg of iron ore to grams, do as
shown below:
Section
1.1
Mathematics and Physics
8.) What are Significant Digits?
Significant digits are the valid digits in a
measurement. The last digit is estimated but is still
considered valid.
Significant digits are only applicable with
measurements.
On a scale, all marked increments are considered
valid.
On a digital scale the last digit is the estimated value.
Section
1.1
Mathematics and Physics
Rule for determining the number of Significant Digits
1.) Non-zero numbers are always significant.
2.) Any zeros between two significant digits are significant.
3.) A final zero or trailing zeros in the decimal portion ONLY are
significant.
0.0007500 Km = .7500 m = 750.0 mm
0.0007500 Km = .7500 m = 750.0 mm
All have four significant digits
Section
1.1
Mathematics and Physics
Atlantic Pacific Rule
Use this diagram to help determine the number of
significant figures in a measured value…
Pacific
Atlantic
If the decimal point is present, start counting digits from the
Pacific (left) side, starting with the first non-zero digit.
If the decimal point is absent start counting digits from the
Atlantic (left) side, starting with the first non-zero digit.
Section
1.1
Mathematics and Physics
9.) How do you deal with addition and subtraction
with significant digits?
When you perform any arithmetic operation, it is
important to remember that the result never can be
more precise than the least-precise measurement.
To add or subtract measurements, first perform the
operation, then round off the result to correspond to
the least-precise value involved.
10 + 11.6 + .2 = 21.8 but we cant report the tenth place because of
the first value
10
11.6
0.2
21.8 so we have to round to 22
Section
Mathematics and Physics
1.1
10.) How do you deal with multiplication and division
with significant digits?
Perform the operation and then report the
smallest number of significant digits as found
in any of the factors.
7 x .125 x 6.125 = 5.359375
1
3
4
=
can only report one sig fig
The answer that can be reported is 5. Just because the
calculator gives us all of those place values doesn’t
mean that all of a sudden we were that precise when we
measured.
Section
1.1
Mathematics and Physics
11.) What is the Scientific Method?
A systematic method of observing,
experimenting and analyzing to answer
questions about the natural world.
12.) What is a hypothesis?
An educated guess about how variables
are related.
Section
1.1
Mathematics and Physics
13.) What is the difference between a
scientific law and a theory?
A scientific law describes relationships in nature
without attempting to explain them. We talk about
what happens but not why. i.e. Law of Gravity
A scientific theory attempts to explain the
phenomenon. i.e. Theory of Evolution
Section
1.1
Mathematics and Physics
Models, Laws, and Theories
A scientific law is a rule of nature that sums up related
observations to describe a pattern in nature.
Notice that the laws do not explain why these phenomena
happen, they simply describe them.
Section
Section Check
1.1
Question 1
The potential energy, PE, of a body of mass, m, raised to a height, h,
is expressed mathematically as PE = mgh, where g is the
gravitational constant. If m is measured in kg, g in m/s2, h in m, and
PE in joules, then what is 1 joule described in base unit?
A. 1 kg·m/s
B. 1 kg·m/s2
C. 1 kg·m2/s
D. 1 kg·m2/s2
Section
Section Check
1.1
Answer 1
Answer: D
Reason:
Section
Section Check
1.1
Question 2
A car is moving at a speed of 90 km/h. What is the speed of the car
in m/s? (Hint: Use Dimensional Analysis)
A. 2.5×101 m/s
B. 1.5×103 m/s
C. 2.5 m/s
D. 1.5×102 m/s
Section
Section Check
1.1
Answer 2
Answer: A
Reason:
Section
Section Check
1.1
Question 3
Which of the following representations is correct when you solve
0.030 kg + 3333 g using scientific notation?
A. 3.333×103 g
B. 3.36×103 g
C. 3×103 g
D. 3363 g
Section
Section Check
1.1
Answer 3
Answer: A
Reason: When you compare place value. The only place value they
have in common is the ones place.
3333
+ 0.030
3333.030 we can only report 3333 as our most precise value.
Section
1.2
Measurement
In this section you will:
Distinguish between accuracy and precision.
Determine the precision of measured quantities.
Section
1.2
Measurement
14.)What is a Measurement?
A measurement is a
comparison between
an unknown quantity
and a standard.
Section
1.2
Measurement
Are these three measurements
in agreement with each other?
.
Section
1.2
Measurement
Comparing Results
When a measurement is made, the results often are reported
with an uncertainty.
Therefore, before fully accepting a new data, other scientists
examine the experiment, looking for possible sources of errors,
and try to reproduce the results.
A new measurement that is within the margin of uncertainty
confirms the old measurement.
Section
1.2
Measurement
Precision Versus Accuracy
Click image to view the movie.
Section
1.2
Measurement
15.) What is precision?
The degree of exactness. How repeatable a
value is.
Student 3 is the most precise because the it
has the smallest amount of uncertainty.
Generally precision is ½ of the
Smallest division of the
Instrument.
Section
1.2
Measurement
16.) What is accuracy?
A description of how well the results of a
measurement agree with the “real” value.
Section
1.2
Measurement
17.) What is two point calibration?
A method for checking the accuracy of an
instrument.
Section
1.2
Techniques of Good Measurement
18.) What is a parallax?
The apparent shift in the
position of an object when
viewed from a different angle.
Section
1.2
Measurement
Techniques of Good Measurement
Scales should be read with
one’s eye directly above the
measure.
If the scale is read from an
angle, as shown in figure (b),
you will get a different, and
less accurate, value.
The difference in the readings
is caused by parallax, which is
the apparent shift in the
position of an object when it is
viewed from different angles.
(a)
(b)
Section
Section Check
1.2
Question 1
Ronald, Kevin, and Paul perform an experiment to determine the
value of acceleration due to gravity on the Earth (980 cm/s2). The
following results were obtained: Ronald - 961 ± 12 cm/s2, Kevin - 953
± 8 cm/s2, and Paul - 942 ± 4 cm/s2.
Justify who gets the most accurate and precise value.
A. Kevin got the most precise and accurate value.
B. Ronald’s value is the most accurate, while Kevin’s value is the
most precise.
C. Ronald’s value is the most accurate, while Paul’s value is the
most precise.
D. Paul’s value is the most accurate, while Ronald’s value is the
most precise.
Section
Section Check
1.2
Answer 1
Answer: C
Reason: Ronald’s answer is closest to 980 cm/s2 and hence his
result is the most accurate. Paul’s measurement is the
most precise within 4 cm/s2.
Section
Section Check
1.2
Question 2
What is the precision of an instrument?
A. The smallest division of an instrument.
B. The least count of an instrument.
C. One-half of the least count of an instrument.
D. One-half of the smallest division of an instrument.
Section
Section Check
1.2
Answer 2
Answer: D
Reason: Precision depends on the instrument and the technique
used to make the measurement. Generally, the device with
the finest division on its scale produces the most precise
measurement. The precision of a measurement is one-half
of the smallest division of the instrument.
Section
Section Check
1.2
Question 3
A 100-cm long rope was measured with three different scales. The
answer obtained with the three scales were:
1st scale - 99 ± 0.5 cm, 2nd scale - 98 ± 0.25 cm, and 3rd scale - 99 ±
1 cm. Which scale has the best precision?
A. 1st scale
B. 2nd scale
C. 3rd scale
D. Both scale 1 and 3
Section
Section Check
1.2
Answer 3
Answer: B
Reason: Precision depends on the instrument. The measurement of
the 2nd scale is the most precise within 0.25 cm.
Section
Graphing Data
1.3
In this section you will:
Graph the relationship between independent and dependent
variables.
Interpret graphs.
Recognize common relationships in graphs.
Section
Graphing Data
1.3
19.) What is a variable?
A variable is any factor that might affect
the behavior of an experimental setup.
.
Section
Graphing Data
1.3
Graphing Data
Click image to view the movie.
Section
Graphing Data
1.3
20.) What is the independent variable?
.
The factor that is changed or
manipulated by the experimenter during
the experiment.
Section
Graphing Data
1.3
21.) What is the dependent variable?
The factor that depends on the
independent variable.
.
Section
1.3
Graphing Data
22.) Where are the dependent and
independent variables placed on a
graph?
The independent
.
variable is placed on the
x axis.
The dependent variable
is placed on the y axis
Section
1.3
Graphing Data
23.) What is the line of best fit?
The line that is drawn as
close to all the data
points
as possible. The
.
line of best fit is used for
predictions.
Section
1.3
Graphing Data
Linear Relationships
Scatter plots of data may take many different shapes, suggesting
different relationships.
Section
Graphing Data
1.3
24.) What is a linear relationship?
When the line of best fit is a straight
line.
The relationship can be
written as an equation.
b is the y intercept
m is the slope
Section
1.3
Graphing Data
Linear Relationships
The slope is the ratio of the
vertical change to the
horizontal change. To find the
slope, select two points, A and
B, far apart on the line. The
vertical change, or rise, Δy, is
the difference between the
vertical values of A and B. The
horizontal change, or run, Δx,
is the difference between the
horizontal values of A and B.
Section
Graphing Data
1.3
25.) What is slope?
Slope is the ratio of the vertical change to the
horizontal change.
Slope is easy and fun, its simply rise over run.
m= rise / run
m= Δy / Δx
Note : Δ (delta) means “change in”
Section
1.3
Graphing Data
If y gets smaller when x
gets larger the slope is
negative.
If y gets larger when x
gets larger the slope is
positive.
Section
1.3
Graphing Data
Nonlinear Relationships
When the graph is not a straight line, it means that the
relationship between the dependent variable and the independent
variable is not linear.
26.) What are two types of nonlinear
graphs ( graphs that are not straight lines)?
There are many types of nonlinear relationships
in science. Two of the most common are the
quadratic and inverse relationships.
Section
1.3
Graphing Data
27.) What is a quadratic relationship?
A quadratic relationship
exists when one variable
depends on the square of
another.
A quadratic relationship
can be represented by the
following equation:
The graph shown in the figure
is a quadratic relationship.
Section
1.3
Graphing Data
28.) What is an inverse relationship?
In an inverse relationship, a
hyperbola results when one
variable depends on the inverse
of the other.
An inverse relationship
can be represented by
the following equation:
The graph in the figure shows how the current i
an electric circuit varies as the resistance is
increased. This is an example of an inverse
relationship.
Section
1.3
Graphing Data
Nonlinear Relationships
There are various mathematical models available apart from the
three relationships you have learned. Examples include:
sinusoids—used to model cyclical phenomena; exponential
growth and decay—used to study radioactivity
Combinations of different mathematical models represent even
more complex phenomena.
Section
Graphing Data
1.3
Predicting Values
Relations, either learned as formulas or developed from graphs,
can be used to predict values you have not measured directly.
Physicists use models to accurately predict how systems will
behave: what circumstances might lead to a solar flare, how
changes to a circuit will change the performance of a device, or
how electromagnetic fields will affect a medical instrument.
Section
Section Check
1.3
Question 1
Which type of relationship is shown
following graph?
A. Linear
C. Parabolic
B. Inverse
D. Quadratic
Section
Section Check
1.3
Answer 1
Answer: B
Reason: In an inverse relationship a hyperbola results when one
variable depends on the inverse of the other.
Section
Section Check
1.3
Question 2
What is line of best fit?
A. The line joining the first and last data points in a graph.
B. The line joining the two center-most data points in a graph.
C. The line drawn close to all data points as possible.
D. The line joining the maximum data points in a graph.
Section
Section Check
1.3
Answer 2
Answer: C
Reason: The line drawn closer to all data points as possible, is called
a line of best fit. The line of best fit is a better model for
predictions than any one or two points that help to
determine the line.
Section
Section Check
1.3
Question 3
Which relationship can be written as y = mx?
A. Linear relationship
B. Quadratic relationship
C. Parabolic relationship
D. Inverse relationship
Section
Section Check
1.3
Answer 3
Answer: A
Reason: Linear relationship is written as y = mx + b, where b is the y
intercept. If y-intercept is zero, the above equation can be
rewritten as y = mx.
Section
1.3
Graphing Data
End of Chapter
Section
1.1
Mathematics and Physics
Electric Current
The potential difference, or voltage, across a circuit equals the
current multiplied by the resistance in the circuit. That is, V (volts) = I
(amperes) × R (ohms). What is the resistance of a lightbulb that has
a 0.75 amperes current when plugged into a 120-volt outlet?
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