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Transcript of Physics
compare other quantities to.
- For example centimeters and inches are both units
and they can be compared because 10 centimeters
equals one inch
- All measurements must have a standard quantity. - The SI system contains universally accepted units
for scientific measurements.
- There are 7 fundamental units in Physics
-Derived units are combinations of 2 or more
fundamental units. The SI System What is a Unit? Symbols for Units and Quantities - SI units are symbolized with letters. But be
careful because some of the unit symbols are
also used to symbolize formulas.
- For example: A can be ampere
or area. SI Prefixes - SI prefixes are prefixes combined
with SI base units to form new units that are larger or smaller than the base units by a multiple or sub multiple of 10. - For example a 1000 meters can become 1 km Or 0.01 meter can be expressed as 1 centimeter Tools for
- Sin θ = a/c
- Cos θ = b/c
- Tan θ = a/b
- Knowing the length of any two sides
of a right triangle is enough to figure
out the length of the third side using the
Pythagorean theorem. The Pythagorean
theorem uses the formula:
c = a + b Measuring an Angle
- A common unit for measuring
angles is degree (°). The protractor is an
instrument used for measuring angles in degrees
- - Is the branch of mathematics that treats the
relationships between angles and sides of triangles.
Basic trigonometric relationships are used to solve
some types of physics problems
- Important ratios of the sides of a
right triangle in terms of angle
θ include the following: Measuring Length
- Length is commonly measured in the Metric
System with the unit being meters (m). Occasionally
centimeters are more appropriate
- Mass is the amount of matter an object contains,
it can be measured with an electronic balance or
a triple-beam balance
- A mass determined in grams can be
converted to kilograms (kg) by
dividing by 1000 Tools for Measurement Uncertainty
Measurement - Before Adding/Subtracting/Multiplying/Dividing values, they must have the same units.
- After Adding/Subtracting sum or difference is rounded to the same
decimal point value as the least sensitive measurement.
- When Multiplying/Dividing values, the answer is rounded to the
same number of SigFigs as the lowest value SigFigs in the given.
*The product can only have 2 SigFigs, since 2.6 is the smallest
value of SigFigs. Add, Subtract, Multiply, Divide with measured values Digits that are known with certainty plus the one digit whose value has been estimated are called Significant Digits.
Non-zero numbers are always significant.
The following rules apply in order to the zeroes in a measured value
1)Zeroes before a non-zero are not Significant. (0.002) 1SigFig.
2)Zeroes between non-zero digits are Significant. (0.706) 3SigFigs
3)Zeroes that appear after a nonzero digit are significant only if
a)followed by a decimal.
ex. (40s) 1SigFig.
b)appear right of the decimal point.
ex. (37.0cm) 3SigFigs
(4.100m) 4SigFigs Significant Digits Every measurement has an experimental uncertainty
Uncertainty comes from:
1)Limitation of the measuring Instrument
2)Skill of the person using the instrument
3)Number of Measurements made
If several measurements are made and are nearly identical, the measurements are Precise.
If the measurements are very close to the accepted value
found in a handbook, the measurement is Accurate. Uncertainty in Measurements Scientific
Experimental Designs Graphing Scalar
Vector Quantities Scalar Quantities speed mass work power temperature energy -Physical quantities are put in two categories; scalar and vector quantities.
-A scalar quantity only has magnitude. For example, a scalar quantity would be the measurement of time or mass (ex: 5 seconds; 5 grams). A scalar quantity must have a number with an appropriate unit.
-When adding or subtracting scalar quantities, we use the rules of arithmetic.
-A vector quantity is made up of magnitude and direction. For example, a vector quantity would be the measurement of velocity because it is expressed with a proper unit as well as direction (ex: 5 meters per second, due south).
-When adding or subtracting vector quantities, we use algebraic or geometric methods. Scalar and Vector Quantities Vector Quantities Displacement Weight Force Momentum Velocity Acceleration The velocity of the ball, however, would be a vector quantity because it has magnitude and direction. For example the velocity of the football could be 23 m/s,
due north. . The speed of the ball is a scalar quantity because it doesn't have direction. Speed only measures how fast an object is going. So the speed of the ball could be 23 m/s. Solving Equations
While Using Algebra Solving Equations Using Algebra The six statements used to solve the equations for an unknown quantity are:
When equals are added, they have equal sums.
When equals are subtracted, they have equal remainders.
When equals are multiplied, they have equal products.
When equals are divided, they have equal quotients.
A quantity may be substituted for its equal.
Like powers or roots of equals are equal.
Also, the order of PEMDAS must be used to solve equations for quantities. Credit: Nishat Anjum: Power Point Presentation & Units Nakita Andrews: All Sample Problems Dimensional Analysis - Units on the left side of an equation must always be equivalent to the the units on the right side.
- Quantities can be added or subtracted only if they have the same
units. - Elapsed time can be measured with a
clock or a stopwatch because most events
measured in physics occurs quickly, the unit for
time is measured by seconds (s) Measuring Time Measuring Force - A force is a push or pull on a mass. Forces are
measured with a spring scale, being measured in
Newtons (N). Newtons is a derived
unit from Kg*m/s 2 2 2 2 Add, Subtract, Multiply, Divide
with measured values Percent Error:
- Deals with experimental value and
the most probable value or accepted value.
- Absolute error-the difference between an
experimental value and the accepted value.
- Percent error-a formula that can be
calculated as show below: (x meaning multiply)
Accepted value Data Analysis:
- In an experiment, multiple measurements are made
of a given or identical event.
- Range-the difference between the highest and lowest value
in the data set.
- Mean-the average of a set of “n” measurements.
- Variance-the sum of squares of the differences of the
measurements from the mean, divided by the number of
- Standard Deviation-the square root of the variance. Evaluating Experimental
Results ***Refer to page 14 in your Physics Review Book to see the formulas for these terms*** X 100 Data Two quantities have an indirect
squared proportion if an increase in one
causes a squared decrease in the other.
Directly proportional: y=2x
Inversely proportional: y=12/x
Constant proportion: y=6
Direct squared proportion: y=x
Indirect squared proportion: y=12/x There are several relationships that exist
between quantities measured in physics.
- Two quantities are directly proportional if an
increase in on causes an increase in the other
- Two quantities are inversely proportional if an
increase in one causes a decrease in the other.
- Two quantities have a constant proportion if an
increase in one causes no change in the other.
- Two quantities have a direct squared
proportion if an increase in one causes
a square increase in the other. Mathematical
Relationships Sometimes the line of best fit is extrapolated
which means it is extended beyond the region in
which date was taken.
The inclination of a graphed line is called the
slope. Formula: Extrapolation After you plot the data points on the graph, a line of best fit must be drawn.
Line of best fit: is a straight or curved line which approximates the relationship among a set data points. It usually does not pass through all measured points. Independent variable- the variable that the experimenter
changes. Its graphed on the x-axis.
Dependent- the one that changes as a result of the changes
made by the experimenter. Its graphed on the y-axis.
Graphs are titled as the dependent variable versus the
independent variable. Making a Graph In physics, data collected in experiments is usually represented
by graphical form. Graphing Data 2 2 Question 1
Write in scientific notation: 0.000467 and 32000000
Express 5.43 x 10-3 as a number.
(4.5 x 10-14) x (5.2 x 103) = ?
(6.1 x 105)/(1.2 x 10-3) = ?
(3.74 x 10-3)4 = ?
The fifth root of 7.20 x 1022 = ?
Now remember, just count the zeros. It’s that easy! Questions Multiplication
- When multiplying, we multiply the numbers, add the exponents
1.2 x 104 multiplied by 5 x 106 = 6 x 1010
- When dividing, we divide the numbers, subtract the
exponents 5.5 x 108 divided by 1.1 x 102 = 5 x 106 Multiplying and Dividing Scientific Notation When adding and subtracting the numbers must be expressed in the same power of ten and the same unit!
= 0.32 x 103m + 4.73 x 103 m
3.2 x 102 m + 4.73 x 103 m
= 5.05 x 103m
The same goes for subtraction… Adding and Subtracting Scientific Notation The number is written as a number between 1
and 10 multiplied by 10 raised to a power.
The power of 10 depends on:
- The number of places the decimal point is moved.
- The direction the decimal point is moved.
Left Positive exponent
Right Negative exponent Scientific notation is a way to express very large or very small values. Index Finger Width:
=1.0 x 10-5 km
Representing Small Numbers Number between
1 and 10 Appropriate power
of ten Average Distance from the Earth to the Sun
is approximately 150,000,000 km = 1.5x108 km
150,000,000 = 1.5 x 100,000,000
= 1.5 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
= 1.5 x 108 Representing large numbers Radius of a Hydrogen
= 5.29 x 1011 John Aguinaldo: Uncertainty in Measurements Simbi Akanni: Scientific Measurement Stephen Alexander Tools For Measurement Lejla Bolevic Scalar and vector quantities
& Jeopardy Alex Ab: Graphing Data Cassidy Bello Solving Equations Using Algebra Evaluating Experimental Results
& Handouts Nicole Bianco
Cook, Bernadine. "Topic 1: Measurement
and Mathematics." Brief Review in
Physics: The Physical Setting. 2013
ed. Needham, MA: Prentice Hall, 2003.
1-22. Print. Works Cited