CHABOT COLLEGE CISCO NETWORKING ACADEMY Chabot College Semester 3 Novell IPX.
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![Page 1: Copyright Pearson Education Inc – Modified 8/15 by Scott Hildereth, Chabot College. PowerPoint ® Lectures for University Physics, Thirteenth Edition –](https://reader035.fdocuments.us/reader035/viewer/2022070415/56649e8a5503460f94b8fe5f/html5/thumbnails/1.jpg)
Copyright Pearson Education Inc – Modified 8/15 by Scott Hildereth, Chabot College.
PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman
Chapter 1
Units, Physical Quantities, and Vectors
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Three KEYS for Chapter 1
• Fundamental quantities in physics (length, mass, time)
– Units (meters, kilograms, seconds...)
– Dimensional Analysis
• Force = kg meter/sec2
• Power = Force x Velocity
= kg m2/sec3
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Three KEYS for Chapter 1
• Fundamental quantities in physics (length, mass, time)
– Units (meters, kilograms, seconds...)
– Dimensional Analysis
• Significant figures in calculations
– 6.696 x 104 miles/hour
– 67,000 miles hour
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Three KEYS for Chapter 1
• Fundamental quantities in physics (length, mass, time)
– Units (meters, kilograms, seconds...)
– Dimensional Analysis
• Significant figures in calculations
• Vectors (magnitude, direction, units) 5 m/s at 45°
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What you MUST be able to do…
• Vectors & Vector mathematics
• vector components Ex: v = velocity
• vx = v cosis the “x” component
• vy = v sinis the “y” component
• |v|2 = (vx)2 + (vy)2 5 m/s at 45°
3.54 m/s in “x”
3.54 m/s in “y”
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What you MUST be able to do…
• Vectors & Vector mathematics
– vector components Ex: v = velocity; vx = v cos
– unit vectors (indicating direction only)vx =
vy =
– Adding, subtracting, & multiplying vectors
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Standards and units
• Length, mass, and time = three fundamental quantities (“dimensions”) of physics.
• The SI (Système International) is the most widely used system of units.
– Meeting ISO standards are mandatory for some industries. Why?
• In SI units, length is measured in meters, mass in kilograms, and time in seconds.
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Unit consistency and conversions
• An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”)
• OK: 5 meters/sec x 10 hours =~ 2 x 102 km
(distance/time) x (time) = distance
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Unit consistency and conversions
• An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”)
• OK: 5 meters/sec x 10 hours =~ 2 x 102 km
5 meters/sec x 10 hour x (3600 sec/hour)
= 180,000 meters = 180 km = ~ 2 x 102 km
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Unit consistency and conversions
• An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”)
• OK: 5 meters/sec x 10 hours =~ 2 x 102 km
• NOT: 5 meters/sec x 10 kg = 50 Joules
(velocity) x (mass) = (energy)
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Unit prefixes
• Table 1.1 shows some larger and smaller units for the fundamental quantities.
• Learn these – and prefixes like Mega, Tera, Pico, etc.!
• Skip Ahead to Slide 24 – Sig Fig Example
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Measurement & Uncertainty
No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.
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• The precision – and also uncertainty - of a measured quantity is indicated by its number of significant figures.
–Ex: 8.7 centimeters
• 2 sig figs
• Specific rules for significant figures exist
• In online homework, sig figs matter!
Measurement & Uncertainty
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Significant Figures
Number of significant figures = number of “reliably known digits” in a number.
Often possible to tell # of significant figures by the way the number is written:
• 23.21 cm = four significant figures.
• 0.062 cm = two significant figures (initial zeroes don’t count).
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Numbers ending in zero are ambiguous. Does the last zero mean uncertainty to a factor of 10, or just 1?
Is 20 cm precise to 10 cm, or 1? We need rules!
• 20 cm = one significant figure(trailing zeroes don’t count w/o decimal point)
• 20. cm = two significant figures(trailing zeroes DO count w/ decimal point)
• 20.0 cm = three significant figures
Significant Figures
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Rules for Significant Figures
•When multiplying or dividing numbers, or using functions, result has as many sig figs as term with fewest (the least precise).
•ex: 11.3 cm x 6.8 cm = 77 cm.
•When adding or subtracting, answer is no more precise than least precise number used.
• ex: 1.213 + 2 = 3, not 3.213!
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Significant Figures
•Calculators will not give right # of sig figs; usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point).
•top image: result of 2.0/3.0
•bottom image: result of 2.5 x 3.2
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Scientific Notation
•Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown.
•Ex: cannot easily tell how many significant figures in “36,900”.
•Clearly 3.69 x 104 has three; and 3.690 x 104 has four.
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Measurement & Uncertainty
No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.
Photo illustrates this – it would be difficult to measure the width of this board more accurately than ± 1 mm.
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Uncertainty and significant figures
• Every measurement has uncertainty
–Ex: 8.7 cm (2 sig figs)
• “8” is (fairly) certain
• 8.6? 8.8?
• 8.71? 8.69?
• Good practice – include uncertainty with every measurement!
–8.7 0.1 meters
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Uncertainty and significant figures
• Uncertainty should match measurement in the least precise digit:
–8.7 0.1 centimeters
–8.70 0.10 centimeters
–8.709 0.034 centimeters
–8 1 centimeters
• Not…
–8.7 +/- 0.034 cm
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Relative Uncertainty
•Relative uncertainty: a percentage, the ratio of uncertainty to measured value, multiplied by 100.
•ex. Measure a phone to be 8.8 ± 0.1 cm
What is the relative uncertainty in this measurement?
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Uncertainty and significant figures
• Physics involves approximations; these can affect the precision of a measurement.
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Uncertainty and significant figures
• As this train mishap illustrates, even a small percent error can have spectacular results!
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Conceptual Example: Significant figures
Using a protractor, you measure an angle to be 30°.
(a) How many significant figures should you quote in this measurement?
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Conceptual Example: Significant figures
Using a protractor, you measure an angle to be 30°.
(a) How many significant figures should you quote in this measurement? What uncertainty?
2 sig figs! (30. +/- 1 degrees or 3.0 x 101 +/- 1 degrees)
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Conceptual Example: Significant figures
Using a protractor, you measure an angle to be 30°.
(b) What result would a calculator give for the cosine of this result? What should you report?
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Conceptual Example: Significant figures
Using a protractor, you measure an angle to be 30°.
(b) What result would a calculator give for the cosine of this result? What should you report?
0.866025403, but to two sig figs, 0.87!
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Key Concepts for the Day!
Class Calendar
Mastering Physics Intro Assignment Results
Precision vs. Accuracy
Vectors
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1-3 Accuracy vs. Precision
Accuracy is how close a measurement comes to the true value.
ex. Acceleration of Earth’s gravity = 9.81 m/sec2
Your experiment produces 10 ± 1 m/sec2
• You were accurate! How accurate? Measured by ERROR.
• |Actual – Measured|/Actual x 100%
• | 9.81 – 10 | / 9.81 x 100% = 1.9% Error
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Accuracy vs. Precision
•Accuracy is how close a measurement comes to the true value
• established by % error
•Precision is a measure of repeatability of the measurement using the same instrument.
• established by uncertainty in a measurement
• reflected by the # of significant figures
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Accuracy vs. Precision
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Accuracy vs. Precision
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Accuracy vs. Precision ?
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Accuracy vs. Precision ?
Use least-squares fit to find line that minimizes deviation
Large error bars (uncertainty in
measurements) = not very precise…
Lots of data IMPROVES fit
and overall precision
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Accuracy vs. Precision Example
•Example:
You measure the acceleration of Earth’s gravitational force in the lab, which is accepted to be 9.81 m/sec2
• Your experiment produces 8.334 m/sec2
•Were you accurate? Were you precise?
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Accuracy vs. Precision
Accuracy is how close a measurement comes to the true value. (established by % error)
ex. Your experiment produces 8.334 m/sec2
for the acceleration of gravity (9.81 m/sec2)
Accuracy: (9.81 – 8.334)/9.81 x 100% = 15% error
Is this good enough? Only you (or your boss/customer) know for sure!
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Accuracy vs. Precision
Precision is the repeatability of the measurement using the same instrument.
ex. Your experiment produces 8.334 m/sec2
for the acceleration of gravity (9.81 m/sec2)
Precision indicated by 4 sig figs
Seems (subjectively) very precise – and precisely wrong!
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Accuracy vs. Precision
Better Technique: Include uncertainty
Your experiment produces
8.334 m/sec2 +/- 0.077 m/sec2
Your relative uncertainty is
.077/8.334 x 100% = ~1%
But your error was ~ 15%
NOT a good result!
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Accuracy vs. Precision
Better Technique: Include uncertainty
Your experiment produces
8.3 m/sec2 +/- 1.2 m/sec2
Your relative uncertainty is
1.2 / 8.3 x 100% = ~15%
Your error was still ~ 15%
Much more reasonable a result!
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Accuracy vs. Precision
•Precision is a measure of repeatability of the measurement using the same instrument.
• established by uncertainty in a measurement
• reflected by the # of significant figures
• improved by repeated measurements!
•Statistically, if each measurement is independent
• make n measurements (and n> 10)
•Improve precision by √(n-1)
• Make 10 measurements, % uncertainty ~ 1/3
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1-6 Order of Magnitude: Rapid Estimating
Quick way to estimate calculated quantity:
• round off all numbers in a calculation to one significant figure and then calculate.
• result should be right order of magnitude
• expressed by rounding off to nearest power of 10
• 104 meters
• 108 light years
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Order of Magnitude: Rapid Estimating
Example: 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.
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Order of Magnitude: Rapid Estimating
Example: Volume of a lake
Volume = x r2 x depth
= ~ 3 x 500 x 500 x 10
= ~75 x 105
= ~ 100 x 105
= ~ 107 cubic meters
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Order of Magnitude: Rapid Estimating
Example: Volume of a lake
Volume = x r2 x depth
= 7,853,981.634 cu. m
~ 107 cubic meters
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1-6 Order of Magnitude: Rapid Estimating
Example: Thickness of a page.
Estimate the thickness of a page of your textbook.
(Hint: you don’t need one of these!)
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Solving problems in physics
• The textbook offers a systematic problem-solving strategy with techniques for setting up and solving problems efficiently and accurately.
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Solving problems in physics
• Step 1: Identify relevant concepts, variables, what is known, what is needed, what is missing.
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Solving problems in physics
• Step 2: Set up the Problem – MAKE a SKETCH, label it, act it out, model it, decide what equations might apply. What units should the answer have? What value?
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Solving problems in physics
• Step 3: Execute the Solution, and EVALUATE your answer! Are the units right? Is it the right order of magnitude? Does it make SENSE?
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Solving problems in physics
• Good problems to gauge your learning
– “Test your Understanding” Questions throughout the book
– Conceptual “Clicker” questions linked online
– “Two dot” problems in the chapter
• Good problems to review before exams
– BRIDGING Problem @ end of each chapter ***
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Vectors and scalars
• A scalar quantity can be described by a single number, with some meaningful unit
• 4 oranges
• 20 miles
• 5 miles/hour
• 10 Joules of energy
• 9 Volts
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Vectors and scalars
• A scalar quantity can be described by a single number with some meaningful unit
• A vector quantity has a magnitude and a direction in space, as well as some meaningful unit.
• 5 miles/hour North
• 18 Newtons in the “x direction”
• 50 Volts/meter down
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Vectors and scalars
• A scalar quantity can be described by a single number with some meaningful unit
• A vector quantity has a magnitude and a direction in space, as well as some meaningful unit.
• To establish the direction, you MUST first have a coordinate system!
• Standard x-y Cartesian coordinates common
• Compass directions (N-E-S-W)
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Drawing vectors
• Draw a vector as a line with an arrowhead at its tip.
• The length of the line shows the vector’s magnitude.
• The direction of the line shows the vector’s direction relative to a coordinate system (that should be indicated!)
x
y
z
5 m/sec at 30 degrees from the
x axis towards y in the xy plane
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Drawing vectors
• Vectors can be identical in magnitude, direction, and units, but start from different places…
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Drawing vectors
• Negative vectors refer to direction relative to some standard coordinate already established – not to magnitude.
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Adding two vectors graphically
• Two vectors may be added graphically using either the head-to-tail method or the parallelogram method.
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Adding two vectors graphically
• Two vectors may be added graphically using either the head-to-tail method or the parallelogram method.
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Adding two vectors graphically
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Adding more than two vectors graphically
• To add several vectors, use the head-to-tail method.
• The vectors can be added in any order.
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Adding more than two vectors graphically—Figure 1.13
• To add several vectors, use the head-to-tail method.
• The vectors can be added in any order.
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Subtracting vectors
• Reverse direction, and add normally head-to-tail…
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Subtracting vectors
• Figure 1.14 shows how to subtract vectors.
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Multiplying a vector by a scalar
• If c is a scalar, the product cA has magnitude |c|A.
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Addition of two vectors at right angles
• First add vectors graphically.
• Use trigonometry to find magnitude & direction of sum.
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Addition of two vectors at right angles
• Displacement (D) = √(1.002 + 2.002) = 2.24 km
• Direction = tan-1(2.00/1.00) = 63.4º East of North
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Note how the final answer has THREE things!
• Answer: 2.24 km at 63.4 degrees East of North
• Magnitude (with correct sig. figs!)
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Note how the final answer has THREE things!
• Answer: 2.24 km at 63.4 degrees East of North
• Magnitude (with correct sig. figs!)
• Units
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Note how the final answer has THREE things!
• Answer: 2.24 km at 63.4 degrees East of North• Magnitude (with correct sig. figs!)
• Units
• Direction
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Components of a vector
• Represent any vector by an x-component Ax and a y-component Ay.
• Use trigonometry to find the components of a vector: Ax = Acos θ and Ay = Asin θ, where θ is measured from the +x-axis toward the +y-axis.
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Positive and negative components
• The components of a vector can be positive or negative numbers.
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Finding components
• We can calculate the components of a vector from its magnitude and direction.
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Calculations using components
• We can use the components of a vector to find its magnitude and direction:
• We can use the components of a set of vectors to find the components of their sum:
2 2 and tan yx y
x
AA A A
A
, x x x x y y y yR A B C R A B C
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Adding vectors using their components
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Unit vectors
• A unit vector has a magnitude of 1 with no units.
• The unit vector î points in the +x-direction, points in the +y-direction, and points in the +z-direction.
• Any vector can be expressed in terms of its components as A =Axî+ Ay + Az .jj
kk
jj
kk
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The scalar product
The scalar product of two vectors (the “dot product”) is
A · B = ABcos
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The scalar product
The scalar product of two vectors (the “dot product”) is
A · B = ABcos
Useful for
•Work (energy) required or released as force is applied over a distance (4A)
•Flux of Electric and Magnetic fields moving through surfaces and volumes in space (4B)
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Calculating a scalar product
By components, A · B = AxBx + AyBy + AzBz
Example: A = 4.00 m @ 53.0°, B = 5.00 m @ 130°
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Calculating a scalar product
By components, A · B = AxBx + AyBy + AzBz
Example: A = 4.00 m @ 53.0°, B = 5.00 m @ 130°
Ax = 4.00 cos 53 = 2.407
Ay = 4.00 sin 53 = 3.195
Bx = 5.00 cos 130 = -3.214
By = 5.00 sin 130 = 3.830
AxBx + AyBy = 4.50 meters
A · B = ABcoscos(130-53) = 4.50 meters2
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The vector product
•The vector product (“cross product”) A x B of two vectors is a vector
•Magnitude = AB sin
•Direction = orthogonal (perpendicular) to A and B, using the “Right Hand Rule”
A
B
A x B
x
y
z
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The vector cross product
The cross product of two vectors is
A x B (with magnitude ABsin
Useful for
•Torque from a force applied at a distance away from an axle or axis of rotation (4A)
•Calculating dipole moments and forces from Magnetic Fields on moving charges (4B)
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The vector product
• The vector product (“cross product”) of two vectors has magnitude
and the right-hand rule gives its direction.
| | sin
ABA B