Physics 201 General Physics Prof. Susan Coppersmith Prof. Albrecht Karle

Course information • Course homepage • Let’s have a quick look: • http://www.physics.wisc.edu/undergrads/courses/ fall09/201/ – Find there detailed information on syllabus, homework, exams, grading, discussion, labs

• Syllabus: – – – –

Lectures: Typically 1 Chapter per week from textbook Two discussion sessions One Lab One homework (Always due on Thursdays)

Textbook, e-book and WebAssign • The textbook is available in electronic form as an e-book. – Paul Tipler and Gene Mosca, Physics for Scientists and Engineers, 6th ed. – You can read it from any computer with access to internet. http://webassign.net/login.html. – This is by far the cheapest solution. If you like to buy it in real

paper, it is also available as softcover in 2 volumes (this course covers the 1st volume)

• WebAssign:

– This is our homework assignment system. Problems are taken from the textbook but numbers are randomized. – Let’s have a quick look into WebAssign: – Intro to WebAssign – Student Guide to WebAssign ©2008 by W.H. Freeman and Company

Discussions, Labs TA’s Our team of Teaching Assistants will be your instructors in discussions and labs: Sections Your TA -------------------------------• 301 302 Eunsong Choi • 303 309 Jialu Yu • 304 310 Jared Schmitthenner • 305 311 Andrew Long • 306 307 Daniel Schroeder

Office hours Monday 4:20pm – 5:10pm Tuesday 10:45am – 11:45am 11am – 11:50am 1:20pm – 2:10pm 2:25pm – 3:15pm Wednesday 11am – 11:50am 4:20pm – 5:10pm Thursday 11am – 11:50am 12:05pm – 12:55pm 1:20pm – 2:10pm 2:25pm – 3:15pm 2:30pm – 3:30pm (best by appointment)

Jared Prof. Coppersmith Dan Jialu Andrew Eunsong Jared Dan Eunsong Jialu Andrew Prof. Karle

Nature of Science Theory and observation Theories are made to explain observations. Theories will make predictions, (so that they are testable). Observations and experiments are used to test if the prediction is accurate. The cycle continues. In history, physics and astronomy, have set the ground rules of modern science. ©2008 by W.H. Freeman and Company

Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC) • Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question.) • He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan) • From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision. • An example of great science!

Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC) • Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question) • He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan) • From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision. • An example of great science!

Units • Physical quantities have units! • Example: Unit of length

– Eratosthenes used the unit stadion. (The hellenic stadion was pretty big: 185m) – In the Middle ages many kingdoms had different definitions of a foot, etc.

• Today, the scientific community uses the SI system of units. There are 7 basic units, such as

– Length: Meter (Based on the speed of light: length of path traveled by light in 1/299,792,458s) – Mass: kg (Platinum cylinder in International Bureau of Weights and Measures, Paris) – Time: s (Time required for 9,192,631,770 periods of radiation emitted by cesium atoms.)

SI Units SI Base quantities Length

meter

m

Time

second

s

Mass

kilogram

kg

Electric Current

ampere

A

Temperature

kelvin

K

Amount of substance

mole

mol

Luminous intensity

candela

cd

©2008 by W.H. Freeman and Company

Prefixes • Depending on the scale one often likes to use prefixes. • Example, for length it is convenient to use km = 1000m when traveling by car, or nm=10^-9m when discussing molecular scale objects.

Conversions • Conversions between units are very helpful. The use of different units has again and again lead to errors, sometimes with bad consequences. • The conversion of units is also a frequent source of errors engineering and science (and exams). • But it is easy to avoid. • Avoid skipping the units (for example because it is less writing time) – Are all the ingredients for a problem in the same units? If not, it is good practice to perform the conversion, before doing any algebra. – Basic SI units are always safe – It is OK to us km or nm, but need to take care that you don’t mix m and km – Develop good practice.

• We will expect that you give results with units, also in exams.

Derived quantities and dimensions

m2 m3

m/s

m/s2 N=kg•m/s2 N/m2=kg/m•s2 kg/m3 …

Measurement and Significant figures • A measurement has a precision (or error). • Measurement of the distance Earth – moon with laser pulse based on travel time of light. Error: a few cm! (position of the mirror) • What is the relative error?

The Greek astronomer Hipparch, ~200BC determined the distance of the moon to about ~70 Earth diameters, 5% precision, not too bad.

Measurement and Significant figures • A measurement has a precision (or error). • Significant figures reflect the precision of the measurement.

Example: • Pocket calculator • whiteboard, • WebAssign intro

Measurement and Significant figures • Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). • The top calculator shows the result of 2.0 / 3.0. • The bottom calculator shows the result of 2.5 x 3.2.

The universe by orders of magnitude

©2008 by W.H. Freeman and Company

Order of magnitude: Rapid Estimating A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Such back on the envelope estimates are very helpful for double checking a result of a calculation.

Diagrams are also very useful in making estimations.

Tire treads

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

How many grains of sand on a beach?

©2008 by W.H. Freeman and Company

Phys 201 Fall 2009 Tuesday, September 8, 2009 Chapter 1: Measurement and vectors

Review from last Dme: converDng units • Units in every equaDon have to match! It is a very good idea to keep units as well as numbers when solving equaDons.

The density of seawater was measured to be 1.07 g/cm3. This density in SI units is A. B. C. D. E.

1.07 kg/m3 (1/1.07) × 103 kg/m3 1.07 × 103 kg 1.07 × 10–3 kg 1.07 × 103 kg/m3

The density of seawater was measured to be 1.07 g/cm3. This density in SI units is A. 1.07 kg/m3 B. (1/1.07) × 103 kg/m3 C. 1.07 × 103 kg D. 1.07 × 10–3 kg E. 1.07 × 103 kg/m3

If K has dimensions ML2/T2, the k in K = kmv2 must A. B. C. D. E.

have the dimensions ML/T2. have the dimension M. have the dimensions L/T2. have the dimensions L2/T2. be dimensionless.

If K has dimensions ML2/T2, the k in K = kmv2 must A. have the dimensions ML/T2. B. have the dimension M. C. have the dimensions L/T2. D. have the dimensions L2/T2. E. be dimensionless.

Vectors • In one dimension, we can specify distance with a real number, including + or – sign. • In two or three dimensions, we need more than one number to specify how points in space are separated – need magnitude and direcDon. Madison, WI and Kalamazoo, MI are each about 150 miles from Chicago.

DenoDng vectors • Two of the ways to denote vectors: – Boldface notaDon: A – “Arrow” notaDon: A

€

Displacement is a vector

©2008 by W.H. Freeman and Company

Adding displacement vectors

©2008 by W.H. Freeman and Company

“Head‐to‐tail” method for adding vectors

©2008 by W.H. Freeman and Company

Vector addiDon is commutaDve

©2008 by W.H. Freeman and Company

Adding three vectors: vector addiDon is associaDve.

©2008 by W.H. Freeman and Company

A vector’s inverse has the same magnitude and opposite direcDon.

©2008 by W.H. Freeman and Company

SubtracDng vectors

©2008 by W.H. Freeman and Company

Example 1‐8. What is your displacement if you walk 3.00 km due east and 4.00 km due north?

©2008 by W.H. Freeman and Company

Components of a vector

©2008 by W.H. Freeman and Company

Components of a vector along x and y

©2008 by W.H. Freeman and Company

Magnitude and direcDon of a vector

©2008 by W.H. Freeman and Company

Adding vectors using components

©2008 by W.H. Freeman and Company

Cx = Ax + Bx Cy = Ay + By

Unit vectors A unit vector is a dimensionless vector with magnitude exactly equal to one.

©2008 by W.H. Freeman and Company

The unit vector along x is denoted The unit vector along y is denoted The unit vector along z is denoted

Which of the following vector equaDons correctly describes the relaDonship among the vectors shown in the ﬁgure?

A. B. C. D.

A+ B −C =0 A− B +C =0 A− B −C =0 A+ B +C =0

E. None of these is correct.

Which of the following vector equaDons correctly describes the relaDonship among the vectors shown in the ﬁgure?

A. B. C. D.

A+ B −C =0 A− B +C =0 A− B −C =0 A+ B +C =0

E. None of these is correct.

Can a vector have a component bigger than its magnitude? Yes No

Can a vector have a component bigger than its magnitude? • Yes • No The square of a magnitude of a vector R is given in terms of its components by R2 = Rx2 + Ry2 . Since the square is always positive, no component can be larger than the magnitude of the vector.

ProperDes of vectors: summary

©2008 by W.H. Freeman and Company

Course information • Course homepage • Let’s have a quick look: • http://www.physics.wisc.edu/undergrads/courses/ fall09/201/ – Find there detailed information on syllabus, homework, exams, grading, discussion, labs

• Syllabus: – – – –

Lectures: Typically 1 Chapter per week from textbook Two discussion sessions One Lab One homework (Always due on Thursdays)

Textbook, e-book and WebAssign • The textbook is available in electronic form as an e-book. – Paul Tipler and Gene Mosca, Physics for Scientists and Engineers, 6th ed. – You can read it from any computer with access to internet. http://webassign.net/login.html. – This is by far the cheapest solution. If you like to buy it in real

paper, it is also available as softcover in 2 volumes (this course covers the 1st volume)

• WebAssign:

– This is our homework assignment system. Problems are taken from the textbook but numbers are randomized. – Let’s have a quick look into WebAssign: – Intro to WebAssign – Student Guide to WebAssign ©2008 by W.H. Freeman and Company

Discussions, Labs TA’s Our team of Teaching Assistants will be your instructors in discussions and labs: Sections Your TA -------------------------------• 301 302 Eunsong Choi • 303 309 Jialu Yu • 304 310 Jared Schmitthenner • 305 311 Andrew Long • 306 307 Daniel Schroeder

Office hours Monday 4:20pm – 5:10pm Tuesday 10:45am – 11:45am 11am – 11:50am 1:20pm – 2:10pm 2:25pm – 3:15pm Wednesday 11am – 11:50am 4:20pm – 5:10pm Thursday 11am – 11:50am 12:05pm – 12:55pm 1:20pm – 2:10pm 2:25pm – 3:15pm 2:30pm – 3:30pm (best by appointment)

Jared Prof. Coppersmith Dan Jialu Andrew Eunsong Jared Dan Eunsong Jialu Andrew Prof. Karle

Nature of Science Theory and observation Theories are made to explain observations. Theories will make predictions, (so that they are testable). Observations and experiments are used to test if the prediction is accurate. The cycle continues. In history, physics and astronomy, have set the ground rules of modern science. ©2008 by W.H. Freeman and Company

Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC) • Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question.) • He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan) • From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision. • An example of great science!

Example: Determination of the Earth diameter by Eratosthenes (276 BC– 195 BC) • Eratosthenes wanted to determine the diameter of the Earth. (Yes, the standard model at the time was that the Earth was round – that was not the question) • He observed the angle of the sun at the same time in Alexandria and some 800km South of Alexandria (Syene= Aswan) • From the difference, he was able in inclination, records indicate that he was able to determine the Earth’s diameter to within 2% precision. • An example of great science!

Units • Physical quantities have units! • Example: Unit of length

– Eratosthenes used the unit stadion. (The hellenic stadion was pretty big: 185m) – In the Middle ages many kingdoms had different definitions of a foot, etc.

• Today, the scientific community uses the SI system of units. There are 7 basic units, such as

– Length: Meter (Based on the speed of light: length of path traveled by light in 1/299,792,458s) – Mass: kg (Platinum cylinder in International Bureau of Weights and Measures, Paris) – Time: s (Time required for 9,192,631,770 periods of radiation emitted by cesium atoms.)

SI Units SI Base quantities Length

meter

m

Time

second

s

Mass

kilogram

kg

Electric Current

ampere

A

Temperature

kelvin

K

Amount of substance

mole

mol

Luminous intensity

candela

cd

©2008 by W.H. Freeman and Company

Prefixes • Depending on the scale one often likes to use prefixes. • Example, for length it is convenient to use km = 1000m when traveling by car, or nm=10^-9m when discussing molecular scale objects.

Conversions • Conversions between units are very helpful. The use of different units has again and again lead to errors, sometimes with bad consequences. • The conversion of units is also a frequent source of errors engineering and science (and exams). • But it is easy to avoid. • Avoid skipping the units (for example because it is less writing time) – Are all the ingredients for a problem in the same units? If not, it is good practice to perform the conversion, before doing any algebra. – Basic SI units are always safe – It is OK to us km or nm, but need to take care that you don’t mix m and km – Develop good practice.

• We will expect that you give results with units, also in exams.

Derived quantities and dimensions

m2 m3

m/s

m/s2 N=kg•m/s2 N/m2=kg/m•s2 kg/m3 …

Measurement and Significant figures • A measurement has a precision (or error). • Measurement of the distance Earth – moon with laser pulse based on travel time of light. Error: a few cm! (position of the mirror) • What is the relative error?

The Greek astronomer Hipparch, ~200BC determined the distance of the moon to about ~70 Earth diameters, 5% precision, not too bad.

Measurement and Significant figures • A measurement has a precision (or error). • Significant figures reflect the precision of the measurement.

Example: • Pocket calculator • whiteboard, • WebAssign intro

Measurement and Significant figures • Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). • The top calculator shows the result of 2.0 / 3.0. • The bottom calculator shows the result of 2.5 x 3.2.

The universe by orders of magnitude

©2008 by W.H. Freeman and Company

Order of magnitude: Rapid Estimating A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Such back on the envelope estimates are very helpful for double checking a result of a calculation.

Diagrams are also very useful in making estimations.

Tire treads

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

©2008 by W.H. Freeman and Company

How many grains of sand on a beach?

©2008 by W.H. Freeman and Company

Phys 201 Fall 2009 Tuesday, September 8, 2009 Chapter 1: Measurement and vectors

Review from last Dme: converDng units • Units in every equaDon have to match! It is a very good idea to keep units as well as numbers when solving equaDons.

The density of seawater was measured to be 1.07 g/cm3. This density in SI units is A. B. C. D. E.

1.07 kg/m3 (1/1.07) × 103 kg/m3 1.07 × 103 kg 1.07 × 10–3 kg 1.07 × 103 kg/m3

The density of seawater was measured to be 1.07 g/cm3. This density in SI units is A. 1.07 kg/m3 B. (1/1.07) × 103 kg/m3 C. 1.07 × 103 kg D. 1.07 × 10–3 kg E. 1.07 × 103 kg/m3

If K has dimensions ML2/T2, the k in K = kmv2 must A. B. C. D. E.

have the dimensions ML/T2. have the dimension M. have the dimensions L/T2. have the dimensions L2/T2. be dimensionless.

If K has dimensions ML2/T2, the k in K = kmv2 must A. have the dimensions ML/T2. B. have the dimension M. C. have the dimensions L/T2. D. have the dimensions L2/T2. E. be dimensionless.

Vectors • In one dimension, we can specify distance with a real number, including + or – sign. • In two or three dimensions, we need more than one number to specify how points in space are separated – need magnitude and direcDon. Madison, WI and Kalamazoo, MI are each about 150 miles from Chicago.

DenoDng vectors • Two of the ways to denote vectors: – Boldface notaDon: A – “Arrow” notaDon: A

€

Displacement is a vector

©2008 by W.H. Freeman and Company

Adding displacement vectors

©2008 by W.H. Freeman and Company

“Head‐to‐tail” method for adding vectors

©2008 by W.H. Freeman and Company

Vector addiDon is commutaDve

©2008 by W.H. Freeman and Company

Adding three vectors: vector addiDon is associaDve.

©2008 by W.H. Freeman and Company

A vector’s inverse has the same magnitude and opposite direcDon.

©2008 by W.H. Freeman and Company

SubtracDng vectors

©2008 by W.H. Freeman and Company

Example 1‐8. What is your displacement if you walk 3.00 km due east and 4.00 km due north?

©2008 by W.H. Freeman and Company

Components of a vector

©2008 by W.H. Freeman and Company

Components of a vector along x and y

©2008 by W.H. Freeman and Company

Magnitude and direcDon of a vector

©2008 by W.H. Freeman and Company

Adding vectors using components

©2008 by W.H. Freeman and Company

Cx = Ax + Bx Cy = Ay + By

Unit vectors A unit vector is a dimensionless vector with magnitude exactly equal to one.

©2008 by W.H. Freeman and Company

The unit vector along x is denoted The unit vector along y is denoted The unit vector along z is denoted

Which of the following vector equaDons correctly describes the relaDonship among the vectors shown in the ﬁgure?

A. B. C. D.

A+ B −C =0 A− B +C =0 A− B −C =0 A+ B +C =0

E. None of these is correct.

Which of the following vector equaDons correctly describes the relaDonship among the vectors shown in the ﬁgure?

A. B. C. D.

A+ B −C =0 A− B +C =0 A− B −C =0 A+ B +C =0

E. None of these is correct.

Can a vector have a component bigger than its magnitude? Yes No

Can a vector have a component bigger than its magnitude? • Yes • No The square of a magnitude of a vector R is given in terms of its components by R2 = Rx2 + Ry2 . Since the square is always positive, no component can be larger than the magnitude of the vector.

ProperDes of vectors: summary

©2008 by W.H. Freeman and Company