Chapter 1: A Physics Toolkit

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Chapter 1: A Physics Toolkit

Physics Ms. Pollock 2015 - 2016

1.1 Mathematics and Physics

• • • Branch of science that involves study of the physical world; energy, matter, and their relationships Many related careers: astronomy, engineering, computer science, education, medicine http://blogs.discovermagazine.com/crux/files/2015/02/planets_iau_2.jpg

1.1 Mathematics and Physics

• • • Mathematics powerful language of physics Equations important for modeling observations and making predictions Numerical results used to support conclusions • http://izquotes.com/quotes-pictures/quote-the-miracle-of-the-appropriateness-of-the-language-of mathematics-for-the-formulation-of-the-laws-e-p-wigner-278064.jpg

Example Problem 1

• • • • • The potential difference (V), or voltage, across a circuit equals the current (I) multiplied by the resistance (R) in the circuit. That is, V (volts) = I (amperes) X R (ohms). What is the resistance of a lightbulb that has a 0.75 amperes current when plugged into a 120-volt outlet?

I = 0.75 amperes, V = 120 volts, R = ?

V = IR; R = V / I R = (120 V) / 0.75 A R = 160 

Practice Problem #1

• A lightbulb with a resistance of 50.0 ohms is used in a circuit with a 9.0-volt battery. What is the current through the bulb?

I = V/R I = 9 V / 50  I = 0.18 A

Practice Problem #2

• An object with uniform acceleration a, starting from rest, will reach a speed of v in time t according to the formula v = at. What is the acceleration of a bicyclist who accelerates from rest to 7.00 m/s in 4.00 s?

A = v/t A = (7.00 m/s) (4.00 s) A = 1.75 m/s 2

Practice Problem #3

• How long will it take a scooter accelerating at 0.400 m/s 2 speed of 4.00 m/s 2 ?

to go from rest to a T = v/a T = (4.00 m/s 2 ) (0.400 m/s 2 ) T = 10 s

Practice Problem #4

• The pressure on a surface is equal to the force divided by the area: P = F/A. A 53 kg woman exerts a force (weight) of 520 newtons. If the pressure exerted on the floor is 32,500 N/m 2 , what is the area of the soles of her shoes?

A = F/P A = 520 N 32,500 N/m 2 A = 0.016 m 2

SI Units

• Internationally recognized system of measurement • 7 base units, combinations of base units for derived units • Real-life use: GPS; 3-dimensional location

Base Quantity

Length Mass Time Temperature Amount of substance Electric current Luminous intensity

Base Unit

Meter Kilogram Second Kelvin Mole Ampere Candela

Symbol

m Kg s K Mol A cd

SI Units

• • • Regulated by International Bureau of Weights and Measures (France) Standard for US kept at National Institute of Science and Technology (Maryland) Conversions of size with prefixes https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRx qFQoTCLyg3rjD cYCFcuSDQodUM4HVg&url=http%3A%2F%2Fwww.radiolab.org%2Fstory%2Fkg%2F&ei=azS1Vfy B8ulNtCcn7AF&psig=AFQjCNG0pTqsJm2OhLenBSMNrWVLxPeCJg&ust=1438025164890918

SI Prefixes

• • Chart with SI conversions on page 6 of the textbook.

https://figures.boundless.com/9232/large/prefix2.png

Dimensional Analysis

• • • • • Solving physics problems often involves unit conversion.

Dimensional analysis – treating units as algebraic quantities Used to select conversion factors – allows units to cancel May require series of conversions http://www.chemistryland.com/CHM151S/01 Foundation/DimensionalAnalysis/NewApproach.gif

Practice Problem #5

• How many megahertz is 750 kilohertz?

750 kHz X 1 MHz = 0.75 MHz 1000 kHz

Practice Problem #6

• Convert 5021 centimeters to kilometers.

5021 cm X 1 km = 0.0521 km 10000 cm

Practice Problem #7

• How many seconds are in a leap year?

1 leap year X 366 days X 24 h X 60 min X 60 s = 31,622,400 s 1 leap year 1 day 1 h 1 min

Practice Problem #8

• Convert the speed 5,300 m/s to km/h.

5300 m X 1 km = 5.3 km 1000 m 1s X 1 min X 1 h = 0.000278 h 60 s 60 min 5.3 km = 19064.75 km/h 0.000278 h

Significant Digits

• • • • Valid digits in a measurement Last digit given in measurement ALWAYS uncertain Based on limitations of measurement device and limitations of person doing measuring http://mathsfirst.massey.ac.nz/Algebra/Decimals/images/zeros1.gif

Rules for Significant Digits

• • • • All non-zero numbers significant Lead zeros not significant Ending zeros not significant, unless decimal present Place-holding zeros not significant

Arithmetic with Significant Digits

• • • • Result of calculation never more precise than least-precise For addition and subtraction: round to least precise value involved For multiplication and division: round to least precise value involved No uncertainty involved with counting (exact numbers) or conversion factors

Practice Problem #9

• • • A. 6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = 26.281  26.3 cm B. 1.6 km + 1.62 m + 1200 cm = 160000 cm + 162 cm + 1200 cm = 161362 cm  1.6 km 160000 cm or 1600 m or

Practice Problem #10

• • A. 10.8 g – 8.264 g = 2.536 g  2.5 g B. 4.75 m – 0.4168 m = 4.3332  4.33 m

Practice Problem #11

• • A. 139 cm X 2.3 cm = 319.7 cm 2  320 cm 2 B. 3.2145 km X 4.23 km = 13.597335 km 2  13.6 km 2

Practice Problem #12

• • A. 13.78 g  11.3 mL = 1.21946903 g/mL  1.22 g/mL B. 18.21 g  4.4 cm 3 = 4.13863636 g/cm 3  4.1 g/cm 3

Scientific Methods

• • • Making observations, doing experiments, creating models or theories Used by all scientists to describe phenomena Must be reproducible

Scientific Methods

• • • Not set steps Can be completed in different order and repeated as needed http://www.google.com/imgres?imgurl=http://scienceinvestigators.wikispac

es.com/file/view/scientif_method_OK.png/442326542/scientif_method_O K.png&imgrefurl=http://scienceinvestigators.wikispaces.com/The%2BScient ific%2BMethod&h=642&w=710&tbnid=VEYOMoLZSVmQ9M:&docid=d Qk6MaTZ70IFoM&hl=en&ei=WkG1VcX6CIemNtOUg6gD&tbm=isch&ve d=0CCQQMygJMAlqFQoTCMWPx-PP-cYCFQeTDQodU8oANQ

1.1 Section Review

• • • • 13. Why are concepts in physics described with formulas?

Formulas concise and used to predict new data 14. The fore of a magnetic field on a charged, moving particle is given by F = Bqv, where F is the force in kg·m/s2, q is the charge in A·s, and v is the speed in m/s. B is the strength of the magnetic field, measured in teslas, T. What is 1 tesla described in base units?

1 kg/A·s 2

1.1 Section Review

• • • • • • • • • 15. A proton with charge 1.60 X 10 -19 the force on the proton.

A·s is moving at 2.4 X 10 5 m/s through a magnetic field of 4.5 T. You want to find A. Substitute the values into the equation you will use. Are the units correct?

F = Bqv = (4.5 kg/A·s 2 )(1.60 X 10 -19 A·s)(2.4 X 10 5 m/s); force measured in kg·m/s 2 , which is correct B. The values are written in scientific notation, m X 10

n

. Calculate the 10

n

answer.

part of the equation to estimate the size of the 10 -14 ; answer 20 X 10 -14 or 2 X 10 -13 C. Calculate your answer. Check it against your estimate from part b.

1.728 X 10 -13 kg·m/s 2 ; very close to estimate D. Justify the number of significant digits in your answer.

The least precise value is 4.5, so the answer can have two significant figures. The rounded answer is 1.7 X 10 -13 kg·m/s 2

1.1 Section Review

• • • • 16. Rewrite F = Bqv to find v in terms of F, q, and B.

V = F/Bq

17. An accepted value for the acceleration due to gravity is 9.801 m/s 2 . In the experiment with pendulums, you calculate that the value is 9.4 m/s 2 . Should the accepted value be tossed out to accommodate your new findings? Explain.

The value 9.801 has been established by repeated experiments. To reject the value would require an explanation of why it is wrong. Physical factors could explain the variation in the result.

Measurement

• • • Comparison between an unknown quantity and a standard Measurements reported with uncertainty to confirm or refute results http://www.uncertainnumbers.com/notes/_images/error_and_uncertainty_interval.png

Precision Versus Accuracy

• • • • Both characteristics of measured values Precision – how close measurements are to each other; shown by significant figures Accuracy – how close measurements are to accepted value; shown by comparison to standard http://wps.prenhall.com/wps/media/objects/165/169061/SW-comart/fig1_2_5.gif

Techniques of Good Measurement

• • • • Important to use instruments correctly Common source of error angle of measurement (parallax) Variation in accuracy of GPS https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd= &cad=rja&uact=8&ved=0CAcQjRxqFQoTCKiz0-Td cYCFUifgAodwmAJag&url=https%3A%2F%2Fgcps.desire2learn.com%2Fd2 l%2Flor%2Fviewer%2FviewFile.d2lfile%2F6605%2F7813%2FScale_Drawing s_print.html&ei=ClC1VaiGIci ggTCwaXQBg&psig=AFQjCNGaEs1L6SX0WZvSfJCitPAB8HxzBA&ust=1 438032216140797

1.2 Section Review

• 18. Some wooden rulers do not start with 0 at the edge, but have it set in a few millimeters. How could this improve the accuracy of the ruler?

• • The edge of the ruler can be worn over time, changing the accuracy of the ruler.

• 19. You find a micrometer that has been badly bent. How would it compare to a new, high-quality meterstick in terms of its precision? Its accuracy?

The micrometer would be precise, but less accurate than the new meterstick.

1.2 Section Review

• 20. Does parallax affect the precision of a measurement that you make? Explain.

• No, precision is based on the closeness of measurements to each other. As long as the parallax is maintained, the precision is as well.

• • 21. Your friend tells you that his height is 182 cm. In your own words, explain the range of heights implied by this statement.

His height between 181.5 and 182.5 cm. The uncertainty is  0.5 cm.

1.2 Section Review

• • • • • • • 22. A box has a length of 18.1 cm and a width of 19.2 cm, and it is 20.3 cm tall.

A. What is its volume? 7050 cm 3 B. How precise is the measure of length? Of volume?

Length is precise to 0.1 cm. Volume is precise to 10 cm 3 .

C. How tall is a stack of 12 of these boxes? 243.6 cm D. How precise is the measure of the height of one box? Of 12 boxes?

The height of one box is precise to 0.1 cm, as is the height of 12 boxes.

1.2 Section Review

• 23. Your friend states in a report that the average time required to circle a 1.5-mi track was 65.414 s. This was measured by timing 7 laps using a clock with a precision of 0.1 s. How much confidence do you have in the results of the report? Explain.

• Result never more precise than least precise measurement; calculated average lap time greater than precision possible with clock

Graphing Data

• • • Graphs designed to convey information quickly and simply Patterns more readily evident http://www.schoolatoz.nsw.edu.au/detresources/iStock_000015151608Small_LSvpzPdLDE_l.png

Identifying Variables

• • • • Only one factor changed at a time in experiment Variable – any factor that might affect the behavior of an experimental setup Independent – factor changed or manipulated Dependent – factor that depends on independent variable

Line Graphs

• • • • • • Shows how dependent variable changes with independent variable Linear relationship: y = mx + b Slope =  Y/ 

X

Quadratic relationship: y = ax

2 bx + c +

Inverse relationship: y = a/x

https://jrlf8z.wikispaces.com/file/view/graph_2.JPG/34302007/graph_2.JPG

Practice Problems

• 24. The mass values of specified volumes of pure gold nuggets are given in the table.

Volume (cm 3 )

1.0

2.0

3.0

4.0

5.0

Mass (g)

19.4

38.6

58.1

77.4

96.5

Practice Problems

• A. Plot mass versus volume from the values given in the table and draw the curve that best fits all points.

120 100 80 60 40 20 0 Density of Gold 2 3 19.4

4 5

Practice Problems

• • • • • • B. Describe the resulting curve.

Straight line C. According to the graph, what type of relationship exists between the mass of the pure gold nuggets and their volume?

Linear relationship D. What is the value of the slope of this graph? Include the proper units.

19g/cm 3

Practice Problems

• • • • E. Write the equation showing mass as a function of volume for gold.

m = (19 g/cm 3 )V F. Write a word interpretation for the slope of the line.

The mass for each cubic centimeter of pure gold is 19 g.

Predicting Values

• • • Known values used to make predictions Important to know how to extrapolate from data Models used to predict how systems will behave

1.3 Section Review

• 25. Graph the following data. Time is the independent variable.

Название диаграммы 14 12 10 2 0 8 6 4 0 5 10 15 Speed (m/s) 20 25 30 35

1.3 Section Review

• 26. What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume?

• • When the volume of the material is zero, there is a nonzero total mass. This could happen if the mass of the container were included.

• 27. Use the relation illustrated in Figure 1-16 (page 16) to determine the mass required to stretch the spring 15 cm.

16 g

1.3 Section Review

• • • • 28. Use the relation in Figure -18 (page 18) to predict the current when the resistance is 16 ohms.

7.5 A 29. In your own words, explain the meaning of a shallower line, or a smaller slope than the one in Figure 1-16, in the graph of stretch versus total mass for a different spring.

Spring with line of smaller slope stiffer, so more mass required to stretch to one centimer.

Chapter 1 Homework

• • • • Appendix B: Additional Problems Page 858 #1 – 12 You DO NOT have to write the question.

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