Physics 100 Prep for Engineering Studies Winter 2010 – 2011

Physics 100Prep for Engineering StudiesWinter 2010 – 2011

Dr. Joseph J. TroutDisque [email protected]@drexel.edu

mailto:[email protected]

Dimensions:Length Meter (m) Mass Kilogram (kg)Time Second (s)

Dimensions:Length: meter1790 - One ten-millionth of the distance from the equator to either pole.1889 - Platinum- iridium rod1960 - 1,650,763.73 wavelength of orange light produced by krypton-861983 - Distance light travels in 1/ 299,792,458 of a second.

Time: second1/86,400 of a mean solar day9,192,631,770 oscillations of a cesium atom.

Mass: kilogramplatinum – iridium cylinder

Scientific Notation:

1000=103=1 X 103

2000=2 X 1000=2X 103

2345=2.345 X 1000=2.345 X 103


245600000


2456000008 7 6 5 4 3 2 1


245600000=2.456 X 108

8 7 6 5 4 3 2 1


0.015=1.5 X 0.01=1.5 X 1100

=1.5 X 10−2

Prefixes:

yotta Y 1024

zetta Z 1021

exa E 1018

peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hecto h 102

deka da 101

deci d 10-1

centi c 10-2

milli m 10-3

micro µ 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24

Prefixes:

yotta Y 1024

zetta Z 1021

exa E 1018

peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hecto h 102

deka da 101

deci d 10-1

centi c 10-2

milli m 10-3

micro µ 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24

Prefixes:

yotta Y 1024

zetta Z 1021

exa E 1018

peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hecto h 102

deka da 101

deci d 10-1

centi c 10-2

milli m 10-3

micro µ 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24

Prefixes:

Mass

Length

Time

1kilogram=1kg=1000 g=1 X 103g

1centimeter=1cm=0.01m=1 X 10−2m1kilometer=1 km=1000m=1 X 103m

1microsecond=1 s=0.000001 s=1 X 10−6 s1nanosecond=1ns=0.000000001 s=1 X 10−9 s

1mile=1.609 km=1609m1 km=0.621mi1hr=3600 s1 year=3.156 X 107 s1 kg=0.0685 slug1 lb=4.448N

1mile=1.609 km

1mile1.609 km

=1

1.609 km1mile

=1

Conversion Factors:

1mile=1.609 km

1mile1.609 km

=1

5 km=?miles

5 km1mile1.609 km =3.11mi

1mile=1.609 km

5 km=?miles

5 km1mile1.609 km =3.11mi

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m 3600 s

1hr

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m 3600 s

1hr =44.75mph

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m 3600 s

1hr =44.75mph

1hr=3600 s1mi=1609m

20ms=?mph

20ms 1mile1609m 3600 s

1hr =44.75mph

1hr=3600 s1mi=1609m

60mph=?m /s

60mihr 1609m

1mi 1hr3600 s =26.82m /s

1hr=3600 s1mi=1609m

60mph=?m /s

60mihr 1609m

1mi 1hr3600 s =26.82m /s

1mi=1609m

3mi3=?m3

3mi31609m1mi

3

=1.25 X 1010m3

2mih2 = ________________m

s2

2mih2 1609m

1mi 1h3600 s 2

=2.48 X 10−4m / s2

Scalar – Magnitude only.

Example: mass, distance, speed Example: m, x, v

Vector – Magnitude and Direction.

Example: displacement,velocity, acceleration, forceExample: x ,v ,a , F

Distance – scalar – magnitude of the total distance traveled.

Displacement – vector – distance between final position and initial position AND the direction.

Measurement:

Systematic Error or Uncertainty

Each error in measurement have the same sign.

Example: A meter stick which has been worn down on one side by a millimeter. If you measure something the errors will all add up and the measurement you make will be LONGER than the actual distance.

Measurement:

Random Error or Uncertainty

Chance variations in measurement. These errors are unavoidable. They are just as likely to be positive as negative.These errors can be minimized by taking many measurements and averaging them together.

Example: Three people make a measurement that with the same meter stick but end up with slightly different readings.

Measurement:

Absolute Error

The difference between the value of your measurement and the accepted, published, or theoretical value.

absolute error = experimental value − accepted value

Measurement:Relative Error

The difference between the value of your measurement and the accepted, published, or theoretical value “compared” to the accepted, published, or theoretical value.

relative error = experimental value − accepted value accepted value

% rel err = exp value − acc value acc value

X 100 %


Accepted Value g=9.80m/ s2

Measured Value g=9.76m / s2

Absolute Error =9.76m/ s2−9.80m / s2=−0.04m / s2



Measured Value g=9.76m/ s2

Absolute Error =9.76m / s2−9.80m/ s2=−0.04m/ s2

Rel Error =9.76m/ s2−9.80m / s2

9.8m / s2 =−0.0041



Measured Value g=9.76m/ s2

Absolute Error =9.76m / s2−9.80m/ s2=−0.04m/ s2

Rel Error =9.76m/ s2−9.80m / s2

9.8m / s2 =−0.0041

% Rel Error =9.76m/ s2−9.80m/ s2

9.8m/ s2 X 100%=−0.41 %

PRECISIONThe degree of consistency or reproducibility of a measurement.The more precise the measurement, the less the difference between two observations of the same event.

PRECISIONMost skilled observer can not estimate readings better than 1/10 of the smallest division.

Example: If the smallest division on a meter stick is a cm, then the best you could hopefully estimate would be 1/10 of a cm or 1 mm.

1.0 2.0 3.0 4.0 5.0 cm

1.0 2.0 3.0 4.0 5.0 cm

L=3.0 cm

1.0 2.0 3.0 4.0 5.0 cm

L=3.5cm

2.0 4.0

L=2.8 cm

1.0 2.0 3.0 4.0

2.0 3.0 4.0

L=2.8 cm

1.0 2.0 3.0 4.0

For most of the experiments in Fundamentals of Physics, you will assume that the best you can estimate a scale reading is 1/10 of the smallest division.

2.0 3.0 4.0

L=2.8cm±0.1cm

1.0 2.0 3.0 4.0

For most of the experiments in Fundamentals of Physics, you will assume that the best you can estimate a scale reading is 1/10 of the smallest division.

Review:

Review

Review 1mile=1609m1km=0.621mi1hr=3600 s1 year=3.156 X 107 s1kg=0.0685 slug1 lb=4.448N

43mph=____________m/ s


43mph=____________m/ s

43mih 1609m

1mi 1h3600 s =19.22m / s


60m/ s=____________mph

60ms 1mi1609m 3600 s

1h =134.24mph


6.0m/ s2=____________mih2

6.0ms2 =1mi1609m 3600 s

1h 2

=4.83 X 104mih2

Review 1mile=1609m1km=0.621mi1hr=3600 s1 year=3.156 X 107 s1kg=0.0685 slug1 lb=4.448N2.54 cm=1 in.

12 in.3=____________ cm3

12 in.32.54 cm1 in.

3

=196.64 cm3=1.9664 X 10−4m


12 in.3=____________ cm3

12 in.32.54cm1 in.

3

=196.64 cm3=1.9664 X 10−4m≠1.9664m3


12 in.3=____________ cm3

12 in.32.54cm1 in.

3

=196.64 cm3=1.9664 X 10−4m≠1.9664m3

Probably 20 % of the class will make this error in physics one. Don't let it be you.


Accepted Value v=3.20m/ sMeasured Value vexp=3.22m/ s

Absolute Error =3.22m/ s−3.20m/ s=0.02m/ s

Rel Error =3.22m / s−3.20m/ s3.20m/ s

=0.00625m/ s

% Rel Error =3.22m/ s−3.20m / s3.20m/ s

X 100%=0.625 %

Review

Reading Significant Figures:

●The first significant figures in a measurement is the first digit other than zero , counting from the left to the right. ●Zeroes to left of the first of the first nonzero digit are not significant.●Zeroes which occur between two significant digits are significant since they are part of the measurement.●Final zeros in a measurements containing decimal fractions are significant.●The number of significant digits are independent of the measurement unit.


The first significant figures in a measurement is the first digit other than zero , counting from the left to the right.

29.85ml34.002mi53.0 gal

33339.78 km56.34 s

0.003467 ns


The first significant figures in a measurement is the first digit other than zero , counting from the left to the right.

29.85ml34.002mi53.0 gal

33339.78 km56.34 s

0.003467 ns


(2) Zeroes to left of the first of the first nonzero digit are not significant.

0.004ml34.002mi0.2324 gal

0.00004578 km0.34 s


(2) Zeroes to left of the first of the first nonzero digit are not significant.

0.004ml34.002mi0.2324 gal

0.00004578 km0.34 s


(3)Zeroes which occur between two significant digits are significant since they are part of the measurement.

0.004ml34.002mi0.2324 gal

0.00004578 km0.3004 s


(3)Zeroes which occur between two significant digits are significant since they are part of the measurement.

0.004ml34.002mi0.2324 gal

0.00004578 km0.3004 s


(4) Final zeros in a measurements containing decimal fractions are significant.

0.00400ml34.0020mi0.23240 gal

0.00004578 km0.30040 s


(4) Final zeros in a measurements containing decimal fractions are significant.

0.00400ml34.0020mi0.23240 gal

0.00004578 km0.30040 s


(5) The number of significant digits are independent of the measurement unit.

10.6 cm=106mm=0.106m=0.000106 km

All have 3 sig figs.

Rounding off Significant FiguresRounding off Significant Figures

42.5444.78

67459.5623.455080.003452

434 4757543

If the first digit to the right of the last significant digit is less than 5, it is dropped.

If the first digit to the right of the last significant digit is greater than or equal to 5, add 1.

Rounding off Significant FiguresRounding off Significant FiguresIf the first digit to the right of the last significant digit is less than 5, it is dropped.

If the first digit to the right of the last significant digit is greater than or equal to 5, add 1.

42.54 42.544.7844.8

67459.566746023.4550823.455

0.0034520.00345

434 4757543

Addition and Subtraction with Addition and Subtraction with Significant FiguresSignificant Figures

Round off to the precision of the least precise measurement.

331.46m / s14.9m / s=331.5m / s14.9m / s=346.4m / s

Addition and Subtraction with Addition and Subtraction with Significant FiguresSignificant Figures

Round off to the precision of the least precise measurement.

60.0mm14.99mm=60.015.0mm=75.0mm

68

Addition and Subtraction with Significant FiguresAddition and Subtraction with Significant Figures

v=2.390 X 102m / s4.5609 X 102m / sv=2.390 X 102m / s4.561 X 102m / s

v=6.951 X 102m / s

T=56.2oF45.234oFT=56.2o F45.2o F

T=111.4oF

69

Multiplication and Division with Significant FiguresMultiplication and Division with Significant Figures

Number of significant figures in the result is no greater than number of significant figures in the measurement with fewest significant figures.

L=34.78cmW=2.767 cm

A=L X W=34.78 cm X 2.767 cm≠96.23626cm=96.24cm

70



M = 20.23 kg

l=3.0 cmw=1.0cm

h=2.0cm

71



M = 20.23 kg

l=3.6cmw=1.0cm

h=2.8cm

V=l wh=3.6 cm 1.0 cm 2.8 cm=10.08cm3=10.0cm3

72



M = 20.23 kg

l=3.6cmw=1.0cm

h=2.8cm

V=l wh=10.08cm3=10 cm3 1.0m100.0 cm

3

=1.0 X 10−5m3

=MV = 20.23kg

1.0 X 10−5m3=2.0 X 106 kg /m3

73



l=21.3±0.2cmw=9.80±0.1cm

A=l w=21.3±0.2cm 9.80±0.1cm A≈[21.3cm 9.80 cm ±21.3cm 0.1 cm ±0.2cm 9.80 ±0.2 0.1 ]

A≈209±4 cm2

74



l=12.71mw=7.46m

A=l w=12.71 7.46 A=94.8166m2=94.8m2

75

Scientific NotationScientific Notationa=2.0 X 103

b=3.0 X 103

ab=2.0 X 1033.0 X 103=2.03.0 X 103=5.0 X 103

a=1.73 X 105

b=2.9 X 104

ab=1.73 X 1052.9 X 104

ab=1.73 X 1050.29 X 105

ab=2.02 X 105=2.0 X 105

76

Scientific NotationScientific Notationa=1.245 X 103

b=2.70 X 102

a∗b=1.245 X 1032.70 X 102 a∗b=1.245 3.7 103102

a∗b=3.3615 X 105=3.36 X 105

a=6.0 X 108

b=2.0 X 104

a /b=6.0 X 108

2.0 X 104

a /b=6.02.0

X 108−4=3.0 X 104

77

Chapter 11 Plane Geometry

78

A

B

C

Vertex

BAC

79

A

B

CVertex

BAC=90o Right Angle

80

A

BC

Vertex

BAC=180o Straight Angle

81

A

B

CVertex

BAC90o Acute Angle

82

A

B

CVertex

BAC90o Obtuse Angle

83

1

2

1 is acute.2 is obtuse.

1 and 2 are adjacent.

84

12

12=180o

Supplemental Angles Supplemental Angles

85

1

2

12=90o

Complimentary Angles Complimentary Angles

86

1

Vertical Angles Vertical Angles

2

1 ,2

87

1

Vertical Angles Vertical Angles

2

12

1 ,21 ,2

88

12

3

5

4

6

78

3 and 6 ,4 and 5 Alternate Interior. 1 and 8 ,2 and 7 Alternate Exterior.

4 and 6 ,3 and 5 Interior. 1 and 7 ,2 and 8 Exterior.

1 and 5 ,2 and 6,3 and 7,4 and 8 Corresponding.

89

12

3

5

4

6

78




Theorems of Equal Angles: Two angles are said to be equal if they have equal measures.

90




1. Vertical angles are equal.

Vertical Angles

91




1. Vertical angles are equal.2. Alternate Interior, alternate exterior, corresponding Angles are equal.

Vertical Angles

92

1. Vertical angles are equal.2. Alternate Interior, alternate exterior, corresponding Angles are equal.3. If the right and left sides of two angles are parallel to each other, the angles are equal.

1

2

93

1. Vertical angles are equal.2. Alternate Interior, alternate exterior, corresponding Angles are equal.3. If the right and left sides of two angles are parallel to each other, the angles are equal.3. If the right and left sides of two angles are perpendicular to each other, the angles are equal.

1

2

94

1

Central AngleCentral Angle

Inscribed AngleInscribed Angle

2

1

C

2

95

TRIANGLESTRIANGLES

96

TRIANGLESTRIANGLES

Triangle - Formed by three line segments called sides.Vertex – point common to two sides.Altitude – Perpendicular line segment drawn from any vertex to opposing side.

Base

97

TRIANGLES – Right TriangleTRIANGLES – Right Triangle

Leg

Leg

Hypotenuse

98

TRIANGLESTRIANGLES

Scalene – no two sides are of equal length.Acute – each angle less than 90 degrees.Obtuse – one angle greater than 90 degrees.Right – One angle equals 90 degrees.

99

TRIANGLESTRIANGLES

Isosceles – Two of the sides are equal.Acute – each angle less than 90 degrees.Obtuse – one angle greater than 90 degrees.Right – One angle equals 90 degrees.

100

Congruence of TRIANGLESCongruence of TRIANGLES

If two triangles can be made to coincide by superposition, they are said to be congruent.

A

B

C

A'

B'

C'

101


A

B

C

A'

B'

C' ABC≈ A' B ' C '

102


A

B

C

A'

B'

C' ABC≈ A' B ' C '

1.) AB=A' B ' BC=B ' C ' B=B '

2.)A=A ' C=C ' AC=A' C '

3.) AB=A' B ' BC=B ' C ' AC=A' C '

B

A C B 'A '

C '

103

Similarity of TRIANGLESSimilarity of TRIANGLES

A

B

C

A'

B'

C'B

A C

A ' C '

B '

Dimensions of one are a constant ratio of the other.

ABC ~ A' B ' C '

104


A

B

C

A'

B'

C'

ABC ~ A' B ' C '

1.)A=A ' B=B '2.) AB /AC=A' B ' /A' C ' A=A'

3.) AB / A' B '=AC / A' C '=BC /B ' C '4.)A=A ' B=B ' C=C '5.) Their corresponding sides are respectively parallel or perpendiculiar.

B

A C

A ' C '

B '

105


A

B

C

A'

B'

C'

ABC ~ A' B ' C '

6.) The hypotenuse and a leg of one are respectively proportional to the hypotenuse and a leg of the other .7.) An acute angle of one is equal to an acute angleof the other.

B

A=90o C

A '=90o C '

B '

hyp

hyp'

106

Other Theorems of TRIANGLESOther Theorems of TRIANGLES

A

B

C

1.) Sum of the angles of every triangles is 180o .

2.) Sum of any two sides is greater than third,difference of any two sides is less than the third

3.) Angles opposite equal sides are equal, and conversely.

4.) The largest angle in a triangle lies opposite the largestand conversely.

B

A C

107

Other Theorems of TRIANGLESOther Theorems of TRIANGLES

A

B

C

5.) Line parallel to one side of a triangle divides the other two sides into proportional segments.

AD /DB=AE /EC

B

A C A

B

C

B

A C

D

E

108

AB=30m

AC=?

A B

C

109

AB=30m

AC=?

A B , B '

C

C '

A'

DE=2m

A' B '=5m

Similar Triangles

110

AB=30m

AC=?

A B , B '

C

C '

A'

DE=2m

A' B '=5m

Similar Triangles

111

AB=30m

AC=?

A B , B '

C

C '

A'

DE=2m

A' B '=5m

Similar Triangles

112

AB=30m

AC=?

A B , B '

C

C '

A'

A' C '=2m

A' B '=5mACAB

= A' C 'A' B '

113

AB=30m

AC=?

A B , B '

C

C '

A'

A' C '=2m

A' B '=5mACAB

= A' C 'A' B '

AC=AB[ A' C 'A ' B ' ]=30m[ 2m5m ]=12m

114

m

115

m

w=mg

Dotted line drawn perpendicular to ramp.

116

m

w=mg

90o−


117

m

w=mg

90o−


118

m

w=mg

90o−

Normal x,y coordinate system.

F N

119

m

w=mg

90o−


F N

120

m

w=mg

90o−


F N

90o−

121

m

w=mg

90o−


F N

90o−

122

123

124

125

126

Pythagorean TheoremPythagorean Theorem

r2=x2 y2

r

xy

127

Pythagorean TheoremPythagorean Theorem

r2=x2 y2

r=x2 y2

r=3m 24m 2=5m

r=?

x=3my=4m

128

Quadrilaterals:Quadrilaterals:Quadrilateral – plane figure bounded by four line segments.

Parallelogram – opposite sides are parallel.

Trapezoid – Only one pair of parallel opposite sides.

Rhombus – parallelogram with all sides being equal.

Rectangle – parallelogram with four right angles.

Square – rectangle with four equal sides.

129

Quadrilaterals:Quadrilaterals:Quadrilateral – plane figure bounded by four line segments.Parallelogram – opposite sides are parallel.Trapezoid – Only one pair of parallel opposite sides.Rhombus – parallelogram with all sides being equal.Rectangle – parallelogram with four right angles.Square – rectangle with four equal sides.

Rectangle Square Parallelogram

Rhombus Trapezoid

130

Quadrilaterals:Quadrilaterals:A Quadrilateral is a parallelogram if any of the following:

1.) Two sides are equal and parallel.

2.) Each interior angle is equal to the interior opposite angle.

3.) Diagonals bisect one another.

4.) Opposite sides are equal in length.

131

Parallelogram:Parallelogram:A diagonal of a parallelogram divides it into two congruent triangles.

Two angles with a common side in a parallelogram are supplementary.

The measure of the sum of the four angles is:180 o + 180 o = 360 o .

A

A A

132

Parallelogram:Parallelogram:Special Properties:

1.) Rhombus - diagonals are perpendicular

2.)Rhombus – diagonals bisect angles.

3.)Rectangle – square of the length of the diagonal is equal to sum of the square of the lengths of the two adjacent sides.

4.) Rectangle – two diagonals are equal.

5.) A square ( parallelogram, rhombus, rectangle) has all properties listed.

133

Circles and ArcsCircles and Arcs

Diameter

Radius

134


SecantSecant

TangentTangent

ChordChord

135


Sector

Arc

Semicircle

Quadrant

136

sagitta

137

An inscribed angle is measured by one-half if the intercepted arc.

138

An inscribed angle is measured by one-half if the intercepted arc.

Arc 1/3 of circle, or 13 360o=130o

=130o

2=65o

139

Documents

Physics 100 Prep for Engineering Studies Winter 2010 – 2011