phys 218 - texas a&m universitypeople.physics.tamu.edu/kamon/teaching/phys218/slide… · ·...

PHYS 218

1

http://people.physics.tamu.edu/kamon/teaching/phys218/

1) Lectures

2) Exams

3) Recitation Quizzs

4) Lab Reports

5) MasteringPhysics HWs

Syllabus Version 2.2

2

Syllabus : Course

3

MP Cours ID MPKAMON01330

>75%

Syllabus : Exam and Grade

4

5

Syllabus : Schedules

6

Syllabus : Course Schedule

7

Syllabus : Course Schedule

8

Syllabus : Lab Schedule

9

Syllabus : Lab Schedule

10

Deep Impact on Grade http://people.physics.tamu.edu/kamon/teaching/phys218/

11

Your TAs

Introduction

Chapter 1: Introduction

The Nature of Science

Observation Experimental Data

Models, Theories, Laws

Application (Engineering)

12

Introduction


E = m c2

Nuclear Power


Observation Experimental Data

13

Introduction

e.g., d = 107 m

(Distance between North Pole and Equator)

[Conversion: 1.609 km = 1 mi ]

62,150 mi

62.150 k mi

6.2150 x 104 mi

Scientific notation 14

Introduction 15

Introduction

Wrong units,

$125M Loss!

16

Also refer to Table 1.2,

Figure 1.8, and Example

1.3.

As this train mishap

illustrates, even a small

percent error can have

spectacular results!

Introduction

15 ± 1 m (1 digit in uncertainty, same “10’s” as

last digit)

1) 15.052 ± 1 m

(Makes I look like an amateur…)

2) 15 ± 1.05 m (Same thing)

3) 15.1 ± 0.1 m (Ok)

4) 15 ± 10 m (Ok)

Number of Significant Figures

17

Introduction

Scientific Notation and Error Propagation

2214

15

228312

28

31

2

electron

/smkg1098.1

107...881.

kg(m/s)10(2.99...)19.1

m/s] 108[2.9979245

kg]101[9.1

-x

x

xx

xx

x

x

cmE

18

Introduction

2214

15

228312

28

31

2

electron

/smkg1098.1

107...881.

kg(m/s)10(2.99...)19.1

m/s] 108[2.9979245

kg]101[9.1

-x

x

xx

xx

x

x

cmE

19

Scientific Notation and Error Propagation

Introduction

Problem Solving

You need to understand the concepts first in

order to solve the problems.

You need a model in order to solve almost

any problem.

Physicists/engineers are famous for coming

up with simplified models for complicated

problems.

The first step is always “Draw a Diagram!” (DaD)

20

Introduction 21

Identity, Set up, Execute, Evaluate

Introduction

Problem: How many gallons of gasoline are

used in the U.S. in one day?

22

Introduction

V = N x D / M

Where

N = #cars

D = average driving

distance (mi)

M = gas mileage (mi/gl)

23



Introduction

V = N x D / M

Where

N = #cars

D = average driving

distance (mi)


N = 200,000,000 people

x 50%(adults) x

50%(owners)

= 50,000,000

D = 30 mi

M = 10 mi/gl

24



Introduction

V = N x D / M

Where

N = #cars

D = average driving

distance (mi)


N = 200,000,000 people

x 50%(adults) x

50%(owners)

= 50,000,000

D = 30 mi

M = 10 mi/gl

V = 150,000,000 gl

25



Introduction

Some Techniques

Order-of-magnitude Estimate

A rough estimate is made by rounding off all

numbers to one significant figure and its

power of 10, and after the calculation is made,

again, only one significant figure is kept.

Triangulation

26

Introduction

Back-of-the-envelope Calculation

(Rapid Estimating)

20 m

1200 m

Estimate volume of a lake.

Order of Magnitude

27

Introduction

Back-of-the-envelope Calculation

(Rapid Estimating)

20 m

1200 m

V = h p r2

~ (10) (3) (500)2

= 7.50 x 106 m3

~ 8 x 106 m3

Estimate volume of a lake.

28

Order of Magnitude

Introduction

You want to measure the height of a building. You stand 2m (2 strides) away from a 3m pole and see that it’s “in line” with the top of the building. You pace off about 16 more strides from the pole to the building. What is the height of the building?

Triangulation

© Physics for Scientists and Engineers,

D. Giancoli, 3rd ed. Prentice Hall 29

Introduction

Draw a Diagram!!!!



Introduction

B A

x

D

A:D = (A+B) : (x–C)

Label them!!!

C



Introduction

B A

x

D

A:D = (A+B) : (x–C)

(x–C) x A = (A+B) x D

x–C = (A+B) x D/A

x = (A+B) x D/A + C

Solve them!!

C



Introduction

B A

x

D

A:D = (A+B) : (x–C)

(x–C) x A = (A+B) x D

x–C = (A+B) x D/A

x = (A+B) x D/A + C

x = 15 m

Find the answer!

C



Introduction

Vectors and Scalars

Vector

A quantity that has direction & magnitude.

Examples: displacement, velocity, acceleration

Scalar

A quantity that has only magnitude.

Examples: temperature, mass

34

Introduction

Displacement (Vector)

x

y

35

Introduction

Direction: North Magnitude: 2.6 km

x

y

36

Introduction

Direction: East Magnitude: 4.0 km

x

y

37

Introduction

Direction: 45o North of East Magnitude: 3.1 km

x

y

38

Introduction

Direction: ? Magnitude: ?

x y

D1

D2

D3

DR

DR

D1

D2 D3

39

Introduction

Direction: ? Magnitude: ?

x y

D1 0 km 2.6 km

D2 4.0 km 0 km

D3 2.19 km 2.19 km

DR

DR

D1

D2 D3

Adding vectors by components

40

Introduction

Direction: 37.7o North of East Magnitude: 7.83 km

x y

D1 0 km 2.6 km

D2 4.0 km 0 km

D3 2.19 km 2.19 km

DR 6.19 km 4.79 km

DR

D1

D2 D3

)(tan1

22

RxRy

RyRxR

D/D

DDD

41

Introduction

rx

ry

r = (rx) i + (ry) j ^ ^ ￫

Unit Vectors

)hat"" (with ˆ,ˆ,ˆ

)hat"" (with ˆ,ˆ,ˆ

faced) (bold kj,i,

zyx

kji

Various notations:

x component of vector r

y component of vector r

42

Introduction

rx

ry

Two Vectors

u = (ux) i + (uy) j ^ ^ ￫

r + u = ? ￫￫

r = (rx) i + (ry) j ^ ^ ￫

43

Introduction

Vector Operations

x2.0 longer,

Opposite direction

x1.5 longer,

Same direction

44

Introduction

[Quick Quiz 1] Find:

(a)A+B

(b)AB

(c) A+B+C

(d) A+BC

(e) BC

(f) AC

45

Introduction

[Quick Quiz 1] Find:

(a)A+B

(b)AB

(c) A+B+C

(d) A+BC

(e) BC

(f) AC

46

Adding vectors using their components

• Follow Examples 1.7 and 1.8.

Fig. 1.22 47

Introduction

You are traveling on a curved

road in Bryan/College Station

area at varying speed.

Direction & magnitude

Position & Velocity Vectors (A powerful tool to describe motion in 2D or 3D)

Position &

Velocity

In more complicated situation

Change in

position vector

Change in

velocity vector

48

O

Introduction

Watch! Change in its

position vectors!

A

C

B

E

F

D

r = (x) i + (y) j ￫￫￫

O

49

Position Vector

Introduction

One more time …

Change in

position vector

A

C

B

E

F

D Displacement Vectors

[AB] [BC]

[CD]

[DE]

[EF]

r = (x) i + (y) j ￫￫￫

O

Displacement

Vectors

A

C

B

E

F

D

O 50

Position Vector

Introduction

Change of its Position

Vector in Time!

Displacement Vectors

[AB] [BC]

[CD]

[DE]

[EF]

r = (x) i + (y) j ￫￫￫

Velocity Vectors

[AB] /Dt = vave(AB)

[BC] /Dt = vave(BC)

[CD] /Dt = vave(CD)

[DE] /Dt = vave(DE)

[EF] /Dt = vave(EF)

51

Position Vector A

C

B

E

F

D

O

Displacement Vectors / Time

A

C

B

E

F

D

O

Introduction 52

[Quick Quiz 2] Can the displacement vector (Dr) for a particle moving (from P1 to P2) in the x-y plane ever be longer than the length of path (Dl) traveled by the particle over the same time interval?

[A]

[Quick Quiz 2] Can the displacement vector (Dr) for a particle moving (from P1 to P2) in the x-y plane ever be longer than the length of path (Dl) traveled by the particle over the same time interval?

(Dr)x = x2 – x1

(Dr)y = y2 – y1

No. Not always Dr = Dl

Note: Dr = r2 – r1

= (Dr)x i + (Dr)y j

￫￫￫

￫￫

53

[A]

Introduction

Scalar Product • The scalar product (also called the “dot product”) of two vectors is

• Figures 1.25 and 1.26 illustrate the

scalar product.

• Find an angle using the scalar product.

cos .ABA B

. z zx x y yA B A B A BA B

Figs. 1.25–1.26 54

Vector Product • The vector product (“cross product”) of two vectors has magnitude

and the right-hand rule gives its direction. See Figures 1.29 and 1.30.

| | sin ABA B

Figs. 1.29–1.30

55

Calculating the Vector Product

• Use ABsin to find the

magnitude and the

right-hand rule to find

the direction.

• Refer to Example

1.12.

Fig. 1.32

56

Introduction

Today’s class

SI units

Dimensional analysis

Scientific notation

Error propagation

DaD, ISEE

Vector and Vector

Products.

Next class

Chapter 2

57

Summary

phys 218 - texas a&m universitypeople.physics.tamu.edu/kamon/teaching/phys218/slide… · ·...

Documents