PHYS 218 - Texas A&M Universitypeople.physics.tamu.edu/kamon/teaching/phys218/slide… · ·...
Transcript of PHYS 218 - Texas A&M Universitypeople.physics.tamu.edu/kamon/teaching/phys218/slide… · ·...
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PHYS 218
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http://people.physics.tamu.edu/kamon/teaching/phys218/
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1) Lectures
2) Exams
3) Recitation Quizzs
4) Lab Reports
5) MasteringPhysics HWs
Syllabus Version 2.2
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Syllabus : Course
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MP Cours ID MPKAMON01330
>75%
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Syllabus : Exam and Grade
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Syllabus : Schedules
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Syllabus : Course Schedule
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Syllabus : Course Schedule
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Syllabus : Lab Schedule
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Syllabus : Lab Schedule
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Deep Impact on Grade http://people.physics.tamu.edu/kamon/teaching/phys218/
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Your TAs
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Introduction
Chapter 1: Introduction
The Nature of Science
Observation Experimental Data
Models, Theories, Laws
Application (Engineering)
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Introduction
The Nature of Science
E = m c2
Nuclear Power
The Nature of Science
Observation Experimental Data
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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
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Introduction 15
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Introduction
Wrong units,
$125M Loss!
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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!
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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
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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
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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
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Scientific Notation and Error Propagation
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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)
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Introduction 21
Identity, Set up, Execute, Evaluate
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Introduction
Problem: How many gallons of gasoline are
used in the U.S. in one day?
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Introduction
V = N x D / M
Where
N = #cars
D = average driving
distance (mi)
M = gas mileage (mi/gl)
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Problem: How many gallons of gasoline are
used in the U.S. in one day?
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Introduction
V = N x D / M
Where
N = #cars
D = average driving
distance (mi)
M = gas mileage (mi/gl)
N = 200,000,000 people
x 50%(adults) x
50%(owners)
= 50,000,000
D = 30 mi
M = 10 mi/gl
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Problem: How many gallons of gasoline are
used in the U.S. in one day?
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Introduction
V = N x D / M
Where
N = #cars
D = average driving
distance (mi)
M = gas mileage (mi/gl)
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
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Problem: How many gallons of gasoline are
used in the U.S. in one day?
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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
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Introduction
Back-of-the-envelope Calculation
(Rapid Estimating)
20 m
1200 m
Estimate volume of a lake.
Order of Magnitude
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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.
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Order of Magnitude
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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
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Introduction
Draw a Diagram!!!!
© Physics for Scientists and Engineers,
D. Giancoli, 3rd ed. Prentice Hall 30
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Introduction
B A
x
D
A:D = (A+B) : (x–C)
Label them!!!
C
© Physics for Scientists and Engineers,
D. Giancoli, 3rd ed. Prentice Hall 31
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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
© Physics for Scientists and Engineers,
D. Giancoli, 3rd ed. Prentice Hall 32
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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
© Physics for Scientists and Engineers,
D. Giancoli, 3rd ed. Prentice Hall 33
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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
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Introduction
Displacement (Vector)
x
y
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Introduction
Direction: North Magnitude: 2.6 km
x
y
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Introduction
Direction: East Magnitude: 4.0 km
x
y
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Introduction
Direction: 45o North of East Magnitude: 3.1 km
x
y
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Introduction
Direction: ? Magnitude: ?
x y
D1
D2
D3
DR
DR
D1
D2 D3
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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
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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
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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
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Introduction
rx
ry
Two Vectors
u = (ux) i + (uy) j ^ ^ →
r + u = ? → →
r = (rx) i + (ry) j ^ ^ →
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Introduction
Vector Operations
x2.0 longer,
Opposite direction
x1.5 longer,
Same direction
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Introduction
[Quick Quiz 1] Find:
(a)A+B
(b)AB
(c) A+B+C
(d) A+BC
(e) BC
(f) AC
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Introduction
[Quick Quiz 1] Find:
(a)A+B
(b)AB
(c) A+B+C
(d) A+BC
(e) BC
(f) AC
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Adding vectors using their components
• Follow Examples 1.7 and 1.8.
Fig. 1.22 47
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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
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Introduction
Watch! Change in its
position vectors!
A
C
B
E
F
D
r = (x) i + (y) j → → →
O
49
Position Vector
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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
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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
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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]
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[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
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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
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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
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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
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Introduction
Today’s class
SI units
Dimensional analysis
Scientific notation
Error propagation
DaD, ISEE
Vector and Vector
Products.
Next class
Chapter 2
57
Summary