Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily...
-
Upload
judith-grindle -
Category
Documents
-
view
214 -
download
0
Transcript of Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily...
![Page 1: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/1.jpg)
Basic Physics
![Page 2: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/2.jpg)
Introduction
1. What is Physics?
2. Give a few relations between physics and daily living experience
3. Review of measurement and units SI, METRIC, ENGLISH
![Page 3: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/3.jpg)
VECTOR AND SCALAR
Scalar is a quantity which only signifies its magnitude without its direction. (+ / - )Ex. 1kg of apple, 273 degrees centigrade, etc.
Vector is a quantity with magnitude and direction. (+ / - )Ex. Velocity of a moving object – a car with a velocity of 100 km/hr due to North West, etc.
![Page 4: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/4.jpg)
VECTOR AND SCALAR
Writing conformity
F Bold font
F Italic font signifying its magnitude
F Normal Font with an arrow
head on top of it (Use this)
![Page 5: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/5.jpg)
VECTOR AND SCALAR
Defining a Vector by:
1. Cartesian Vector
Ex. F = 59i + 59j + 29k N
the magnitude is F = (592 + 592 + 292)
F = 88.33 N
Due to which is the vector ??
![Page 6: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/6.jpg)
VECTOR AND SCALAR
X (i)
Z(k)
Y(j)
F = 59i + 59j + 29k N
O
![Page 7: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/7.jpg)
VECTOR AND SCALARDefining a Vector by:2. Unit Vector
Ex. F = F u (use the previous example)
=
F for magnitude (F2 = Fx2 + Fy
2 + Fz2)
u for direction (dimensionless and unity)
uFF
![Page 8: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/8.jpg)
VECTOR AND SCALARMagnitude F = (592 + 592 + 292)
F = 88.33 N
Direction =
= 0.67i + 0.67j + 0.33k
= cos-1 0.67 = 47.9 0 (angle from x-axis) = cos-1 0.67 = 47.9 0 (angle from y-axis) = cos-1 0.33 = 70.7 0 (angle from z-axis)
59i + 59j + 29k88.33
u
u
![Page 9: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/9.jpg)
VECTOR AND SCALAR
X (i)
Z (k)
Y (j)
F = 88.33 N
U
FU = 0.67i + 0.67j + 0.33k
= 47.9 0
= 47.9 0
= 70.7 0
O
![Page 10: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/10.jpg)
VECTOR AND SCALAR
Defining a Vector by:3. Position Vector
Similar to unit vector, it differs on how to locate the vector’s direction which is using the point coordinate.
Ex. F = F u (see next example)
r (position vector)r (position vector magnitude)u =
![Page 11: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/11.jpg)
VECTOR AND SCALAR
U
6 m
4 m
2 m
Given:
F = 150 N
Required:
a. F ?
b. , , ?
X (i)
Z (k)
Y (j)
F
O
A
![Page 12: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/12.jpg)
VECTOR AND SCALAR
Solution:
rr
u =
F = F u
=2i + 4j + 6k
7.48
= 0.27i + 0.53j +0.80ku
![Page 13: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/13.jpg)
VECTOR AND SCALAR
Solution:
F = F u
= 150 (0.27i + 0.53j +0.80k)
F = 40.5i + 79.5j + 120k
= cos-1 0.27 = 74.3 0 (angle from x-axis) = cos-1 0.53 = 58.0 0 (angle from y-axis) = cos-1 0.80 = 36.9 0 (angle from z-axis)
a.
b.
![Page 14: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/14.jpg)
VECTOR AND SCALAR
Operations of Vector
1. Addition
2. Subtraction
3. Dot Product
4. Cross Product
![Page 15: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/15.jpg)
VECTOR AND SCALAR
1. Addition
F1
RF2
R = F1 F2+
R = (F1x + F2x) i + (F1y + F2y) j + (F1z+F2z) k
=Ry
Rx
Tan -1
O
![Page 16: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/16.jpg)
VECTOR AND SCALAR
1. Addition
F1
RF2
R = F1 F2+
R = (F1x + F2x) i + (F1y + F2y) j + (F1z+F2z) k
=Ry
Rx
Tan -1
O
Resultant is directed from initial tail towards final arrow head
![Page 17: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/17.jpg)
VECTOR AND SCALAR
2. Subtraction F1
RF2
R = F1 F2-
R = (F1x - F2x) i + (F1y - F2y) j + (F1z - F2z) k
=Ry
Rx
Tan -1
O
![Page 18: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/18.jpg)
VECTOR AND SCALAR
2. Subtraction F1
RF2
R = F1 F2-
R = (F1x - F2x) i + (F1y - F2y) j + (F1z - F2z) k
=
Ry
Rx
Tan -1O
Take note and watch out !!!
(the sense is opposite to the given
diagram)
![Page 19: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/19.jpg)
VECTOR AND SCALAR
3. Dot Product
F
d
X (i)
Z (k)
Y (j)
F
![Page 20: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/20.jpg)
VECTOR AND SCALAR
A . B = AB cos (General Formula)
Vector Magnitude
The angle between vectors (between their tails)
Cartesian Unit vector dot product
i . i = 1
i . j = 0 i . k = 0 k . j = 0
j . j = 1 k . k = 1
![Page 21: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/21.jpg)
VECTOR AND SCALAR
From Example:• F . d = Fd cos (Using Vectors’ magnitude)
= (Fxi + Fyj + Fzk) . (dxi + dyj + dzk)
= Fx dx + Fy dy + Fz dz (Using Component
Vector)
The dot product of two vectors is called scalar product since the result is a scalar and not a vector
![Page 22: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/22.jpg)
The dot product is used to determine:
1. The angle between the tails of the vectors.
VECTOR AND SCALAR
= cos -1A . B
AB
2. The projected component of a vector V onto an axis defined by its unit vector u
![Page 23: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/23.jpg)
Welcome to
the
Jungle
![Page 24: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/24.jpg)
VECTOR AND SCALAR
X (i)
Z (k)
Y (j)O
B
A
C
F = 100 N
Given : Figure 1
Required:
1.
2. FBA (Magnitude)
Fig.1
Example:
![Page 25: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/25.jpg)
VECTOR AND SCALAR
Solution :
1. Angle
Find position vectors from B to A and B to C
rBA = -200i – 200j + 100k
r BC = -0i – 300j + 100k = – 300j + 100k
cos =rBA . rBC
rBA rBC=
0 + 60000 + 10000
(300)(316.23)=
70000
94869= 0.738
= Cos -1 0.738 = 42.45 o (answer)
![Page 26: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/26.jpg)
VECTOR AND SCALAR
Solution :
=rBA uBA =
rBA
2. FBA
-200i – 200j + 100k
300= -0.667i – 0.667j + 0.33k
rBC uBC =
rBC =
-0i – 300j + 100k
316.2= – 0.949j + 0.316k
FBC = FBC . uBC = 100 . (– 0.949j + 0.316k) = -94.9j + 31.6k
FBA = FBC . uBA = (-94.9i + 31.6j) . (-0.667i – 0.667j + 0.33k)
= 63.3 + 10.5 = 73.8 N (answer)
![Page 27: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/27.jpg)
VECTOR AND SCALAR
Solution :
Alternative Solution
FBA = (100 N) (cos 42.45o)
= 73.79 N
FBA = FBA uBA = 73.79 (-0.667i - 0.667j + 0.33k)
= -49.2i – 49.2j + 24.35k
![Page 28: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/28.jpg)
VECTOR AND SCALAR
4. Cross Product
B
A
F
X (i)
Z (k)
Y (j)O
![Page 29: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/29.jpg)
VECTOR AND SCALAR
A = B x C A is equal to B cross C
Apply the right hand rule
i
j k
i x j = k
j x k = i
k x i = j
j x i = -k
k x j = -i
i x k = -j
i x i = 0
j x j = 0
k x k = 0+
-
![Page 30: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/30.jpg)
VECTOR AND SCALAR
Right Hand Rule
![Page 31: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/31.jpg)
VECTOR AND SCALAR
Right Hand Rule
![Page 32: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/32.jpg)
VECTOR AND SCALAR
Right Hand Rule
![Page 33: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/33.jpg)
VECTOR AND SCALAR
Right Hand Rule
……. (answer for yourself)
![Page 34: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/34.jpg)
VECTOR AND SCALAR
A = B x C
= (Bx i + By j + Bz k) x (Cx i + Cy j + Cz k)
i j k
Bx By Bz
Cx Cy Cz
=
= (By Cz – Bz Cy)i + (Bz Cy – Bx Cz)j + (Bx Cy – By Cx)zA
i j k
Bx By Bz
Cx Cy Cz
=i j
Bx By
Cx Cy
+-
= (By Cz – Bz Cy)i – (Bx Cz – Bz Cx)j + (Bx Cy – By Cx)z
![Page 35: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/35.jpg)
VECTOR AND SCALAR
A = B x C
= (Bx i + By j + Bz k) x (Cx i + Cy j + Cz k)
i j k
Bx By Bz
Cx Cy Cz
=
= (By Cz – Bz Cy)i + (Bz Cy – Bx Cz)j + (Bx Cy – By Cx)zA
i j k
Bx By Bz
Cx Cy Cz
=i j
Bx By
Cx Cy
+-
= (By Cz – Bz Cy)i – (Bx Cz – Bz Cx)j + (Bx Cy – By Cx)z
Full caution for the +/- sign
and subscripts
![Page 36: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/36.jpg)
VECTOR AND SCALAR
Example: Given : Figure 2
Required :
1. Mo (Moment at point O)
2. My (Moment about y axis)
B
A
F = 100N
X (i)
Z (k)
Y (j)O
Mo
![Page 37: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/37.jpg)
VECTOR AND SCALAR
Solution:Finding the vectors neededF = F u
= 100400i – 250j – 200k
(4002 + 2502 + 2002)( )
F = 78.07i – 48.79j – 39.04k
OA = 400j
OB = 400i + 150j – 200k
![Page 38: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/38.jpg)
VECTOR AND SCALAR
B
A
F = 100 N
X (i)
Z (k)
Y (j)
O
Mo
400j
400i + 150j – 200k
F = 78.07i – 48.79j – 39.04k
![Page 39: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/39.jpg)
VECTOR AND SCALAR
Mo =
=
Mo = -15616i – 31228k N.mm
FOA x
i j k
0 400 0
78.07 -48.79 -39.04
Mo = 34914.86 N.mm
= cos-1 (-0.447) = 116.55 0 (angle from x-axis) = cos-1 0 = 90.0 0 (angle from y-axis) = cos-1 0.894 = 26.57 0 (angle from z-axis)
![Page 40: Basic Physics. Introduction 1.What is Physics? 2.Give a few relations between physics and daily living experience 3.Review of measurement and units SI,](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b0aee550346cf5a8b4d0b/html5/thumbnails/40.jpg)
VECTOR AND SCALAR
Mo =
Mo = -15616i – 31228k N.mm
FOB x
Mo = 34914.86 N.mm
= cos-1 (-0.447) = 116.55 0 (angle from x-axis) = cos-1 0 = 90.0 0 (angle from y-axis) = cos-1 0.894 = 26.57 0 (angle from z-axis)
i j k
400 150 -200
78.07 -48.79 -39.04
=