Transcript Physics 101: Lecture 1 Notes

Lecture 4: Introduction to Physics
PHY101
Chapter 1 :
• Scalars and Vectors (1.5)
Physics 101: Lecture 4, Pg 1
Vectors
Vectors are graphically represented by arrows:
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The direction of the physical quantity is given by
the direction of the arrow.
The magnitude of the quantity is given by the
length of the arrow.
Physics 101: Lecture 4, Pg 2
Addition of Vectors
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Graphical: Tail-to-head method
Resultant of Forces (Addition of Vectors)
Physics 101: Lecture 4, Pg 3
Graphical Method - Example
You are told to walk due east for 50 paces, then
30 degrees north of east for 38 paces, and then due south
for 30 paces.
What is the magnitude and direction of your total
displacement ?
Answer:
magnitude: 84 paces
direction: 7.5 degrees south of east
Physics 101: Lecture 4, Pg 4
Addition of Vectors
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Using components (A,B lie in x,y plane):
C = A+B = Ax + Ay + Bx + By = Cx+Cy
Cx and Cy are called vector components of C.
They are two perpendicular vectors that are parallel
to the x and y axis.
Ax,Ay and Bx, By are vector components of A and B.
Physics 101: Lecture 4, Pg 5
Scalar Components of a Vector (in 2 dim.)
Vector components of vector A:
A = Ax +Ay
 Scalar components of vector A:
A = Ax x +Ay y
Ax and Ay are called scalar
components of A.
x and y are unit vectors.
Equivalently:
A=(Ax,Ay)
A is a vector pointing from the
origin to the point with
coordinates Ax,Ay.
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Physics 101: Lecture 4, Pg 6
Scalar Components of a Vector (in 2 dim.)
Scalar
components of vector A:
A = Ax x +Ay y
|A|, q known:
|Ax|= |A| Cos q
|Ay|=|A| Sin q
Ax, Ay known:
A2=(Ax )2+(AY)2
q= Tan-1 |Ay|/|Ax|
Physics 101: Lecture 4, Pg 7
Addition of Vectors
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Using scalar components (A,B lie in x,y plane):
C = A+B = Ax x + Ay y+ Bx x+ By y= Cx x+Cy y
1. Determine scalar components of A and B.
2. Calculate scalar components of C :
Cx = Ax+Bx and Cy=Ay+By
3. Calculate |C| and q :
C2=(Cx )2+(CY)2
q= Tan-1 |Cy|/|Cx|
Physics 101: Lecture 4, Pg 8
Component Method - Example
You are told to walk due east for 50 paces (A), then
30 degrees north of east for 38 paces (B), and then due
south for 30 paces (C).
What is the magnitude and direction of your total
displacement R=A+B+C ?
1. Determine scalar components of A,B,C:
Ax=50 p. , Ay=0, Bx=38 p. cos 30 , By=38 p. sin 30
Cx=0, Cy=-30 p.
2. Determine Rx,Ry:
Rx=Ax+Bx+Cx=83 p. Ry=Ay+By+Cy=-11 p.
3. Determine R:
R=(Rx2+Ry2)1/2=84 p.
q=Tan-1 Ry/Rx=7.5 degrees below the +x axis
Physics 101: Lecture 4, Pg 9
Addition of Vectors
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vector sum
Physics 101: Lecture 4, Pg 10
Components of a Vector - Example
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What is the magnitude of the vector F=-5 x-6 y ?
What angle does it make with the +x direction ?
Answer:
F=(-5,-6), Fx=-5, Fy=-6, F=(52+62)1/2= 7.8
q=Tan-1 |Fy|/|Fx| = 50 degrees
Angle with the +x direction: (180+q) degrees=230 degrees
Physics 101: Lecture 4, Pg 11
Lecture 4:
• Scalars and Vectors
• Vector addition using scalar components
of a vector
I strongly suggest that you try the
example problems in the textbook.
If you have trouble with any of them, please
go to office hours for help!
Physics 101: Lecture 4, Pg 12