Chapter 4 The Laws of Motion 1. Force 2. Newtons Laws 3. Applications 4. Friction.
Martha Casquetemarthacasqueteutpa.weebly.com/uploads/2/0/9/9/... · 13 Two students are moving a...
Transcript of Martha Casquetemarthacasqueteutpa.weebly.com/uploads/2/0/9/9/... · 13 Two students are moving a...
Martha Casquete
Read Chapter 3 (Vectors) HW3 Set due next Tuesday, 9/17 Pg. 68 – 70: 1, 4, 11, 16, 26, 32, 43 (8th edition)
Question/Observation Thursdays
Research Q/O Tuesdays with HW (due date
Tuesdays)
Coordinate Systems
Vector and Scalar Quantities
Properties of Vectors
Component of Vector and Unit Vectors
Distance and displacement
Average velocity and average speed
Instantaneous velocity and speed
Acceleration
Free fall acceleration:
a = g =- 9.80 m/s2
Would you risk your life driving drunk?
Intro
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002
1gttvxx
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In 2-D : describe a location in a plane
• by polar coordinates : distance r and angle • by Cartesian coordinates :
distances x, y, parallel to axes
with: x = rcosθ y = rsinθ x
y
r
( x , y )
0 x
y
• Since we know the Cartesian coordinates, we can find r and :
• x
ytan
22 yxr
A fly lands on one wall of a room. The lower left corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. If the fly is located at the point having coordinates (2.00, 1.00) m , (a) how far is it from origin? (b) What is its location in polar coordinates?
Physical quantities are classified as scalars, vectors, etc.
Scalar : described by a real number with units
examples: mass, charge, energy . . .
Vector : described by a scalar (its magnitude) and a direction in space
examples: displacement, velocity, force . . .
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Vectors have direction, and obey different rules of arithmetic.
Scalars : ordinary or italic font (m, q, t . . .) Vectors : - Boldface font (v, a, F . . .) - arrow notation
Pay attention to notation :
“constant v” and “constant v” mean different things!
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.) . . F ,a ,v(
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Magnitude : a scalar, is the “length” of a vector.
e.g., Speed, v = |v| (a scalar), is the magnitude of velocity v
3.3 Properties of Vectors
Direction
Commutative Law Associative Law of addition
ABBA
CBACBA
)()(
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CBA
e.g.
A B
Triangle Method Parallelogram Method
A
B
A
B
BAC
BAC
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CBA
e.g.
A
B
A
B
BAC
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Two students are moving a refrigerator. One pushes with a force of 200 newtons, the other with a force of 300 newtons. Force is a vector. The total force they (together) exert on the refrigerator is:
a) equal to 500 newtons b) equal to newtons c) not enough information to tell
22 300200
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Two students are moving a refrigerator. One pushes with a force of 200 newtons (in the positive direction), the other with a force of 300 newtons in the opposite direction. What is the net force ?
a)100N
b)-100N
c) 500N
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A A
2
3
A
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Multiplication: scalar vector = vector
Later in the course, we will use two other types of multiplication: the “dot product” , and the “cross product”.
Follow the steps for Example 2.3 from your book (pg. 60)
define the axes first
are scalars
axes don’t have to be horizontal and vertical
the vector and its components form a right triangle with the vector on the hypotenuse
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) (and , , zyx vvv
x
y
vy
vx
v
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cos vvx
x
y
vy
vx
v
yv
sin vvy
xv
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yx vvv
x
y
v
v1tan
Choose the correct response to make the sentence true: A component is
(a) always
(b) never
( c ) sometimes
…..larger than the magnitude of the vector.
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---Specify a given direction Define coordinate unit vectors i, j, k along the x, y, z axis.
z
y
x
i
j
k
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A vector can be written in terms of its components: A
kAjAiAA zyx
i
j
A
Ax i
Ay j
Ay j
Ax i
A
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Ax
Ay A
By
Bx
B
By
Bx
B
Ay
Ax
A
C
Cx
Cy
If A + B = C , then:
zzz
yyy
xxx
BAC
BAC
BAC
Three scalar equations from one vector equation!
Tail to Head
BA
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CBA
In components (2-D for simplicity) :
jiji )( )( yxyyxx CCBABA
The unit-vector notation leads to a simple rule for the components of a vector sum:
Eg: A=2i+4j B=3i-5j
A+B = 5i-j A - B = -i+9j
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Magnitude : the “length” of a vector. Magnitude is a scalar.
In terms of components: On the diagram, vx = v cos vy = v sin
x
y
vy
vx
v
e.g., Speed is the magnitude of velocity: velocity = v ; speed = |v| = v
22|| yx vv v
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Example 2
While exploring a cave, a spelunker starts at the entrance and moves the following distances in a horizontal plane. She goes 75.0 m north, 250 m east, 125m at an angle θ = 30˚ north of east, and 150 m south. Find her resultant displacement from the cave entrance.
vector quantities must be treated according to the rules of vector arithmetic
vectors add by the triangle rule or parallelogram rule (geometric method)
a vector can be represented in terms of its Cartesian components using the “unit vectors” i, j, k these can be used to add vectors (algebraic method)
if and only if:
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A
BAC
zzzyyyxxx BACBACBAC