Embed Size (px)
Citation preview
Dynamics Notes Part 1 Vector Analysis
1
October 05, 2017
Outcomes
Curriculum Outcomes:
Vector Analysis of Forces and Motion (15 hours)¨ use vector analysis in two dimensions for systems involving two or more masses, relative motions, static equilibrium, and static torques (ACP‑1)
¨ use vectors to represent forces and acceleration of an object when acted on by unbalanced forces (325‑5)
What you will be able to do:• Use vector analysis to solve 2D problems involving...> relative velocities> forces at an angle and inclined planes> forces acting on multiple objects> static equilibrium and torque
Scalars vs Vectors
Scalars vs Vectors
Magnitude MagnitudeDirection&
AmountQuantity
MeasurementNumber[ ]
Distance: 5 mSpeed: 110 km/hTime: 46 mins
Acceleration: 2 m/s2Mass: 75 kgEnergy: 120 JWork: 80 J
Displacement: 5 m [W]Velocity: 110 km/h [E]
Acceleration: 2 m/s2 @ 45Force: 500 N [down]
Momentum: 45 kgm/s [right]
o
Describing Motion
Dynamics Notes Part 1 Vector Analysis
2
October 05, 2017
+/ Directions
Describing MotionWhen performing calculations using vectors, you must show opposite directions using +/‑ signs. Set them yourself if the question hasn't done it. Usually, we use the conventions below, but it's really up to you as long as you are consistent.
Positive Directions: up, right, north, & eastNegative Directions: down, left, south, & west
Graphing Vectors
Graphical Vector AnalysisVectors are represented by arrows. • The length of the arrow corresponds to the magnitude (size/value/number) of the vector quantity. • The direction in which the arrow points corresponds to the direction of the vector quantity.1‑Dimensional Examples 2‑Dimensional Examples
A jogger runs 3.5 km East.
A falling object accelerates 9.81 m/s2 downward.
A ship travels 40 km/h [W 35° S].
A golf ball is lauched up 16° from horizontal with a velocity of 54 m/s.
Dynamics Notes Part 1 Vector Analysis
3
October 05, 2017
Graphing Vectors
Graphical Vector AnalysisVectors are represented by arrows. • The length of the arrow corresponds to the magnitude (size/value/number) of the vector quantity. • The direction in which the arrow points corresponds to the direction of the vector quantity.1‑Dimensional Examples 2‑Dimensional Examples
A jogger runs 3.5 km East.
A falling object accelerates 9.81 m/s2 downward.
3.5 km
9.81 m/s 2
A ship travels 40 km/h [W 35° S].
A golf ball is lauched up 16° from horizontal with a velocity of 54 m/s.
35°
40 km/h
16°54 m/s
Graphing Vectors
Graphical Vector AnalysisYou must ALWAYS use a ruler and a protractor when graphing vectors or making a scale drawing.
You must also show what scale you're using.
Dynamics Notes Part 1 Vector Analysis
4
October 05, 2017
Examples
Example 1: 2.1 km [N 40° W] Example 2: 6.5 m [E 18° S]
Example 3: 20 m/s [W 65° S] Example 4: 2.1 km [E 70° N]
Graphical +
Dynamics Notes Part 1 Vector Analysis
5
October 05, 2017
Mathematical +
Graphical Vector AdditionOften, an object's motion is described by several individual vectors, as shown in the example below. There are some special rules about how to add individual vectors together to find the total, or resultant vector.
Example: A student walks from her home to school each morning, along the path shown here.Individual displacement vectors are shown in blue:
d1 = 110 m [E]d2 = 230 m [N]d3 = 200 m [E]d4 = 68 m [N]
The total displacement vector from home to school is shown in red.
d1
d2
d3d4
d
Mathematical +
Mathematical Vector AdditionExample: A student walks from her home to school each morning, along the path shown here.
d1
d2
d3d4
d
110 m [E] + 200 m [E]
230 m [N] + 68 m
[N]
dx
dy
1) Use Pythagorean Theorem to find the magnitude (size) of the resultant vector:
a2 + b2= c2 dx2 + dy2= d2
2) Use trig to find the angle of the resultant vector:tanθ = opp θ = tan‑1 dy
adj dx
θ
[ ]d = 430 m [E44°N]Answer
Dynamics Notes Part 1 Vector Analysis
6
October 05, 2017
Example 1
Example 1
Dynamics Notes Part 1 Vector Analysis
7
October 05, 2017
p. 93, 94
Example 2
Dynamics Notes Part 1 Vector Analysis
8
October 05, 2017
Example 3
p. 102103 #17
Dynamics Notes Part 1 Vector Analysis
9
October 05, 2017
p. 102103 #1820
Example 4
Dynamics Notes Part 1 Vector Analysis
10
October 05, 2017
Example 4
Example 4
Dynamics Notes Part 1 Vector Analysis
11
October 05, 2017
Example 4
Example 5
Dynamics Notes Part 1 Vector Analysis
12
October 05, 2017
Example 5
Example 5
Dynamics Notes Part 1 Vector Analysis
13
October 05, 2017
p. 110 #2124
Sep 187:57 AM
Dynamics Notes Part 1 Vector Analysis
14
October 05, 2017
Sep 188:04 AM
Sep 188:10 AM
Dynamics Notes Part 1 Vector Analysis
15
October 05, 2017
p. 110 #2527
Sep 188:22 AM
Dynamics Notes Part 1 Vector Analysis
16
October 05, 2017
p. 459 #13
Vector ComponentsExample: Determine the x‑ and y‑ components of the displacement vector d = 64 m @ 120 from the x ‑axis.
Sep 198:01 AM
Dynamics Notes Part 1 Vector Analysis
17
October 05, 2017
Sep 198:01 AM
Sep 198:01 AM
Dynamics Notes Part 1 Vector Analysis
18
October 05, 2017
Example p. 460
Sep 198:32 AM
Dynamics Notes Part 1 Vector Analysis
19
October 05, 2017
p. 463 #46
Sep 2211:37 AM
Dynamics Notes Part 1 Vector Analysis
20
October 05, 2017
#4
#5
Dynamics Notes Part 1 Vector Analysis
21
October 05, 2017
#6
