displacement and force in two dimensions
TRANSCRIPT
![Page 1: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/1.jpg)
Displacement and Force in
Two Dimensions
![Page 2: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/2.jpg)
Lesson 1: Vectors
![Page 3: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/3.jpg)
OBJECTIVE: 1. To graphically add vectors2. To discuss vector components3. To add and subtract vectors.
Section 1: Vectors
![Page 4: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/4.jpg)
What does this symbol mean?
![Page 5: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/5.jpg)
![Page 6: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/6.jpg)
What does this symbol mean?
![Page 7: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/7.jpg)
No or Prohibited
![Page 8: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/8.jpg)
What does this symbol mean?
![Page 9: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/9.jpg)
![Page 10: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/10.jpg)
What does this symbol mean?
![Page 11: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/11.jpg)
![Page 12: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/12.jpg)
Other Signs and symbols we encounter everyday
![Page 13: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/13.jpg)
• Daily situations use abstractions as well as math everywhere we go.
• Can symbols be used to express an idea or concept?
![Page 14: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/14.jpg)
a)
b)
c)
1. What does these arrows mean?2. What two properties of arrows being illustrated by these examples?
![Page 15: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/15.jpg)
Two properties: Size (magnitude) or direction
a)
b)
c)
![Page 16: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/16.jpg)
Remember…A vector is a quantity that has both magnitude and direction.
Example of Vector Quantities: Displacement, velocity, acceleration, and force
![Page 17: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/17.jpg)
Vector Components
![Page 18: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/18.jpg)
Angled Vectors Have Two Components
![Page 19: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/19.jpg)
Adding and Subtracting vectors
![Page 20: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/20.jpg)
Vectors: Distance and DisplacementsTotal Distance
Total Displacement
5 steps south
5 steps north
10 steps west
10 Steps north
10 steps west
10 Steps north
5 steps south
5 steps north
5 steps south
10 steps west
5 steps north
10 Steps north
10 steps west
5 steps north
10 Steps north
5 steps south
5 steps south
10 Steps north
5 steps north
10 steps west
![Page 21: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/21.jpg)
Vectors: Distance and DisplacementsTotal Distance
Total Displacement
5 steps south
5 steps north
10 steps west
10 Steps north
30 5
10 steps west
10 Steps north
5 steps south
5 steps north
30 5
5 steps south
10 steps west
5 steps north
10 Steps north
30 5
10 steps west
5 steps north
10 Steps north
5 steps south
30 5
5 steps south
10 Steps north
5 steps north
10 steps west
30 5
![Page 22: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/22.jpg)
Free-body diagrams
![Page 23: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/23.jpg)
SIMPLE EXERCISE
A book is at rest on a tabletop. Diagram the forces acting on the book.
![Page 24: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/24.jpg)
SIMPLE EXERCISE
A book is at rest on a tabletop. Diagram the forces acting on the book.
![Page 25: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/25.jpg)
As you watch… • Identify the forces acting on the cup.
Displacement and Force in Two DimensionsCopyright © McGraw-Hill Education
![Page 26: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/26.jpg)
Displacement and Force in Two Dimensions
Follow UpMake a force diagram for each of the following situations:• The car is at rest.• The car accelerates and the cup remains on the roof.• The car accelerates and the cup falls off the roof.
Copyright © McGraw-Hill Education
![Page 27: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/27.jpg)
Exercise on Free-body diagram
![Page 28: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/28.jpg)
Lab Activity 2: Adding Vectors
![Page 29: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/29.jpg)
ANSWER TO THE LAB ACTIVITY
• Does the sum of the forces measured by the two spring scales equal the weight of the hanging object? Is the sum greater than the weight? Less than the weight?
• The sum of the weight on both scales is apparently greater than the weight of the hanging object.
![Page 30: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/30.jpg)
ANSWER TO THE LAB ACTIVITY
• Critical Thinking Draw an equilateral triangle, with one side vertical. If the two sides of the triangle are 2.0 N, explain the size of the third side. How is it possible that 2 N 2 N 2 N?
![Page 31: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/31.jpg)
ANSWER TO THE LAB ACTIVITY• Critical Thinking Draw an equilateral triangle, with one
side vertical. If the two sides of the triangle are 2.0 N, explain the size of the third side. How is it possible that 2 N 2 N 2 N?
• Because vector addition accounts for both direction and magnitude, 2 N 2 N can equal 2 N if the two forces are added as vectors. One way to think about the net force acting on an object is to imagine replacing all of the individual forces with a single force that has the same effect. The purpose of vector resolution is to determine the magnitude and direction of that net force.
![Page 32: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/32.jpg)
How do we add them?
![Page 33: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/33.jpg)
For right angles
![Page 34: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/34.jpg)
Quick exercise
![Page 35: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/35.jpg)
Quick exercise
![Page 36: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/36.jpg)
Using Trigonometry to Determine a Vector's Direction
MNEMONIC: SOH CAH TOA (to remember the sine, cosine and tangent functions)
![Page 37: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/37.jpg)
Quick Exercise• Eric leaves the base camp and hikes 11 km,
north and then hikes 11 km east. Determine Eric's resulting direction of displacement.
![Page 38: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/38.jpg)
Quick Exercise• Eric leaves the base camp and hikes 11 km,
north and then hikes 11 km east. Determine Eric's resulting displacement.
![Page 39: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/39.jpg)
Lab Activity 1: Walking Vectors(Displacement)
Purpose: To let you experience one example of a vector.
![Page 40: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/40.jpg)
Practical ApplicationGroup work: • Research on one practical application of vector in
real life. Be ready to share your output in class next meeting.
• Use of visual materials are highly encouraged (powerpoint, videos, animations, actual objects, etc.)
![Page 41: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/41.jpg)
Practical Application of vectors• Architecture and Engineering: computing for forces so that the
building will be stable and will not collapse. Example: Isolation technique or ball bearings for earthquake proof buildings
http://imaginationstationtoledo.org/content/2011/03/can-you-build-an-earthquake-proof-building/
![Page 42: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/42.jpg)
Practical Application of vectorsMeteorology• Wind direction• Typhoon formation• Tornado formation
![Page 43: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/43.jpg)
Practical Application of vectorsNavigation
![Page 44: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/44.jpg)
Practical Application of vectorsSports• Movements and direction of players/ball can be
represented by vectors or arrowsExample: A quarter pass
![Page 45: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/45.jpg)
Practical Application of vectorsSports• a billiard game• with an understanding of vectors, billiards players can
predict where both balls will go following a collision, allowing them to sink more target balls while keeping the cue ball safely on the table.
![Page 46: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/46.jpg)
Practical Application of vectors• Projectile motion of bombarding rockets• Flight testing
![Page 47: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/47.jpg)
Lesson 2: Friction
![Page 48: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/48.jpg)
Simple Demonstration1. Push the ice cube on the table. 2. Wipe the table with tissue to make it dry3. Push the eraser with the same force you applied
towards the ice cube.
A. What do you notice about the behavior of the two objects?B. Give possible reasons for their difference.C. What is the first thing that enters your mind when you hear
the word friction?FRICTION is a type of force between two touching objects.
![Page 49: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/49.jpg)
TYPE OF FRICTION1. Kinetic or Dynamic Friction - force exerted on one surface by another when the two surfaces rub against each other because one or both surfaces are moving.2. Static Friction - the force exerted on one surface by another when there is no motion between the two surfaces. (You need to push harder)
![Page 50: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/50.jpg)
TYPE OF FRICTION• An applied force is balanced by static friction
up to a maximum limit. When this limit is exceeded, the object begins to move.
![Page 51: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/51.jpg)
On what does a friction force depend?
Example: Rubber shoes and concrete floorSocks and polished wood
![Page 52: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/52.jpg)
How much Friction is there?
![Page 53: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/53.jpg)
How is Coefficient of Kinetic Friction Determined?
![Page 54: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/54.jpg)
![Page 55: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/55.jpg)
Sample Problem
• A book is resting on the table. The coefficient of Kinetic friction between the table and the book is 13.5. If the book weighs 500 N, what horizontal force is needed to push the book at a constant speed?
![Page 56: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/56.jpg)
Page 133
![Page 57: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/57.jpg)
Critical Thinking
• Which one is better, a low friction between surface or high friction between surfaces?
- it depends on the situation. Low friction situations include pistons in engines and skis on snow. High friction is desired include erasers on paper or a flag twirler’s gloves gripping the flagpole.
![Page 58: Displacement and force in two dimensions](https://reader034.vdocuments.mx/reader034/viewer/2022042500/5880f2b21a28abc3368b4d01/html5/thumbnails/58.jpg)
Critical Thinking
• When it is good enough to have high coefficient of friction between two surfaces?
- running shoes on a track, sandpaper on a wood, car breaks on wheels, and car tires on roads.