Chapter 5 Displacement and Forces in Two...
Transcript of Chapter 5 Displacement and Forces in Two...
![Page 1: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/1.jpg)
Chapter 5
Displacement and
Forces in Two
Dimensions
![Page 2: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/2.jpg)
Vectors:
• Vectors have both ____________and
_____________.
• Vectors must be added using _________
________________.
• You can add vectors _______________as
long as you ________________ their
_______________________________.
2
![Page 3: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/3.jpg)
Measuring Angles
• GEOGRAPHICAL :
• MATHEMTATICAL:
![Page 4: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/4.jpg)
4
Vector Direction Examples
• 35 m/s, 40⁰ E of N
• 10 N, 210⁰
![Page 5: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/5.jpg)
PH Ch 4 Vector 5
Resultant Vector • The ______________________________.
• Always drawn from the _______________
to the ___________________.
• Direction should always be measured
between the _______________ and the
__________________.
![Page 6: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/6.jpg)
6
Adding Vectors Method 1:
1. Scaled Vector Diagram/Graphically
• Decide on a _____________________________
• Using a ______ to measure the __________ and a
____________ to measure __________________ draw
the vectors tip to tail.
• Draw the ___________________ from the ______ of the
first to the ______ of the last vector.
• Use a ruler to measure the _______________ of the
resultant vector. Convert using __________________.
• Use a protractor to measure the ___________________
_____________________________________________.
![Page 7: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/7.jpg)
PH Ch 4 Vector
![Page 8: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/8.jpg)
8
Adding Vectors Method 2:
1.Mathematical Method
• If the two vectors
being added are at
_______________,
the magnitude can be
found using the
_________________
and the direction can
be found using _____
_________________.
![Page 9: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/9.jpg)
• If the two vectors being added
are _____________
________________, the
magnitude can be found using
the _____________________
and the direction can be found
using ____________________
PH Ch 4 Vector
![Page 10: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/10.jpg)
Trig Review:
Trig Functions
PH Ch 4 Vector
![Page 11: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/11.jpg)
Law of Cosines
PH Ch 4 Vector
![Page 12: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/12.jpg)
Law of Sines
PH Ch 4 Vector
![Page 13: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/13.jpg)
13
EX: Add these vectors.
• 2.0 m/s, 90 deg
• 7.0 m/s, 0 deg
![Page 14: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/14.jpg)
14
EX:
Add the following vectors.
15 km South
13 km East
![Page 15: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/15.jpg)
15
Examples:
1. A person walks 100m N and loses all sense if direction. Without
knowing the direction, she walks 100m again. Draw a vector
representation and determine the range of her displacement.
![Page 16: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/16.jpg)
PH Ch 4 Vector
2. You are traveling from SMCC to Jackson for the football
game. You travel 30 km west, 20 km north, and 10 km west.
Find your displacement (magnitude and direction) both
graphically and mathematically.
![Page 17: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/17.jpg)
3. A person jogs 15 km west and then turns to the right at a 45
degree angle and continues to run 25 more kilometers. Find the
resultant vector for the jogger.
![Page 18: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/18.jpg)
Components of a Vector – the
________________________
that make up the __________
![Page 19: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/19.jpg)
19
Components
• You can use _______ to
find the components.
![Page 20: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/20.jpg)
*Be careful if the angle is bigger than ___degrees.
You may have to use a ___________________
to find the components.
PH Ch 4 Vector
![Page 21: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/21.jpg)
21
Method 3: Vector
Resolution/Components
Two or more vectors can be added by:
• Resolving each vector into its _________
_______________.
• _____all the x-components to form the
________________________________:
Rx = Ax + Bx + Cx…
• _____ all the y-components to form the
________________________________: Ry = Ay + By + Cy…
![Page 22: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/22.jpg)
PH Ch 4 Vector 22
• Use the ___________
_______ to find the
_____________ of the
resultant R.
R2 = Rx2 + Ry
2
• Use ___________ to
find the __________
of R.
![Page 23: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/23.jpg)
PH Ch 4 Vector
![Page 24: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/24.jpg)
Examples:
A bus travels 23 km on a straight road
that is 30º N of E. What are east and
north components of its displacement?
![Page 25: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/25.jpg)
EX:
Add the following three vectors using the
component method: A is 4 m south, B is 7.3 m northwest, C is 6 m 30⁰ south of
west.
![Page 26: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/26.jpg)
PH Ch 4 Vector
![Page 27: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/27.jpg)
Example:
You’re a pilot & are instructed to go around a
massive thunderstorm. The control tower tell
you take a detour & follow these 3 paths :
100 km, 45o N of E ,
65 km, 10o S of E
20 km, 5⁰ S of E
What is the plane’s displacement from where
it began it’s detour?
![Page 28: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/28.jpg)
PH Ch 4 Vector
![Page 29: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/29.jpg)
FRICTION
• _____________ friction force: the force
exerted on _________________________
when the objects are in _____________
EX:
• µ = “mu” = ____________________
• Ff is proportional to the force _______
______________________________
![Page 30: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/30.jpg)
FRICTION
• __________ friction
force: the force
exerted on one
surface by another
surface when there is
__________between
the two surfaces.
EX:
![Page 31: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/31.jpg)
FRICTION
• Eventually there is a ___________to this static friction force – once the __________ is _________than the _______________ ____________, the object will begin to ___________.
• Until this point, _______________ exactly ___________ the __________________.
• Maximum Static Friction Force:
![Page 32: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/32.jpg)
FRICTION
• Besides the ____________,
friction also depends on the ____
____________ that are in contact.
• Different surfaces have ________
___________________________
• Table p.317
![Page 33: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/33.jpg)
EX: You push a 25 kg wooden
box across a wooden floor at a
constant speed of 1 m/s. How
much force do you exert on the
box?
![Page 34: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/34.jpg)
EX:
A small child is dragging a heavy, rubber-
soled shoe by its laces across a sidewalk
at a constant speed of 0.35 m/s. If the
shoe has a mass of 1.56 kg, what is the
horizontal component of the force exerted
by the child? μ = 0.65
PH Ch 4 Vector
![Page 35: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/35.jpg)
EX:
• If the child pulls with an extra 2 N in the
horizontal direction, what will be the
acceleration of the shoe?
PH Ch 4 Vector
![Page 36: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/36.jpg)
PH Ch 4 Vector
Inclined Planes • Inclined Plane____________
• _________________
• The force of _____________ acts in the ______________ direction.
• The ___________force acts in a direction _____________ to the surface.
![Page 37: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/37.jpg)
PH Ch 4 Vector
Components Analyzing forces on inclined planes will
involve resolving the __________________ into _______________________________.
- one _____________ to the surface:____
- one _____________ to the surface: ____
The ___________ force is the force that can cause an object to ____________________
![Page 38: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/38.jpg)
PH Ch 4 Vector
Forces on an Inclined Plane
The _______________ always ________ the
angle between ________ and _________.
Use _____________ to find the components.
![Page 39: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/39.jpg)
PH Ch 4 Vector
Practice
![Page 40: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/40.jpg)
PH Ch 4 Vector
![Page 41: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/41.jpg)
PH Ch 4 Vector
Example
A trunk weighing 562 N
is resting on a plane
inclined 30º above the
horizontal. Find the
normal and frictional
forces.
![Page 42: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/42.jpg)
PH Ch 4 Vector
![Page 43: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/43.jpg)
PH Ch 4 Vector
Example
A 62 kg person on skis is
going down a hill sloped
at 37º. The coefficient
of kinetic friction
between the skis and
the snow is 0.15. How
fast is the skier going 5
s after starting from
rest?
![Page 44: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/44.jpg)
PH Ch 4 Vector
![Page 45: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/45.jpg)
PH Ch 4 Vector
Equilibrant
Equilibrant – a __________ that puts an
object in _________________.
To find the equilibrant:
Find the _____________ of all the forces
on the object.
The equilibrant is the ________________
but ________________________.
![Page 46: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/46.jpg)
PH Ch 4 Vector
![Page 47: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/47.jpg)
EX: What is the equilibrant for an 8 N force
applied at 0º,a 6 N force applied at 90º,
and a 7 N force applied at 60º?
PH Ch 4 Vector
![Page 48: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/48.jpg)
PH Ch 4 Vector
![Page 49: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/49.jpg)
EX: What is the tension in each
cable?
PH Ch 4 Vector
![Page 50: Chapter 5 Displacement and Forces in Two Dimensionsmrsmyersphysics.weebly.com/uploads/1/3/3/0/13301533/chapter_5_… · 2. You are traveling from SMCC to Jackson for the football](https://reader034.fdocuments.net/reader034/viewer/2022052408/5f093e357e708231d425e76e/html5/thumbnails/50.jpg)
PH Ch 4 Vector