Upload
amable
View
56
Download
0
Embed Size (px)
DESCRIPTION
Physics: Problem Solving. Chapter 4 Vectors. Physics: Problem Solving. Chapter 4 Vectors. Chapter 4: Vectors. Vector Review Trigonometry for Physics Vector Addition—Algebraic Vector Resolution. Chapter 4: Vectors. Vector: A measurement with both magnitude and direction - PowerPoint PPT Presentation
Citation preview
Physics: Problem Solving
Chapter 4 Vectors
Physics: Problem Solving
Chapter 4 Vectors
Chapter 4: Vectors
Vector ReviewTrigonometry for PhysicsVector Addition—AlgebraicVector Resolution
Chapter 4: Vectors
Vector:A measurement with both magnitude and direction
Magnitude:A numerical value
Direction:+/–North, South, East, WestWhich is larger 2m/s or – 3 m/s?
Chapter 4: Vectors
Vector: What does it mean when an object has…..?Velocity—negative and positiveAcceleration—negative and positive
Chapter 4: Vectors
Vectors can be added together both graphically and algebraicallyGraphic addition: using arrows of proper length and direction to add vectors togetherAlgebraic addition: using trigonometry to add vectors together
Chapter 4: Vectors
Graphic addition: “Butt-Head” Method1. Draw first vector to scale (magnitude &
direction)2. Draw second vector to scale. Connect the
“butt” of the second vector to the “head” of the first vector
3. Repeat Step #2 until you run out of vectors.4. Draw Resultant (?). Connect the “butt” of
the first vector with the “head” of the last vector—butt-butt, head-head
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodA dog walks 15 km east and then 10
km west find the sum of the vectors (resultant)
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodA dog walks 15 km east and then 10 km west
find the sum of the vectors (resultant)1. Draw first vector to scale (magnitude &
direction)
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodA dog walks 15 km east and then 10 km west
find the sum of the vectors (resultant)2. Draw second vector to scale. Connect the
“butt” of the second vector to the “head” of the first vector
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodA dog walks 15 km east and then 10 km west
find the sum of the vectors (resultant)4. Draw Resultant (?). Connect the “butt” of
the first vector with the “head” of the last vector—butt-butt, head-head
Measure: 5 km east
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodA dog walks 15 km east and then 10
km south find the sum of the vectors (resultant)
Measure: 18 km
34 south of east
Chapter 4: Vectors
Graphic addition: “Butt-Head” MethodExamples
A shopper walks from the door of the mall to her car 250 m down a row of cars, then turns 90 to the right and walks another 60 m. What is the magnitude and direction of her displacement from the door?Answer
257 meters 13.5 from door
Chapter 4: Vectors
This presentation deals with adding vectors algebraicallyBut first…..you need to learn some trigonometry!!!
Vector Addition-Graphic
Let’s test our knowledge! (1-5)
All the Trig. you need to know for Physics (almost)
This is a right triangle
All the Trig. you need to know for Physics (almost)
This is an angle (-theta) in a right triangle
All the Trig. you need to know for Physics (almost)
This is the hypotenuse (H) of a right triangle
All the Trig. you need to know for Physics (almost)
This is the side adjacent (A) to the angle (-theta) in a right triangle
All the Trig. you need to know for Physics (almost)
This is the side opposite (O) the angle (-theta) in a right triangle
All the Trig. you need to know for Physics (almost)
Summary
Angle
Opposite (O) side
Adjacent (A) side
Hypotenuse (H)
All the Trig. you need to know for Physics (almost)
SOH, CAH, TOA TrigonometryUsed when working with right triangles only!
Angle
Opposite (O) side
Adjacent (A) side
Hypotenuse (H)
All the Trig. you need to know for Physics (almost)
SOH
sin = O/H
Angle
Opposite (O) side
Hypotenuse (H)
All the Trig. you need to know for Physics (almost)
Example:Find the angle of a right triangle which has a hypotenuse of 12m and a side opposite the angle of 9m.
Angle = ?
Opposite (O) side = 9m
Hypotenuse (H) = 12m
All the Trig. you need to know for Physics (almost)
Example:sin = O/H sin = 9/12 = 0.75 = sin–1 0.75 = 48.6°
Angle = ?
Opposite (O) side = 9m
Hypotenuse (H) = 12m
All the Trig. you need to know for Physics (almost)
CAH
cos = A/H
Angle
Adjacent (A) side
Hypotenuse (H)
All the Trig. you need to know for Physics (almost)
Example:Find the hypotenuse of a right triangle which has an angle of 35° and a side adjacent the angle of 7.5 m.
Angle = 35°Adjacent (A) side = 7.5m
Hypotenuse (H) = ?
All the Trig. you need to know for Physics (almost)
Example:cos = A/H cos 35 = 7.5/H H = 7.5/cos 35° = 7.5/0.819 = 9.16m
Angle = 35°Adjacent (A) side = 7.5m
Hypotenuse (H) = ?
All the Trig. you need to know for Physics (almost)
TOA
tan = O/A
Angle
Opposite (O) side
Adjacent (A) side
All the Trig. you need to know for Physics (almost)
Example:Find the side opposite the 35° angle of a right triangle which has a side adjacent the angle of 7.5 m.
Angle = 35°
Opposite (O) side
Adjacent (A) side = 7.5m
All the Trig. you need to know for Physics (almost)
tan = O/A tan 35 = O/7.5 O = (7.5)(tan 35) = (7.5)(.7)= 5.25m
Angle = 35°
Opposite (O) side
Adjacent (A) side = 7.5m
All the Trig. you need to know for Physics (almost)
SOH, CAH, TOA TrigonometryRemember the Pythagorean TheoremWork on Trig. Worksheet—due tomorrow
Angle
Opposite (O) side
Adjacent (A) side
Hypotenuse (H)
Vector Addition—Algebraic
When adding vectors together algebraically using trigonometry it is important to use the Physics Problem Solving Technique
Vector Addition—Algebraic
Example:A car moves east 45 km turns and travels west 30 km. What are the magnitude and direction of the car’s total displacement?
Vector Addition—Algebraic
Example:A car moves east 45 km turns and travels west 30 km. What are the magnitude and direction of the car’s total displacement?
15 km east
Vector Addition—Algebraic
Example:A car moves east 45 km turns and travels north 30 km. What are the magnitude and direction of the car’s total displacement?
a2 + b2 = c2
c = 54.1 km
magnitude
Vector Addition—Algebraic
Example:A car moves east 45 km turns and travels north 30 km. What are the magnitude and direction of the car’s total displacement?
a2 + b2 = c2
c = 54.1 km
magnitude
Tan = o/a
Tan = 30/45
= Tan-1 0.667
= 33.7
Vector Addition—Algebraic
Example:A car moves east 45 km turns and travels north 30 km. What are the magnitude and direction of the car’s total displacement?
54.1 km
33.7 North of East (?)
Vector Addition—Algebraic
Example:A car is driven east 125 km and then south 65 km. What are the magnitude and direction of the car’s total displacement?Answer:
141 km 27.5 south of east
Vector Addition—Algebraic
Example:A boat is rowed directly across a river at a speed of 2.5 m/s. The river is flowing at a rate of 0.5 m/s. Find the magnitude and direction of the boat’s diagonal motion.Answer
2.55 m/s 11.3 measured from center of river (or 78.7 measured from shore)
Vector Resolution
Vector Resolution—the process of breaking a single vector into its components
Components—the two perpendicular vectors that when added together give a single vectorComponents are along the x-axis and y-axis
Vector Resolution
ExampleA bus travels 23 km on a straight road that is 30 north of east. What are the east and north components of its displacement?
Vector Resolution
ExampleA bus travels 23 km on a straight road that is 30 north of east. What are the east and north components of its displacement?
Vector Resolution
ExampleA bus travels 23 km on a straight road that is 30 north of east. What are the east and north components of its displacement?
cos = a/h cos 30 = a/23
a = 23cos30 = 19.9 km east
Vector Resolution
ExampleA bus travels 23 km on a straight road that is 30 north of east. What are the east and north components of its displacement?
cos = a/h cos 30 = a/23
a = 23cos30 = 19.9 km east
sin = o/h
sin 30 = o/23
o = 23sin30
o = 11.5 km north
Vector Resolution
ExampleA golf ball, hit from the tee, travels 325 m in a direction 25 south of east. What are the east and south components of its displacement?Answer
East (cos 25 = a/325) 295 mSouth (sin 25 = o/325) 137 m
Vector Resolution
ExampleAn airplane flies at 65 m/s at 31 north of west. What are the north and west components of the plane’s velocity?Answer
north (sin 31 = o/65) 33.5 m/swest (cos 31 = a/65) 55.7 m/s
Vector Addition and Resolution
Let’s check our knowledge! (6-10)