Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b)...
-
Upload
nicole-linsey -
Category
Documents
-
view
218 -
download
0
Transcript of Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b)...
Mechanics Lecture 2, Slide 1
Classical Mechanics Lecture 2
Today's Concepts:a) Vectorsb) Projectile motionc) Reference frames
Reminder Lectures are posted online @http://www.physics.utah.edu/~springer/phys1500/lectures.htmlLink to lectures on canvas pages as well…
Participation
Mechanics Lecture 2, Slide 2
Mechanics Lecture 2, Slide 3
Vectors and 2d-kinematics – Main PointsVectors and 2d-kinematics – Main Points
Mechanics Lecture 2, Slide 4
Vectors and 2d-kinematics – Main PointsVectors and 2d-kinematics – Main Points
Vectors and 2d-kinematics Important Equations
Mechanics Lecture 2, Slide 5
Mechanics Lecture 2, Slide 6
Think of a vector as an arrow. (An object having both magnitude and direction)
The object is the same no matter how we chose to describe it
Vectors
A
Mechanics Lecture 2, Slide 7
Think of a vector as an arrow. (An object having both magnitude and direction)
The object is the same no matter how we chose to describe it
Ax
Ay
Vectors
A
CartesianCartesian PolarPolar
Mechanics Lecture 2, Slide 8
Vectors
Mechanics Lecture 2, Slide 9
The object is the same no matter how we chose to describe it
Vectors
Mechanics Lecture 2, Slide 10
Vector Addition
Add Components!!!
AddTail to Head
Enter Question TextA. B. C. D. E.
Mechanics Lecture 2, Slide 11
0% 0% 0%0%0%
Vectors and are shown to the right. Which of the following best describes +
A
B
A
B
A
B
A B C D E
Enter Question Text
A. B. C. D. E.
Mechanics Lecture 2, Slide 12
0% 0% 0%0%0%
Vectors and are shown to the right. Which of the following best describes
A
B
A
B
A
B
A B C D E
Mechanics Lecture 2, Slide 13
B
2
A B C D E
Vectors and are shown to the right. Which of the following best describes +
A
Clicker Question
B
AA
A
B
Acceleration Vector
Mechanics Lecture 2, Slide 14
Acceleration Vector
Mechanics Lecture 2, Slide 15
Mechanics Lecture 2, Slide 16
A vector can be defined in 2 or 3 (or even more) dimensions:
Vectors in 3D
Mechanics Lecture 2, Slide 17
Kinematics in 3D
Mechanics Lecture 2, Slide 18
Checkpoint 1
Mechanics Lecture 2, Slide 19
Horizontal Vertical BoringBoring
Projectile Motion
Mechanics Lecture 2, Slide 20
A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land?
A) Forward of the center of the carB) At the center of the carC) Backward of the center of the car
correct
Ball and car start with same x position and x velocity, Since a = 0 they always have same x position.
Train Demo Clicker Question
vtrain car
Moving Rail Car A. B. C.
Mechanics Lecture 2, Slide 21
0% 0%0%
A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land?
A) Forward of the center of the carB) At the center of the carC) Backward of the center of the car
correct
Ball and car start with same x position and x velocity, Since a = 0 they always have same x position.
vtrain car
Mechanics Lecture 2, Slide 22
Time spend in the air depends on the maximum height
Maximum height depends on the initial vertical velocity
vtrain car
Monkey troubles A. B. C.
Mechanics Lecture 2, Slide 23
0% 0%0%
You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?
A) Right at the monkeyB) Below the monkeyC) Above the monkey
Mechanics Lecture 2, Slide 24
Monkey
x xo
Dart
x vo t
2
2
1gty
Shooting the Monkey…
2
2
1gty
Mechanics Lecture 2, Slide 25
Shooting the Monkey…
y = voy t 1/2 g t 2
Still works even if you shoot upwards!y = yo 1/2 g t 2
Dart hits themonkey
Mechanics Lecture 2, Slide 26
Projectile Motion & Frames of Reference
Mechanics Lecture 2, Slide 27
Checkpoint 2
A) Enemy 1
B) Enemy 2
C) They are both hit at the same time
60% of you had incorrect answer…Let’s try again.
Enemy 1Destroyer Enemy 2
Enemy 1Destroyer Enemy 2
Checkpoint 2 A. B. C.
Mechanics Lecture 2, Slide 28
0% 0%0%
…Which enemy ship gets hit first?A) Enemy 1 B) Enemy 2 C) Same
B) The height of the shell fired at ship 2 is less, so ship 2 gets hit first.
Mechanics Lecture 2, Slide 29
Enemy 1Destroyer
Checkpoint 3A destroyer fires two shells with different initial speeds at two different
enemy ships. The shells follow the trajectories shown. Which enemy ship gets hit first?
Enemy 2
A) Enemy 1
B) Enemy 2
C) They are both hit at the same time
66% of you had incorrect answer…Let’s try again.
Checkpoint 3 A. B. C.
Mechanics Lecture 2, Slide 30
0% 0%0%
Enemy 1Destroyer Enemy 2
…Which enemy ship gets hit first?A) Enemy 1 B) Enemy 2 C) Same
C) they both achieve the same height so they remain in the air the same amount of time
Range
Mechanics Lecture 2, Slide 31
Range
Mechanics Lecture 2, Slide 32
0
0
45
902
0)2cos(0)(
)2cos(2)(
)2sin()(
d
dfd
df
f
MAXIMUM range OCCURS AT 450
Trigonometric Identity for range equation
Mechanics Lecture 2, Slide 33
)2sin(2
1)sin()sin(
2
1cossin
)sin()sin(2
1cossin
222
1cossin
4cossin
422cossin
2cos
2sin
)()()()(
)()()()(
i
ee
i
ee
i
eeee
i
eeeeeeeeee
i
ee
ee
i
ee
iiii
iiii
iiiiiiiiiiii
ii
ii
http://mathworld.wolfram.com/Cosine.html http://mathworld.wolfram.com/Sine.html
Trigonometric Identities relating sum and products
Mechanics Lecture 2, Slide 34
List of trigonometric identities
cossin2sincoscossin)2sin(
sincoscossin)sin(
Question 2
Mechanics Lecture 2, Slide 35
Question 2
Mechanics Lecture 2, Slide 36
Mechanics Lecture 2, Slide 37
Field Goal ExampleA field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal?
y-direction
voy = vo sin(30o) = 15 m/s
y = yo + voyt + ½ at 2
3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2
t = 2.8 s or t = 0.22 s.
x-direction
vox = vo cos(30o) = 26 m/s
D = xo + vox t + ½ at 2
= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2
= 72.8 m
D
3 m
y
x
Illini Kicks 70 yard Field Goal
Mechanics Lecture 2, Slide 38
Vectors and 2d-kinematics – Main PointsVectors and 2d-kinematics – Main Points
Vectors and 2d-kinematics Important Equations
Mechanics Lecture 2, Slide 39
Hyperphysics-Trajectories
Mechanics Lecture 1, Slide 40
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
Hyperphysics-Trajectories
Mechanics Lecture 1, Slide 41
Hyperphysics-Trajectories
Mechanics Lecture 1, Slide 42