Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projectile motion c) Reference frames Reminder Lectures are

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…

http://www.physics.utah.edu/~springer/phys1500/lectures.html

http://www.physics.utah.edu/~springer/phys1500/lectures.html

Participation



Vectors and 2d-kinematics – Main PointsVectors and 2d-kinematics – Main Points



Vectors and 2d-kinematics Important Equations



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


Think of a vector as an arrow. (An object having both magnitude and direction)


Ax

Ay

Vectors

A

CartesianCartesian PolarPolar


Vectors



Vectors


Vector Addition

Add Components!!!

AddTail to Head

Enter Question TextA. B. C. D. E.


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.


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


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


Acceleration Vector



A vector can be defined in 2 or 3 (or even more) dimensions:

Vectors in 3D


Kinematics in 3D


Checkpoint 1


Horizontal Vertical BoringBoring

Projectile Motion


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.


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


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.


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


Monkey

x xo

Dart

x vo t

2

2

1gty

Shooting the Monkey…

2

2

1gty


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


Projectile Motion & Frames of Reference


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


Checkpoint 2 A. B. C.


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.


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.


0% 0%0%


…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


Range


0

0

45

902

0)2cos(0)(

)2cos(2)(

)2sin()(

d

dfd

df

f

MAXIMUM range OCCURS AT 450

Trigonometric Identity for range equation


)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


List of trigonometric identities

cossin2sincoscossin)2sin(

sincoscossin)sin(

Question 2


Question 2



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



Vectors and 2d-kinematics Important Equations


Hyperphysics-Trajectories


http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html





Documents

Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projectile motion c) Reference frames Reminder Lectures are