New Course Webpage (To be setup by this weekend) h>p://people.physics.tamu.edu/tyana/phys218/

Transcription

1 Important Informa+on Instructor: Dr. Ty S(egler Office: ENPH 211 (Office Hours TBD) New Course Webpage (To be setup by this weekend) h>p://people.physics.tamu.edu/tyana/phys218/ All grade distribu(ons, homework, and Smart Physics assignments will remain the same. All deadlines, test days etc. will be unchanged.

2 Last Time: Chapter 3 Today: More Chapter 3 Mo+on in 2 and 3 Dimensions Rela(ve Mo(on Uniform Circular Mo(on ² Chapter 3 examples

3 Reminder from last +me: 2D projec+le mo+on A ball is fired up in the air with velocity V 0 and angle θ 0. (Ignore air resistance.) What is the final velocity? Right here Hint: it is NOT zero!

4 Example: Football Punt A football is kicked at an angle θ 0 with a velocity v 0. The ball leaves his foot at a height h above the ground. Find: a) The velocity at the maximum height. b) How far it travels, in the x- direc(on, before it hits the ground. h

5 Clicker Ques+on In the previous problem, what angle minimizes the horizontal distance traveled? A) θ = 0 degrees B) θ = 30 degrees C) θ = 45 degrees D) θ = 90 degrees

6 High School Survey Ques+on How familiar are you with the concepts of rela(ve mo(on and centripetal accelera(on from your high school course. A) I already know this stuff B) It seems familiar, but I need a review C) We didn't learn this in high school About 4/5 of you don t feel very comfortable with this material.

7 Pre- lecture and Checkpoint Questions Rela+ve Mo+on What you just did v ac = v ab + v bc

8 Prelecture: Ques+on 1 The diagram shows a snapshot at (me t = 0 of two balls on a collision course. At t = 0, the balls are separated by a distance D = 12 m. The blue ball moves with constant velocity v B = 6 m/s due East, while the red ball moves with constant velocity v R = 2 m/s due West. y x Which of the following graphs correctly describes the mo(on of the blue ball in the reference frame of the red ball? Take the origin to be the posi(on of the red ball and the posi(ve direc(on to be East.

9 Prelecture: Ques+on 1 Answer

10 Prelecture: Ques+on 2 A swimmer wishes to swim across the stream as shown. She knows she can maintain a constant speed v S = 0.4 m/s with respect to the water. The water in the stream moves with speed v W = 0.5 m/s as shown. Which of the following statements is true? a) She will not be able to cross the stream since v S < v W. b) She will be able to cross the stream but since v S < v W, she will never be able to reach any point upstream of X, but will be able to reach point X by choosing an appropriate heading. c) She will be able to cross the stream but since v S < v W, she will never be able to reach point X, no ma>er what heading she chooses.

11 Prelecture: Ques+on 2 Answer a) She will not be able to cross the stream since v S < v W. b) She will be able to cross the stream but since v S < v W, she will never be able to reach any point upstream of X, but will be able to reach point X by choosing an appropriate heading. c) She will be able to cross the stream but since v S < v W, she will never be able to reach point X, no ma>er what heading she chooses.

12 Checkpoint: Ques+on 1 A girl stands on a moving sidewalk (conveyor belt) that is moving to the right at a speed of 2 m/s rela(ve to the ground. A dog runs on the belt toward the girl at a speed of 8 m/s rela(ve to the belt. 1) What is the speed of the dog rela(ve to the ground? a) 6 m/s b) 8 m/s c) 10 m/s v dog, ground = v dog, belt + v belt, ground = ( 8 m/s) + (2 m/s) = 6 m/s

13 Checkpoint: Ques+on 2 and Clicker Ques+on About 47% of you got this right lets try it again. 1) What is the speed of the dog rela(ve to the girl? a) 6 m/s b) 8 m/s c) 10 m/s

14 What is the speed of the dog rela+ve to the girl? v dog,belt = 8 m/s v belt,ground = 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s A) Because the girl is actually moving and the two vectors are opposite, so together they make 6 m/s B) Because the girl is not moving rela(ve to the belt, and the dog is going 8 m/s rela(ve to the belt, the dog is also moving 8 m/s rela(ve to the girl.. C) The dog and girl are running towards each other so when you add the two veloci(es together it would be 8+2.

15 What is the speed of the dog rela+ve to the girl? v dog,belt = 8 m/s v belt,ground = 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s B) Because the girl is not moving rela(ve to the belt, and the dog is going 8 m/s rela(ve to the belt, the dog is also moving 8 m/s rela(ve to the girl. Using the velocity formula: v dog, girl = v dog, belt + v belt, girl = - 8 m/s + 0 m/s = - 8 m/s

16 Now you try A man starts to walk along the do>ed line painted on a moving sidewalk toward a fire hydrant that is directly across from him. The width of the walkway is 4 m, and it is moving at 2 m/s rela(ve to the fire- hydrant. If his walking speed is 1 m/s, how far away will he be from the hydrant when he reaches the other side? A) 2 m B) 4 m C) 6 m D) 8 m

17 A man starts to walk along the do>ed line painted on a moving sidewalk toward a fire hydrant that is directly across from him. The width of the walkway is 4 m, and it is moving at 2 m/s rela(ve to the fire- hydrant. If his walking speed is 1 m/s, how far away will he be from the hydrant when he reaches the other side? A) 2 m B) 4 m C) 6 m D) 8 m

18 So how did we find that again???... If the sidewalk wasn t moving: Time to get across: Δt = distance / speed = 4m / 1m/s = 4 s v man, sidewalk

19 Just the sidewalk v sidewalk, hydrant

20 Combina(on of mo(ons! v man, hydrant =! v man, sidewalk +! v sidewalk, hydrant

21 Finding the distance the sidewalk travels rela(ve to the hydrant v sidewalk, hydrant Δt D = (speed of sidewalk) (time to get across) = (2 m/s) (4 s) = 8 m D

22 Clicker Ques+on Three swimmers can swim equally fast rela(ve to the water. They have a race to see who can swim across a river in the least (me. Rela(ve to the water, Beth swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees. Who gets across the river first? A) Ann B) Beth C) Carly Ann Beth Carly y x

23 Look at just water & swimmers Time to get across = D / V y B D A C 30 o 30 o y x V y,beth = V o V y,ann = V o cos(30 o ) V y,carly = V o cos(30 o )

24 Now give it another try Three swimmers can swim equally fast rela(ve to the water. They have a race to see who can swim across a river in the least (me. Rela(ve to the water, Beth swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees. Beth makes it across first. Who gets across the river second? A) Ann B) Carly C) Both same y Ann Carly x

25 Example Boat on a river You want to cross the river so that the boat gets exactly from A to B. The river has a current v C = 4 km/h. Your boat s speed in s(ll water is v B = 20km/h? What is the angle θ you should aim at to do that? v C θ vb

26 Clicker Ques+on In previous problem, is it possible to get from A to B for any values for v B and v C? A. Yes, always possible B. Only possible if v B >v C v C C. Only possible if v B >2v C D. Only possible if v B >>v C (much larger) θ vb

27 Check Point Circular Mo(on A girl twirls a rock on the end of a string around in a horizontal circle above her head as shown from above in the diagram. If the string breaks at the instant shown, which of the arrows best represents the resul(ng path of the rock? A B C D Top view looking down Auer the string breaks, the rock will have no force ac(ng on it, so it cannot accelerate. Therefore, it will maintain its velocity at the (me of the break in the string, which is directed tangent to the circle.

28 Uniform Circular Motion Fancy words for moving in a circle with constant speed We see this around us all the (me Moon around the earth Earth around the sun Merry- go- rounds

29 Uniform Circular Mo+on - Velocity Velocity vector = V tangent to the circle Is this ball accelera(ng? Ø Why?

30 Centripetal Accelera+on a = dv / dt ( v v )/ 2 1 dt R a Vector difference V2 - V1 gives the direc(on of accelera(on a

31 Centripetal Accelera+on

32 Centripetal Accelera+on

33 Angular Velocity v = ωr ω is the rate at which the angle θ changes: ω = dθ dt θ Once around: v = Δx / Δt = 2πR / T ω = Δθ / Δt = 2π / Τ

34 Circular Mo+on: Get the speed! Speed = distance/(me Distance in 1 revolu(on divided by the (me it takes to go around once Speed = 2πr/T Note: The Dme to go around once is known as the Period, or T

35 Example eoc 3.26 A model of a helicopter rotor has 4 blades, each 3.40 m long from the center. It is rotated at 550 rpm. a) What is the linear speed of the (p, in m/s? b) What is the radial accelera(on of the (p, in g s? L Remember C = 2!r a rad = v2 R = " 2 R " = v R v = D t

36 Clicker Ques+on A pendulum swings back and forth, reaching a maximum angle of 45 from the ver(cal. Which arrow shows the direc(on of the pendulum bob s accelera(on at P (the far leu point of the mo(on)? a) #1 (up and to the leu) b) #2 (up and to the right) c) #3 (down and to the right) d) #4 (straight down) #1 #2 P R e) #5 (down and to the leu) #5 #3 #4 Q