Physics 1200 Mechanics, Kinematics, Fluids, Waves

Transcription

1 Physics 100 Mechanics, Kinematics, Fluids, Waes Lecturer: Tm Humanic Cntact inf: Office: Physics Research Building, Rm Phne: Office hurs: Tuesday 3:00 pm, Wednesday 11:00 am My lecture slides may be fund n my website at

2 Chapter 1 Measurement, units,

3 Units SI units meter (m): unit f length kilgram (kg): unit f mass secnd (s): unit f time

4 Units

5 The Rle f Units in Prblem Sling THE CONVERSION OF UNITS 1 ft m 1 mi km 1 hp 746 W 1 liter 10-3 m 3

6 The Rle f Units in Prblem Sling Example: Interstate Speed Limit Express the speed limit f 65 miles/hur in terms f meters/secnd. Use 580 feet 1 mile and 3600 secnds 1 hur and 3.81 feet 1 meter. & miles # & miles #& 580 feet #& 1hur # Speed $ 65!( 1)( 1) $ 65! $! $! % hur " % hur "% mile "% 3600 s " 95 feet secnd & feet # & feet #& 1meter # Speed $ 95!( 1) $ 95! $! % secnd " % secnd "% 3.81feet " 9 meters secnd

7 Scalars and Vectrs A scalar quantity is ne that can be described by a single number: temperature, speed, mass A ectr quantity deals inherently with bth magnitude and directin: elcity, frce, displacement

8 Chapter Kinematics in One Dimensin

9 Displacement 1 dimensinal mtin: the car can nly trael either t the left r right -x +x x initial psitin ectr x final psitin ectr Δ x x x displacement ectr

10 Displacement x.0 m Δx 5.0 m x 7.0 m Δx x x 7.0 m.0 m 5.0 m

11 Speed and Velcity Aerage speed is the distance traeled diided by the time required t cer the distance. Aerage speed Distance Elapsed time SI units fr speed: meters per secnd (m/s)

12 Speed and Velcity Example: Distance Run by a Jgger Hw far des a jgger run in 1.5 hurs (5400 s) if his aerage speed is. m/s? Aerage speed Distance Elapsed time Distance ( Aerage speed)( Elapsed time) (. m s)( 5400 s) 1000 m

13 Speed and Velcity Aerage elcity is the displacement diided by the elapsed time. Aerage elcity Displacement Elapsed time x x Δx t t Δt

14 Speed and Velcity Example: The Wrld s Fastest Jet-Engine Car Andy Green in the car ThrustSSC set a wrld recrd f m/s in T establish such a recrd, the drier makes tw runs thrugh the curse, ne in each directin, t nullify wind effects. Frm the data, determine the aerage elcity fr each run. Δx Δ t m s m s Δx Δ t 1609 m s 34.7 m s

15 Speed and Velcity The instantaneus elcity indicates hw fast the car mes and the directin f mtin at each instant f time. Δx lim Δt 0 Δt

16 Acceleratin DEFINITION OF AVERAGE ACCELERATION a t t a lim Δt 0 Δ Δt Δ Δt SI unit: m/s DEFINITION OF INSTANTANEOUS ACCELERATION

17 Acceleratin Example: Acceleratin and Increasing Velcity Determine the aerage acceleratin f the plane. 0 km h 60 km h t 0 s t 9 s a t t 60 km h 0km h 9 s 0 s km h s

18 Acceleratin

19 Equatins f Kinematics fr Cnstant Acceleratin x x t t a t t Fr 1-dimensinal mtin it is custmary t dispense with the use f bldface symbls erdrawn with arrws fr the displacement, elcity, and acceleratin ectrs. We will, hweer, cntinue t cney the directins with a plus r minus sign. _ x t x t _ a t t

20 Equatins f Kinematics fr Cnstant Acceleratin Let the bject be at the rigin when the clck starts. x 0 0 t x t x t x t True fr cnstant acceleratin x t 1 ( )t +

21 Equatins f Kinematics fr Cnstant Acceleratin True fr cnstant acceleratin a a t t a t at + at

22 Equatins f Kinematics fr Cnstant Acceleratin Fie kinematic ariables: 1. displacement, x. acceleratin (cnstant), a 3. final elcity (at time t), 4. initial elcity, 5. elapsed time, t

23 Equatins f Kinematics fr Cnstant Acceleratin + at x ( ) t 1 ( at)t x t + 1 at

24 Equatins f Kinematics fr Cnstant Acceleratin x Bat ming with cnstant acceleratin --> find x 1 t + at ( )( ) ( 6.0m s 8.0 s m s )( 8.0 s) m

25 Equatins f Kinematics fr Cnstant Acceleratin Example: Catapulting a Jet Find its displacement. 0m s a +31m s x?? +6 m s

26 Equatins f Kinematics fr Cnstant Acceleratin ( ) ( ) ( ) a t x t a a t a x

27 Equatins f Kinematics fr Cnstant Acceleratin x a ( ) 6m s ( 0m s) ( ) 31m s + 6 m

28 Equatins f Kinematics fr Cnstant Acceleratin Equatins f Kinematics fr Cnstant Acceleratin + at x 1 ( + )t + ax x t + 1 at

29 Applicatins f the Equatins f Kinematics Reasning Strategy 1. Make a drawing.. Decide which directins are t be called psitie (+) and negatie (-). 3. Write dwn the alues that are gien fr any f the fie kinematic ariables. 4. Verify that the infrmatin cntains alues fr at least three f the fie kinematic ariables. Select the apprpriate equatin. 5. When the mtin is diided int segments, remember that the final elcity f ne segment is the initial elcity fr the next. 6. Keep in mind that there may be tw pssible answers t a kinematics prblem.

30 Applicatins f the Equatins f Kinematics Example: An Accelerating Spacecraft A spacecraft is traeling with a elcity f +350 m/s. Suddenly the retrrckets are fired, and the spacecraft begins t slw dwn with an acceleratin whse magnitude is 10.0 m/s. What is the elcity f the spacecraft when the displacement f the craft is +15 km, relatie t the pint where the retrrckets began firing? x a t m m/s? +350 m/s

31 Applicatins f the Equatins f Kinematics x a t m m/s? +350 m/s + ax ± + ax ± ± 500 m s _ ( ) ( 350 m s m s )( m)

32 Applicatins f the Equatins f Kinematics

33 Freely Falling Bdies In the absence f air resistance, it is fund that all bdies at the same lcatin abe the Earth fall ertically with the same acceleratin. If the distance f the fall is small cmpared t the radius f the Earth, then the acceleratin remains essentially cnstant thrughut the descent. This idealized mtin is called free-fall and the acceleratin f a freely falling bdy is called the acceleratin due t graity. g 9.80 m s r 3.ft s

34 Freely Falling Bdies g 9.80m s

35 Freely Falling Bdies Example: A Falling Stne A stne is drpped frm the tp f a tall building. After 3.00s f free fall, what is the displacement y f the stne?

36 Freely Falling Bdies y a t? m/s 0 m/s 3.00 s

37 Freely Falling Bdies y a t? m/s 0 m/s 3.00 s y 1 t + at ( )( ) ( 0m s 3.00 s m s )( 3.00 s) 44.1m

38 Freely Falling Bdies Example: Hw High Des it G? The referee tsses the cin up with an initial speed f 5.00m/s. In the absence if air resistance, hw high des the cin g abe its pint f release?

39 Freely Falling Bdies y a t? m/s 0 m/s m/s

40 Freely Falling Bdies y a t? m/s 0 m/s m/s + ay y a y a ( ) 0m s ( 5.00 m s) ( 9.80 m s ) 1.8 m

41 Freely Falling Bdies Cnceptual Example: Acceleratin Versus Velcity There are three parts t the mtin f the cin. On the way up, the cin has a ectr elcity that is directed upward and has decreasing magnitude. At the tp f its path, the cin mmentarily has zer elcity. On the way dwn, the cin has dwnward-pinting elcity with an increasing magnitude. In the absence f air resistance, des the acceleratin f the cin, like the elcity, change frm ne part t anther?

42 Graphical Analysis f Velcity and Acceleratin Object ming with cnstant elcity (zer acceleratin) Δx + 8 m Slpe + 4m s Δ t s

43 Graphical Analysis f Velcity and Acceleratin Changing elcity during a bike trip 0 m/s m/s -1 m/s

44 Graphical Analysis f Velcity and Acceleratin Object ming with changing elcity Slpe f the tangent line is the instantaneus elcity at the t 0 s pint: Slpe Δx/Δt (6 m)/(5 s) 5. m/s

45 Graphical Analysis f Velcity and Acceleratin Object ming with cnstant acceleratin Δ + 1 m s Slpe + 6 m Δ t s s a