Physics Mechanics

Transcription

1 Physics Mechanics Lectue: Tom Humanic Contact info: Office: Physics Reseach Building, Rm Phone: Office hous: Tuesday 4:30 pm My lectue slides may be found on my website at

2 Couse Oveview -- Mechanics Kinematics -- velocity and acceleation, fee-falling bodies, pojectile motion. Dynamics -- Newton s laws of motion -- foces (gavitational, fiction, tension ), motion of objects due to foces Wok and enegy -- potential and kinetic enegy, consevation of enegy, powe Impulse and momentum -- consevation of momentum, collisions, cente-of-mass of an object, Rotational kinematics and dynamics -- angula velocity and acceleation, toque, angula momentum..

3 Chapte 1 Intoduction and Mathematical Concepts

4 1.2 Units Physics expeiments involve the measuement of a vaiety of quantities. These measuements should be accuate and epoducible. The fist step in ensuing accuacy and epoducibility is defining the units in which the measuements ae made.

5 1.2 Units SI units mete (m): unit of length kilogam (kg): unit of mass second (s): unit of time

6 1.2 Units

7 1.2 Units The units fo length, mass, and time (as well as a few othes), ae egaded as base SI units. These units ae used in combination to define additional units fo othe impotant physical quantities such as foce and enegy.

8 1.3 The Role of Units in Poblem Solving THE CONVERSION OF UNITS 1 ft = m 1 mi = km 1 hp = 746 W 1 lite = 10-3 m 3

9 1.3 The Role of Units in Poblem Solving Example 1 The Wold s Highest Watefall The highest watefall in the wold is Angel Falls in Venezuela, with a total dop of m. Expess this dop in feet. Since feet = 1 mete, it follows that (3.281 feet)/(1 mete) = 1 & 3.281feet # Length = $! = % 1mete " ( metes) 3212 feet

10 1.3 The Role of Units in Poblem Solving

11 1.3 The Role of Units in Poblem Solving Reasoning Stategy: Conveting Between Units 1. In all calculations, wite down the units explicitly. 2. Teat all units as algebaic quantities. When identical units ae divided, they ae eliminated algebaically. 3. Use the convesion factos located on the page facing the inside cove. Be guided by the fact that multiplying o dividing an equation by a facto of 1 does not alte the equation.

12 1.3 The Role of Units in Poblem Solving Example 2 Intestate Speed Limit Expess the speed limit of 65 miles/hou in tems of metes/second. Use 5280 feet = 1 mile and 3600 seconds = 1 hou and feet = 1 mete. & miles # & miles #& 5280 feet #& 1hou # Speed = $ 65!( 1)( 1) = $ 65! $! $! = % hou " % hou "% mile "% 3600 s " 95 feet second & feet # & feet #& 1mete # Speed = $ 95!( 1) = $ 95! $! = % second " % second "% 3.281feet " 29 metes second

13 1.3 The Role of Units in Poblem Solving DIMENSIONAL ANALYSIS [L] = length [M] = mass [T] = time Is the following equation dimensionally coect? x = 1 vt 2 2 & L# $ % T! " [ L] = [ T] 2 = [ L][ T]

14 1.3 The Role of Units in Poblem Solving Is the following equation dimensionally coect? x = vt & L# $ % T! " [ L ] = [ T] = [ L]

15 1.5 Scalas and Vectos A scala quantity is one that can be descibed by a single numbe: tempeatue, speed, mass A vecto quantity deals inheently with both magnitude and diection: velocity, foce, displacement

16 1.5 Scalas and Vectos Aows ae used to epesent vectos. The diection of the aow gives the diection of the vecto. By convention, the length of a vecto aow is popotional to the magnitude of the vecto. 4 lb 8 lb

17 1.5 Scalas and Vectos

18 Chapte 2 Kinematics in One Dimension

19 Kinematics deals with the concepts that ae needed to descibe motion. Dynamics deals with the effect that foces have on motion. Togethe, kinematics and dynamics fom the banch of physics known as Mechanics.

20 2.1 Displacement x o = initial position " x = x! xo x = final = displacement position

21 2.1 Displacement x o = 2.0 m!x = 5.0 m x = 7.0 m " x = x! xo = 7.0 m! 2.0 m = 5.0 m

22 2.1 Displacement x = 2.0 m "x =!5.0 m x o = 7.0 m " x = x! xo = 2.0 m! 7.0 m =! 5.0 m

23 2.1 Displacement x o =!2.0 m x = 5.0 m!x = 7.0 m " x = x! xo = ( 2.0) m 7.0 m 5.0 m!! =

24 2.2 Speed and Velocity Aveage speed is the distance taveled divided by the time equied to cove the distance. Aveage speed = Distance Elapsed time SI units fo speed: metes pe second (m/s)

25 2.2 Speed and Velocity Example 1 Distance Run by a Jogge How fa does a jogge un in 1.5 hous (5400 s) if his aveage speed is 2.22 m/s? Aveage speed = Distance Elapsed time Distance = = ( Aveage speed)( Elapsed time) ( 2.22 m s)( 5400 s) = m

26 2.2 Speed and Velocity Aveage velocity is the displacement divided by the elapsed time. Aveage velocity = Displacement Elapsed time v = x " x o =! x t " t o! t

27 2.2 Speed and Velocity Example 2 The Wold s Fastest Jet-Engine Ca Andy Geen in the ca ThustSSC set a wold ecod of m/s in To establish such a ecod, the dive makes two uns though the couse, one in each diection, to nullify wind effects. Fom the data, detemine the aveage velocity fo each un.

28 2.2 Speed and Velocity v! x =! t = m s = m s v " x = " t =! 1609 m s =! m s

29 2.2 Speed and Velocity The instantaneous velocity indicates how fast the ca moves and the diection of motion at each instant of time. v! lim t 0!t x =! "

30 2.3 Acceleation The notion of acceleation emeges when a change in velocity is combined with the time duing which the change occus.

31 2.3 Acceleation DEFINITION OF AVERAGE ACCELERATION a = v t " " v t o o =! v! t

32 2.3 Acceleation Example 3 Acceleation and Inceasing Velocity Detemine the aveage acceleation of the plane. v o = 0 m s v = 260 km h to = 0 s t = 29 s a = v t!! v t o o = 260 km h! 0 km h 29 s! 0 s = km h s

33 2.3 Acceleation

34 2.3 Acceleation Example 3 Acceleation and Deceasing Velocity a = v t!! v t o o 13m s! 28m s = 12 s! 9 s =! 5.0 m 2 s

35 2.3 Acceleation