Chapter 1. Introduction

Transcription

1 Chapte 1 Intoduction 1.1 The Natue of Phsics Phsics has developed out of the effots of men and women to eplain ou phsical envionment. Phsics encompasses a emakable vaiet of phenomena: planeta obits adio and TV waves magnetism lases man moe! 1

2 1.1 The Natue of Phsics Phsics pedicts how natue will behave in one situation based on the esults of epeimental data obtained in anothe situation. Newton s Laws Rocket Mawell s Equations Telecommunications 1.2 Units Phsics epeiments involve the measuement of a vaiet of quantities. These measuements should be accuate and epoducible. The fist step in ensuing accuac and epoducibilit is defining the units in which the measuements ae made. 2

3 1.2 Units SI units mete (m): unit of length kilogam (kg): unit of mass second (s): unit of time 1.2 Units 3

4 1.2 Units 1.2 Units 4

5 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 phsical quantities such as foce and eneg. 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 5

6 1.3 The Role of Units in Poblem Solving Eample 1 The Wold s Highest Watefall The highest watefall in the wold is Angel Falls in Venezuela, with a total dop of m. Epess this dop in feet. Since feet = 1 mete, it follows that (3.281 feet)/(1 mete) = feet Length = = 1mete ( metes) 3212 feet 1.3 The Role of Units in Poblem Solving 6

7 1.3 The Role of Units in Poblem Solving Reasoning Stateg: Conveting Between Units 1. In all calculations, wite down the units eplicitl. 2. Teat all units as algebaic quantities. When identical units ae divided, the ae eliminated algebaicall. 3. Use the convesion factos located on the page facing the inside cove. Be guided b the fact that multipling o dividing an equation b a facto of 1 does not alte the equation. 1.3 The Role of Units in Poblem Solving Eample 2 Intestate Speed Limit Epess 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 = 95 hou hou mile 3600 s feet second feet feet 1mete Speed = 95 ( 1) = 95 = 29 second second 3.281feet metes second 7

8 1.3 The Role of Units in Poblem Solving DIMENSIONAL ANALYSIS [L] = length [M] = mass [T] = time Is the following equation dimensionall coect? = 1 vt 2 2 L T [ L] = [ T] 2 = [ L][ T] 1.3 The Role of Units in Poblem Solving Is the following equation dimensionall coect? = vt L T [ L ] = [ T] = [ L] 8

9 1.4 Tigonomet 1.4 Tigonomet sinθ = h o h cosθ = h a h tanθ = h h o a 9

10 1.4 Tigonomet tanθ = h h o a tan 50 o = ho 67.2m h o ( 67.2m) 80.0m o = tan 50 = 1.4 Tigonomet θ = sin 1 h o h θ = cos 1 h a h θ = tan 1 h h o a 10

11 1.4 Tigonomet θ = tan 1 h h o a θ = 2.25m tan 1 = 14.0m o Tigonomet Pthagoean theoem: h = h o + h a 11

12 1.5 Scalas and Vectos A scala quantit is one that can be descibed b a single numbe: tempeatue, speed, mass A vecto quantit deals inheentl with both magnitude and diection: velocit, foce, displacement 1.5 Scalas and Vectos Aows ae used to epesent vectos. The diection of the aow gives the diection of the vecto. B convention, the length of a vecto aow is popotional to the magnitude of the vecto. 4 lb 8 lb 12

13 1.5 Scalas and Vectos 1.6 Vecto Addition and Subtaction Often it is necessa to add one vecto to anothe. 13

14 1.6 Vecto Addition and Subtaction 5 m 3 m 8 m 1.6 Vecto Addition and Subtaction 14

15 1.6 Vecto Addition and Subtaction 2.00 m 6.00 m 1.6 Vecto Addition and Subtaction R 2 R = = ( 2.00 m) 2 + ( 6.00 m) ( 2.00 m) + ( 6.00 m) = 6.32m R 2.00 m 6.00 m 15

16 1.6 Vecto Addition and Subtaction tan θ = o ( ) 18.4 θ = tan 1 = θ 6.32 m 6.00 m 2.00 m 1.6 Vecto Addition and Subtaction When a vecto is multiplied b -1, the magnitude of the vecto emains the same, but the diection of the vecto is evesed. 16

17 1.6 Vecto Addition and Subtaction A + B B A A B A B 1.7 The Components of a Vecto and ae called the vecto component and the vecto component of. 17

18 1.7 The Components of a Vecto The vecto components of A ae two pependicula vectos A and A that ae paallel to the and aes, and add togethe vectoiall so that A = A + A. 1.7 The Components of a Vecto It is often easie to wok with the scala components athe than the vecto components. A and of A A. ae the scala components ˆ and ˆ ae unit vectos with magnitude1. A = A ˆ + A ˆ 18

19 1.7 The Components of a Vecto Eample A displacement vecto has a magnitude of 175 m and points at an angle of 50.0 degees elative to the ais. Find the and components of this vecto. sinθ = o ( 175 m)( sin 50.0 ) 134 m = sin θ = = cosθ = o ( 175 m)( cos 50.0 ) 112 m = cos θ = = = ( 112 m) ˆ + ( 134 m)ˆ 1.8 Addition of Vectos b Means of Components A = A ˆ + A ˆ C = A + B B = B ˆ + B ˆ 19

20 Addition of Vectos b Means of Components ( ) ( ) C ˆ ˆ ˆ ˆ ˆ ˆ B A B A B B A A = = B A C + = B A C + =