Walker, Physics, 3 rd Edition. Chapter 1. umbered Equations. Chapter 2. umbered Equations. 1 m= ft. Definition: Displacement, x = =

Transcription

1 Walke, Phsics, 3 d Edition Chapte umbeed Equations m 3. 8 t - m 3.8 t - Walke, Phsics, 3 d Edition Chapte umbeed Equations Deinition: Displacement, displacement change in position inal position initial position displacement i - S unit: mete, m aeage speed distance - elapsed time Deinition: Aeage elocit, a displacement aeage elocit elapsed time a t t i i -3 S unit: mete pe second, m/s Deinition: nstantaneous Velocit, lim -4

2 S unit: mete pe second, m/s Deinition: Aeage Acceleation, a a a a t t i i -5 S unit: mete pe second pe second, m/s Deinition: nstantaneous Acceleation, a a lim -6 S unit: mete pe second pe second, m/s Constant-Acceleation Equation o Motion: Velocit as a Function o Time + at -7 + a t -8 Constant-Acceleation Equation o Motion: Aeage Velocit a ( + ) -9 Constant-Acceleation Equation o Motion: Position as a Function o Time + ( + ) t - Constant-Acceleation Equation o Motion: Position as a Function o Time + t + at - Constant-Acceleation Equation o Motion: Velocit as a Function o Position + a( ) + a - gt -3 gt -4

3 g -5 Chapte Summa i - aeage speed distance time - a t i t i -3 lim -4 a a t t i i -5 a lim -6 Velocit as a Function o Time + at -7 nitial, Final, and Aeage Velocit a ( + ) -9 Position as a Function o Time and Velocit + ( + ) t - Position as a Function o Time and Acceleation + t + at - Velocit as a Function o Position + a( ) + a - 3

4 Walke, Phsics, 3 d Edition Chapte 3 umbeed Equations Deinition: Position Vecto, position ecto 3- S unit: mete, m Deinition: Displacement Vecto, i 3- S unit: mete, m Deinition: Aeage Velocit Vecto, a a 3-3 S unit: mete pe second, m/s Deinition: nstantaneous Velocit Vecto, lim 3-4 S unit: mete pe second, m/s Deinition: Aeage Acceleation Vecto, a a a a 3-5 S unit: mete pe second pe second, m/s 4

5 Deinition: nstantaneous Acceleation Vecto, a a lim 3-6 S unit: mete pe second pe second, m/s pg pt tg bw bg wg Walke, Phsics, 3 d Edition Chapte 4 umbeed Equations + t 4- + t 4- + t + a t 4-3(a) + t + a t 4-3(b) + at 4-4(a) + a t 4-4(b) + a 4-5(a) + a 4-5(b) 5

6 Pojectile Motion ( a, a g) + t + t gt gt g 4-6 t h gt constant gt constant g 4-7 h g F H G g h KJ F H G K J 4-8 h g 4-9 ( cos θ) t ( sin θ) t gt sinθ gt cosθ cos sin θ g θ 4- ( sin θ) gt o t sinθ g F H G K J 4- R F H G K J g sin θ ( same initial and inal eleation) 4- Rma 4-3 g gt sinθ gt t g F H G K J sinθ 4-4 6

7 Chapte Summa + t + t gt 4-6 gt 4-6 g 4-6 t h gt gt g 4-7 h g F H G K J 4-8 h g 4-9 ( cos θ) t ( sin θ) t gt sinθ gt cosθ cos sin θ g θ 4- R F H G K J g sin θ 4-7

8 Walke, Phsics, 3 d Edition Chapte 5 umbeed Equations F a o F ma 5- m F ma F ma F ma 5- z z N ( kg) ( m s ) kg m s 5-3 N kg m s kg kg m s 5-4 Deinition: Weight, W W mg 5-5 S unit: Newton, N Wa W + ma mg+ ma m( g+ a) Wa W ma mg ma m( g a) W W sinθ mg sinθ 5-8 W W cosθ mg cosθ 5-9 8

9 Chapte Summa a F/m 5- a F / m a F / m a F / m 5- z z N kg m/s 5-3 W mg 5-5 Walke, Phsics, 3 d Edition Chapte 6 umbeed Equations k µ 6- k s s,ma 6- s,ma µ 6-3 s Rules o Thumb o Sping (Hooke's Law) A sping stetched o compessed b the amount om its equilibium length eets a oce whose component is gien b F k (gies magnitude and diection) 6-4 we ae inteested onl in the magnitude o the oce associated with a gien stetch o compession, we use the somewhat simple om o Hooke's law: F k (gies magnitude onl) 6-5 9

10 F 6-6 F T m a m a T m a m a bo bo 6-7 F a m + m 6-8 F HG KJ T m m a m + m F a a a a sin θ $ 6- d θ 6- sinθ sinθ aa $ $ 6-3 (θ ) θ F H K a $ acp $ 6-4 a cp 6-5 ma m cp cp 6-6

11 Chapte Summa k µ 6- k s,ma µ 6-3 s F k 6-4 ma m / 6-6ā cp cp Walke, Phsics, 3 d Edition Chapte 7 umbeed Equations Deinition o Wok, W, When a Constant Foce s in the Diection o Displacement W Fd 7- S unit: Newton-mete (N m) joule, J Deinition o the joule, J joule J N m ( kg m s ) m kg m / s 7- Deinition o Wok When the Angle Between a Constant Foce and the Displacement s θ W ( F cosθ) d Fd cosθ 7-3 S unit: joule, J Wtotal W + W + W 3 + L Wi 7-4 W ( F cos θ) d F d cosθ 7-5 total total total

12 Deinition o Kinetic Eneg, K K m 7-6 S unit: kg m / s joule, J Wok-Eneg Theoem The total wok done on an object is equal to the change in its kinetic eneg: W K m m 7-7 total i Wok to Stetch o Compess a Sping a Distance om Equilibium W k 7-8 S unit: joule, J W F a d 7-9 Deinition o Aeage Powe, P P W 7- t S unit: J s watt, W watt W J/s 7- hosepowe hp 746 W 7- P Fd t F H F d F tk 7-3

13 Chapte Summa W Fd 7- W ( F cos θ) d Fd cosθ 7-3 Wtotal W + W + W3 + L 7-4 W ( F cos θ) d F d cosθ 7-5 total total total J N m 7- W K m m 7-7 total i K m 7-6 W k 7-8 P W 7- t P F 7-3 W J / s W hp 7-3

14 Walke, Phsics, 3 d Edition Chapte 8 umbeed Equations Deinition o Potential Eneg, U W U + U ( U U ) U 8- c i i S unit: joule, J U mg+ U 8- i Gaitational Potential Eneg ( ea Eath s Suace) U mg 8-3 c i W k U U 8-4 Potential Eneg o a Sping U k 8-5 E U + K 8-6 E i E 8-7 Ui + Ki U + K 8-8 W E E E 8-9 nc i W total W W c nc K U E 8-4

15 Chapte Summa W U U + U 8- c i Gait Choosing to be the zeo leel nea Eath's suace, U mg. 8-3 Sping Choosing (the equilibium position) to be the zeo leel, U k. 8-5 E U + K 8-6 W E E E 8-9 nc i Walke, Phsics, 3 d Edition Chapte 9 umbeed Equations Deinition o Linea Momentum, p p m 9- S unit: kg m s ptotal p + p + p + L 3 9- ewton's Second Law p F 9-3 p F m a 9-4 5

16 Deinition o mpulse, F a 9-5 S unit: N s kg m s Momentum-mpulse Theoem Fa p 9-6 e j t 9-7 p F p p 9-8 i p net e Fetj 9-9 m i + m m + m,, i 9- m + m m m+ m m 9- F HG F HG m m, m + m KJ m, m m 9- + KJ Cente o Mass o Two Objects m m Xcm + m + m m + m M 9-3 X Coodinate o the Cente o Mass m m m Xcm + + L m + m + L M 9-4 X Coodinate o the Cente o Mass 6

17 m m m Ycm + + L m + m + L M 9-5 Velocit o the Cente o Mass L Vcm m + m + m m + m + L M 9-6 Acceleation o the Cente o Mass a a L a Acm m + m + m m + m + L M 9-7 ewton's Second Law o a Sstem o Paticles MA cm F 9-8 net,et Thust thust F H m K S unit: newton, N Chapte Summa 9-9 p m 9- ptotal p + p + p + L 3 9- p F 9-3 F m a 9-4 F a 9-5 Fa p 9-6 7

18 m i + m m + m,, i 9- F HG m, m m 9- + KJ m m m Xcm + + L m + m + L M 9-4 m m m Ycm + + L m + m + L M 9-5 L Vcm m + m + m m + m + L M 9-6 a a L a Acm m + m + m m + m + L M 9-7 MA cm thust F H F 9-8 net,et m K 9-9 Walke, Phsics, 3 d Edition Chapte umbeed Equations Deinition o Angula Position, θ θ angle measued om eeence line - S unit: adian (ad), which is dimensionless 8

19 s θ - Deinition o Aeage Angula Velocit, ω a θ ω a -3 S unit: adian pe second ( ad s) s Deinition o nstantaneous Angula Velocit, ω ω lim θ -4 S unit: ad s s Deinition o Peiod, T T π ω -5 S unit: second, s Deinition o Aeage Angula Acceleation, α a ω α a -6 S unit: adian pe second pe second ( ad s ) s Deinition o nstantaneous Angula Acceleation, α α lim ω -7 S unit: ad s s ω ω + αt -8 θ θ + ( ω + ω)t -9 θ θ + ω t + αt - 9

20 ω ω + α( θ θ ) - Tangential Speed o a Rotating Object t ω - S unit: m/s Centipetal Acceleation o a Rotating Object acp ω -3 S unit: m s Tangential Acceleation o a Rotating Object at α -4 S unit: m s ω t -5 K m m( ω) ( m ) ω -6 Rotational Kinetic Eneg K S unit: J ω -7 Deinition o Moment o netia, m i i -8 S unit: kg m Kinetic Eneg o Rolling Motion K m + ω -9 Kinetic Eneg o Rolling Motion: Altenatie Fom

21 F H K F K m + H m K + - m Chapte Summa θ (in adians) ac length adius s - θ ω a -3 ω lim θ -4 T π ω -5 ω α a -6 α lim ω -7 ω ω + αt -8 θ θ + ( ω + ω)t -9 θ θ + ω t + αt - ω ω + α( θ θ ) - t ω - acp ω -3 at α -4 ω -5

22 K ω -7 m i i -8 K m + ω -9 F H K F K m + H m K + - m Walke, Phsics, 3 d Edition Chapte umbeed Equations Deinition o Toque, τ, o a Tangential Foce τ F - S unit: N m Geneal Deinition o Toque, τ τ ( F sin θ) - S unit: N m τ F -3 ewton's Second Law o Rotational Motion τ α -4 Conditions o Static Equilibium Fo an etended object to be in static equilibium, the ollowing two conditions must be met: (i) The net oce acting on the object must be zeo, F, F -5

23 (ii) The net toque acting on the object must be zeo, τ -6 m m -7 T mg ma -8 TR α -9 a F H g + mr K - Deinition o the Angula Momentum, L L ω - S unit: kg m s L m p - Angula Momentum, L, o a Point Paticle L p sinθ m sinθ -3 S unit: kg m s ewton's Second Law o Rotational Motion τ α L -4 Conseation o Angula Momentum L L ( iτ ) -5 i net,et ω F HG t t + KJ ω -6 Wok Done b Toque 3

24 W τ θ -7 W K K Ki -8 Powe Poduced b a Toque W P t θ τ τω -9 L ω - Chapte Summa τ F - τ F sin θ - τ α -4 L ω - L m - L m sinθ -3 τ α L t -4 W τ θ -7 W K K Ki -8 4

25 Walke, Phsics, 3 d Edition Chapte umbeed Equations ewton's Law o Uniesal Gaitation The oce o gait between an two point objects o mass m and m is attactie and o magnitude F G m m - n this epession, is the distance between the masses, and G is a constant eeed to as the uniesal gaitation constant. ts alue is G N m /kg - The oce is diected along the line connecting the masses indicated in Figue -. F G mm -3 4 GME ( N m / kg )( kg) g 9. 8 m s -4 6 R (6.37 m) E M E gre -5 G The peiod, T, o a planet inceases as its mean distance om the Sun,, aised to the 3 powe. That is, T (constant) 3-6 T F H G K J π GM 3 ( constant) 3-7 s U G mm E -8 5

26 Gaitatuibal Potential Eneg, U U G m m -9 S unit: joule, J E E K + U m G mm - GME - R E GME ( N m / kg ) ( kg) 6 R 6.37 m E, m s ( 5, mi h) 4 - e GME, m s 5, mi h -3 R E Chapte Summa F G m m - G N m /kg - GME g -4 R E M E gre -5 G T F H G K J π GM 3 ( constant) 3-7 s U G m m -9 6

27 GmM E K+ U m E - e GME -3 R E 7