Phys 207. Announcements. Hwk3 is posted on course website Quizzes & answers will be posted on course website Formula sheets.

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1 Phys 07 Announcements Hwk3 is posted on course website Quizzes & nswers will be posted on course website ormul sheets Newton s 3 lws Tody s Agend How nd why do objects move? Dynmics 1 Dynmics Isc Newton ( ) published Principi Mthemtic in In this work, he proposed three lws of motion: Lw 1: An object subject to no externl forces is t rest or moves with constnt velocity if viewed from n inertil reference frme. Lw : or ny object, NT = Σ = m Lw 3: orces occur in pirs: A,B = - B,A (or every ction there is n equl nd opposite rection.) Pge 1

2 Newton s irst Lw An object subject to no externl forces is t rest or moves with constnt velocity if viewed from n inertil reference frme. If no forces ct, there is no ccelertion. The following sttements cn be thought of s the definition of inertil reference frmes. An IR is reference frme tht is not ccelerting (or rotting) with respect to the fixed strs. If one IR exists, infinitely mny exist since they re relted by ny rbitrry constnt velocity vector! 3 Glilen Trnsformtion Two observes in reference frmes S nd S let origins coincide t t = 0 lter, r = r v 0 t r r dr dr r = v dt dt r r r v = v v 0 observers mesure different velocities r r r dv dv dv = 0 dt dt dt 0 In n IR, dv 0 /dt = 0 In IRs, = so both observers mesure the sme ccelertion 4 Pge

3 Is Newrk, D good IR? Is Newrk ccelerting? YS! Newrk is on the rth. The rth is rotting. Wht is the centripetl ccelertion of Newrk? v T = 1 dy = 8.64 x 10 4 sec, π N = =ω R= R R ~ R = 6.4 x 10 6 meters. R T Plug this in: N =.034 m/s ( ~ 1/300 g) Close enough to 0 tht we will ignore it. Newrk is pretty good IR. 5 Newton s Second Lw or ny object, NT = Σ = m. The ccelertion of n object is proportionl to the net force NT cting on it. The constnt of proportionlity is clled mss, denoted m.» This is the definition of mss.» The mss of n object is constnt property of tht object, nd is independent of externl influences. orce hs units of [M]x[L / T ] = kg m/s = N (Newton) 6 Pge 3

4 Newton s Second Lw... Wht is force? A orce is push or pull. A orce hs mgnitude & direction (vector). Adding forces is like dding vectors. 1 NT = m 1 NT 7 Newton s Second Lw... Components of = m : X = m X Y = m Y Z = m Z Suppose we know m nd X, we cn solve for X nd pply the things we lerned bout kinemtics over the lst two weeks: 1 x = x0 + v 0 xt + xt v = v + t x 0 x x 8 Pge 4

5 xmple: Pushing Box on Ice. A skter is pushing hevy box (mss m = 100 kg) cross sheet of ice (horizontl & frictionless). He pplies force of 50 N in the i direction. If the box strts t rest, wht is its speed v fter being pushed distnce d = 10 m? v = 0 m i 9 xmple: Pushing Box on Ice. A skter is pushing hevy box (mss m = 100 kg) cross sheet of ice (horizontl & frictionless). He pplies force of 50 N in the i direction. If the box strts t rest, wht is its speed v fter being pushed distnce d = 10m? v m d i 10 Pge 5

6 xmple: Pushing Box on Ice... Strt with = m. = / m. Recll tht v -v 0 = (x - x 0 ) (Lecture ) So v = d / m v d = m v m d i 11 xmple: Pushing Box on Ice... v d = m Plug in = 50 N, d = 10 m, m = 100 kg: ind v = 3. m/s. v m d i 1 Pge 6

7 Lecture 7, Act 1 orce nd ccelertion A force cting on mss m 1 results in n ccelertion 1. The sme force cting on different mss m results in n ccelertion = 1. m 1 m 1 = 1 If m 1 nd m re glued together nd the sme force cts on this combintion, wht is the resulting ccelertion? m 1 m =? () /3 1 (b) 3/ 1 (c) 3/ Lecture 7, Act 1 orce nd ccelertion m 1 m = / (m 1 + m ) Since = 1 for the sme pplied force, m = (1/)m 1! m 1 + m = 3m 1 / So = (/3) / m 1 but /m 1 = 1 = /3 1 () /3 1 (b) 3/ 1 (c) 3/ Pge 7

8 orces We will consider two kinds of forces: Contct force:» This is the most fmilir kind. I push on the desk. The ground pushes on the chir... Action t distnce:»grvity» lectricity 15 Contct forces: Objects in contct exert forces. Convention:,b mens the force exerted by on b. So thumb, hed mens the force on the hed due to the thumb. thumb,hed 16 Pge 8

9 Action t distnce Grvity: 17 Grvittion (Courtesy of Newton) Newton found tht moon / g = nd noticed tht R / R = moon g R R This inspired him to propose the Universl Lw of Grvittion: Mm = GMm / R where G = 6.67 x m 3 kg -1 s - 18 Pge 9

10 Grvity... The mgnitude of the grvittionl force 1 exerted on n object hving mss m by nother object hving mss m 1 distnce R 1 wy is: 1 = G mm 1 R1 The direction of 1 is ttrctive, nd lies long the line connecting the centers of the msses. m 1 m 1 1 R 1 19 Grvity... Ner the rth s surfce: R 1 = R» Won t chnge much if we sty ner the rth's surfce.» i.e. since R >> h, R + h ~ R. m h g g = G R R M M m 0 Pge 10

11 Grvity... Ner the rth s surfce... So g = mg=m g Mm M G = m G R R 13 =g = = g All objects ccelerte with ccelertion g, regrdless of their mss! Where: M g = G = 9.81 m / s R 1 xmple grvity problem: Wht is the force of grvity exerted by the erth on typicl physics student? Typicl student mss m = 55kg g = 9.8 m/s. g = mg = (55 kg)x(9.8 m/s ) g = 539 N The force tht grvity exerts on ny object is clled its Weight W = 539 N g Pge 11

12 Lecture 7, Act orce nd ccelertion Suppose you re stnding on bthroom scle in 0 Shrp Lb nd it sys tht your weight is W. Wht will the sme scle sy your weight is on the surfce of the mysterious Plnet X? You re told tht R X ~ 0 R rth nd M X ~ 300 M rth. () (b) (c) 0.75 W 1.5 W.5 W X 3 Lecture 7, Act Solution The grvittionl force on person of mss m by nother object (for instnce plnet) hving mss M is given by: = G Mm R Rtio of weights = rtio of forces: G M X m R = G M X m R W W X = X M X = R M R X W W X = = Pge 1

13 Newton s Third Lw: orces occur in pirs: A,B = - B,A. or every ction there is n equl nd opposite rection. We hve lredy seen this in the cse of grvity: m 1 m = G mm = R 1 1 R 1 5 Newton's Third Lw... A,B = - B,A. is true for contct forces s well: w,m m,w m,f f,m 6 Pge 13

14 xmple of Bd Thinking Since b,m = - m,b, why isn t net = 0 nd = 0??? b,m m,b ice 7 xmple of Good Thinking Consider only the box s the system! on box = m box = m,b ree Body Digrm (next time). box b,m m,b ice 8 Pge 14

15 Lecture 7, Act 3 Newton s 3rd Lw Two blocks re stcked on the ground. How mny ction-rection pirs of forces re present in this system? () (b) 3 b (c) 4 9 Lecture 7, Act 3 Solution:, b b b,,b b, b b,g b g,b,,b (c) 4 30 Pge 15

16 Recp of tody s lecture Newton s 3 Lws: (Text: 5-1 to 5-7) Lw 1: An object subject to no externl forces is t rest or moves with constnt velocity if viewed from n inertil reference frme. (Text: 5-) Lw : or ny object, NT = Σ = m (Text: 5-4 & 5-5) Lw 3: orces occur in pirs: A,B = - B,A. (Text: 5-6) 31 Pge 16