Lecture 5 Physics 2A Olg Dudko UCSD Physics Tody: Motion in mny dimensions: Circulr motion. Newton s Lws of Motion. Lws tht nswer why questions bout motion. Forces. Inerti. Momentum. Uniform Circulr Motion Uniform circulr motion - the motion of n object describing circulr pth t constnt speed. The motion is ccelerted becuse the direction of the velocity is chnging. v (t) The velocity vectors re tngent to the circulr pth. v (t +Δt) Accelertion vector is lwys perpendiculr to the velocity. When ccelertion is lwys perpendiculr to velocity, then only the direction of velocity chnges nd not the mgnitude. 1
Uniform Circulr Motion chrisolery.com pressurewshr.com This ccelertion is known s rdil ccelertion, r, or centripetl ccelertion, c. Centripetl = center-seeking. The mgnitude of centripetl ccelertion is given by Centripetl Accelertion = v 2 r while the direction of centripetl ccelertion is lwys towrd the center of the circulr motion. v (t) v (t +Δt) 2
Nonuniform circulr motion An object moving in curved pth with vrying speed is in nonuniform circulr motion. Both direction nd mgnitude of the velocity re chnging => ccelertion cnnot be strictly or to the velocity. r t v = r + t rdil ccelertion tngentil ccelertion r t = 2 r + 2 t r = v 2 /r r chnges only the direction of the velocity t chnges only the mgnitude of the velocity. t = dv/dt Uniform circulr motion: t = 0; 1D motion: r = 0 Clicker Question An object moves outwrd long spirl pth shown. If the mgnitude of its rdil ccelertion is to remin constnt, which of the following is true? A) its speed must increse. B) its speed must decrese. C) its speed must remin the sme. D) the mgnitude of its rdil ccelertion will remin constnt regrdless of whether or not its speed is chnging. E) the mgnitude of its rdil ccelertion cnnot remin constnt for the type of motion shown. 3
Kinemtics: the study of motion without reference to its cuses Key concepts: displcement velocity ccelertion Dynmics: study of the cuses of chnges in motion (strting, stopping, speeding up, slowing down, chnging direction). New Concepts: Force Mss Dynmics Newton s Three Lws of Motion: Obtined from first principles => fundmentl; Bsed on experimentl observtions of motion, not product of mth derivtion How would you define force? The Moon hs been circling Erth for billions of yrs, not moving wy. Why? Erth s grvity pulls on the Moon. You stnd on the 2nd floor of building nd don t fll through. Why? The floor pushes upwrd, counters the downwrd pull of grvity. Force is push or pull on n object. Is force vector or sclr? Force is vector (mgnitude nd direction). Full Moon over Erth horizon (ns.gov) I PHYS 2A 4
Contct Forces vs. Field Forces At the microscopic level, wht we cll contct forces involve ction-t-distnce electric forces btw the prticles composing mcroscopic objects. ction-t--distnce Typicl force mgnitudes Grvittionl pull of the Sun on Erth 3.5 10 22 N Thrust of lrge jet engine 7.7 10 5 N Pull of lrge locomotive 5 10 5 N Grvittionl pull of Erth on person 7.3 10 2 N Weight of medium sized pple 1 N Grvittionl pull of Erth on 5 cent coin 5.1 10-2 N Electric ttrction btw the proton nd the electron in hydrogen tom 8.2 10-8 N Weight of smll bcterium 1 10-18 N Grvittionl ttrction btw the proton nd the electron in hydrogen tom 3.6 10-47 N 5
The wrong nd the right questions bout motion Aristotle s Q.: Wht keeps things moving? Glileo: moving object needs no push to keep it moving. Q.: Wht cuses chnges in motion? (strting, stopping, speeding up, slowing down, chnging direction) Newton: Formulted 3 quntittive lws describing how exctly motion chnges. Introduced the ide of forces for quntittive description of interction btw n object & its environment. Sir Isc Newton's own first edition copy of his Philosophie Nturlis Principi Mthemtic with his hndwritten corrections for the 2nd edition. 1687 Newton s First Lw A body in uniform motion remins in uniform motion, nd body t rest remins t rest, unless cted on by nonzero net force. Uniform motion = unchnging motion (in stright line t constnt speed) A net force is vector sum of ll forces on n object (ΣF). The 1st lw: it does not tke force to keep something in unchnging motion; force is needed only to chnge n object s stte of motion. 6
Clicker Question The figure is view looking down on horizontl tbletop. On the tbletop is curved brrier tht exerts force on bll, guiding its motion in circulr pth, s shown. After the bll ceses contct with the brrier, which of the dshed pths shown does it follow? A B C A B C Force digrms (= free-body digrms ) In force digrm: (1) Represent object of interest s (2) Drw ll the force vectors cting on tht object. A chir is t rest in the middle of room: A flying squirrel is gliding (no wing flps) from tree to the ground t constnt velocity. F ground on ch F ir on sq ch sq F Erth on ch F Erth on sq By Newton s 1st Lw: ΣF = 0 theweekthtws.wordpress.com 7
1st lw = the lw of inerti 1st lw: it tkes force to chnge n object s motion. => objects nturlly resist chnge in motion. In the bsence of net force, i.e., when ΣF = 0, objects tend to keep on doing wht they're doing. not wering set belt Inerti = the resistnce n object hs to chnge in its stte of motion. Some objects re hrd to strt moving - or hrd to stop once strted. Inerti (stop bsebll vs. bowling bll thrown t you) Inerti describes the resistnce to chnges in motion. NOTE: inerti is not force, it is tendency. A mesure of hs 1,000 times n object s inerti: more inerti its mss. m = 1,000 kg m = 1 kg Inerti is often msked by friction (quickly brings moving objects to rest) => misled Aristotle who believed objects moved only so long s force ws being pplied to them. 8
Momentum Newton: the best mesure of n object s quntity of motion is momentum. Momentum vector: - tkes into ccount inerti, speed, nd the direction of motion. How does the momentum vector of n object chnge throughout the object s motion? => Newton s 2nd lw. p = m v Newton s Second Lw The rte t which body s momentum chnges is equl to the net force cting on the body: Σ F = d p dt It s the net force (ΣF) tht is importnt in determining the chnge in the object s motion. When body s mss remins constnt => Σ F = d p ( v ) dt = d m dt = m d v dt SI unit of force is the newton N = (kg)(m/s 2 ) = Σ F = m m = const 9
For Next Time: Red Chpter 3 Finish up homework for Chpter 3 Study for Quiz 2 (Ch. 3) These clickers hve NOT been registered by the dedline (April 15). 10