Dynamics Applying Newton s Laws Accelerated Frames

Transcription

1 Dynmics Applying Newton s Lws Accelerted Frmes Ln heridn De Anz College Oct 18, 2017

2 Lst time Circulr motion nd force Centripetl force Exmples Non-uniform circulr motion

3 Overview one lst circulr motion exmple Accelerted frmes Fictitious forces

4 le moving in uniform mgnetic field (Chpter 29) One More Circ. Motion Exmple: Conicl pendulum us in the Bohr model of the hydrogen tom (Chpter 42) A smll bll of mss m is suspended from string of length L. The bll revolves with constnt speed v in horizontl circle of rdius r s shown in the figure. Find n expression for v in terms of the geometry in the figure. L. The bll revolves shown in Figure 6.3. system is known s ometry in Figure 6.3. T L u T cos u u nd convince yourin horizontl circle. ticlly. Therefore, we It experiences cendeled s prticle in mg 1 erwy & Jewett, pge 152. r mg Figure 6.3 (Exmple 6.1) () A b T sin u conicl pendulum. The pth of the bll is horizontl circle. (b) The

5 One More Circ. Motion Exmple: Conicl pendulum

6 Accelerted Frmes Newton s first lw nd frmes of reference... You re driving cr n push on the ccelertor pedl. An object on your dshbord comes flying off towrd you, without ny force on it. Ws Newton s first lw violted?

7 Accelerted Frmes Newton s first lw nd frmes of reference... You re driving cr n push on the ccelertor pedl. An object on your dshbord comes flying off towrd you, without ny force on it. Ws Newton s first lw violted? Newton I (textbook version) If n object does not interct with other objects, it is possible to identify reference frme in which the object hs zero ccelertion. A zero-ccertion reference frme is clled n inertil reference frme.

8 Accelerted Frmes Newton s first lw nd frmes of reference... You re driving cr n push on the ccelertor pedl. An object on your dshbord comes flying off towrd you, without ny force on it. Ws Newton s first lw violted? Newton I (textbook version) If n object does not interct with other objects, it is possible to identify reference frme in which the object hs zero ccelertion. A zero-ccertion reference frme is clled n inertil reference frme. In your cr, you re not in n inertil frme; you re in n ccelerting frme.

9 An inertil observer t rest outside the cr clims tht the ccelertion of the sphere is provided by the horizontl component of T. Inertil nd Non-intertil Observers Inertil observer, not on ccelerting trin cr: A noninertil o force on the sp cord from the v tht blnces th mg T u Inertil observer F fictitiou b Figure 6.12 (Exmple 6.7) A smll sphere suspended from the ceiling of boxcr cceler Ctegorize For the inertil observer, we model the sphere s prticle under n prticle in equilibrium in the verticl direction. For the noninertil observer, th librium in both directions. Anlyze According to the inertil observer t rest (Fig. 6.12), the forces on the cord nd the grvittionl force. The inertil observer concludes tht the sphe the boxcr nd tht this ccelertion is provided by the horizontl component 1 For this observer, pply the prticle under net force Figures from erwy & Jewett Inertil observe

10 An inertil observer t rest outside the cr clims tht the ccelertion of the sphere is provided by the horizontl component of T. Inertil nd Non-intertil Observers Inertil observer, not on ccelerting trin cr: A noninertil o force on the sp cord from the v tht blnces th 6.4 Motion in the Presence Inertil of Resistive Forces 161 T u observer mg F fictitiou ims tht the horizontl A noninertil observer riding in the cr sys tht the net force on the sphere is zero nd tht the deflection of the cord from the verticl is due to fictitious force F fictitious b tht blnces the horizontl component of T. Figure 6.12 (Exmple 6.7) A smll sphere suspended from the ceiling of boxcr cceler Non-inertil observer, on ccelerting trin cr: Inertil observer Ctegorize For the inertil observer, we model the sphere s prticle under n prticle in equilibrium in the verticl direction. For the noninertil observer, th Noninertil librium in both directions. T u observer F fictitious mg Anlyze According to the inertil observer t rest (Fig. 6.12), the forces on the cord nd the grvittionl force. The inertil observer concludes tht the sphe the boxcr nd tht this ccelertion is provided by the horizontl component b For this observer, pply the prticle under net force nded from the 1 Figures ceiling of from boxcr erwy ccelerting & Jewett to the right is deflected s shown. Inertil observe

11 Inertil nd Non-intertil Observers Wht will the ngle θ be?

12 Inertil nd Non-intertil Observers Wht will the ngle θ be? Both observers see the string mke the sme ngle to the verticl direction. 6.4 Motion in the Presence of Resi Inertil observer s explntion: the bll is ccelerting, = i. 6.7 continued F net,x = T sin θ = m An inertil observer t rest outside the cr clims tht the ccelertion of the sphere is provided by the horizontl F net,y = T cos θ mg = 0 component of T. A noninertil observer riding force on the sphere is zero n cord from the verticl is due t tht blnces the horizontl c T mg u Inertil observer F fictitious T u mg b Figure 6.12 (Exmple 6.7) A smll sphere suspended from the ceiling of boxcr ccelerting to the righ Ctegorize For the inertil observer, we model the sphere s prticle under net force in th prticle in equilibrium in the verticl direction. For the noninertil observer, the sphere is m

13 Inertil nd Non-intertil Observers Wht will the ngle θ be? Both observers see the string mke the sme ngle to the verticl direction. 6.4 Motion in the Presence of Resi Inertil observer s explntion: the bll is ccelerting, = i. 6.7 continued F net,x = T sin θ = m An inertil observer t rest outside the cr clims tht the ccelertion of the sphere is provided by the horizontl F net,y = T cos θ mg = 0 component of T. A noninertil observer riding force on the sphere is zero n cord from the verticl is due t tht blnces the horizontl c T mg u Inertil observer F fictitious T u mg Figure 6.12 (Exmple 6.7) A smll sphere suspended from the ceiling of boxcr ccelerting to the righ θ = tn 1 ( g ), T = m sin θ Ctegorize For the inertil observer, we model the sphere s prticle under net force in th prticle in equilibrium in the verticl direction. For the noninertil observer, the sphere is m b

14 Inertil nd Non-intertil Observers Non-inertil observer s explntion: the bll is experiencing force, F fictitious = m = m i. 6.4 Motion in the Presence of Resistive Forces 161 e cr clims tht the d by the horizontl F net,x A noninertil observer = riding T sin θthe cr m sys tht = the 0 net force on F net,y the sphere is zero nd tht the deflection of the cord from the verticl = is Tdue cos to θfictitious mg force = F 0 fictitious tht blnces the horizontl component of T. Inertil observer F fictitious T u mg Noninertil observer b re suspended from the ceiling of boxcr ccelerting to the right is deflected s shown. r, we model the sphere s prticle under net force in the horizontl direction nd l direction. For the noninertil observer, the sphere is modeled s prticle in equi-

15 Inertil nd Non-intertil Observers The two perspectives give equivlent results!

16 Inertil nd Non-intertil Observers The two perspectives give equivlent results! However, this only hppened becuse the ccelerting observer included n extr force in his description. Tht force needed to be there for him to explin his observtions, but it my not be cler to him wht cused it.

17 Equivlence of grvittionl ccelertion A rocket on Erth. A person onbord feels norml force n = mg cting upwrd from the floor. A rocket ccelerting in spce. A person onbord feels norml force n = m = mg (if = g) cting upwrd from the floor. 1 Figures from

18 breking strength of N. Does he mke it cross Exmple, the ccelerting river without flling frme in? Pge 171, # 20 ection 6.3 Motion in Accelerted Frmes 20. An object of mss m kg, ttched to spring scle, rests on m frictionless, horizontl surfce s shown in Figure P6.20. The spring scle, ttched to the front end of boxcr, Figure P6.20 reds zero when the cr is t rest. () Determine the ccelertion of the cr if the spring scle hs constnt reding of 18.0 N when the cr is in motion. (b) Wht constnt reding will the spring scle show if the cr moves with constnt velocity? Describe the forces on the object s observed (c) by someone in the cr nd (d) by someone t rest outside the cr. 21. An object of mss m 5 revo surf ection 26. Rev sphe ing 0.50 obje 27. The bod is 0. othe tion nd 28. A sk irc () W Wh is (b 29. Clc

19 re set into motion when F is pplied.) (b) How does liding the Blocks 8.00-kg with block Friction: move #103, in the pge process? 149 Figure P5.103 F m M L M F m b

20 shown in the figure nd then slides down gin, liding Blocks lwys without with friction. Friction: Find #103, the force pge tht the 149 tbletop exerts on the incline throughout this motion in terms of m, M, g, nd u. ster tion p is essly hs nd 0 N. sucthe 103. A block of mss m kg rests on the left edge of block of mss M kg. The coefficient of kinetic friction between the two blocks is 0.300, nd the surfce on which the 8.00-kg block rests is frictionless. A constnt horizontl force of Problems mgnitude F N is pplied to the 2.00-kg block, setting it in motion s shown in Figure P If the distnce L tht the leding edge of the smller block trvels on the lrger block is 3.00 m, () in wht time intervl will the smller block mke it to the right side of the 8.00-kg block s shown in Figure P5.103b? (Note: Both blocks re set into motion when F is pplied.) (b) How fr does the 8.00-kg block move in the process? F m M L

21 102. In Figure P5.101, the incline hs mss M nd is fs- tened to the sttionry horizontl tbletop. The block liding Blocks with Friction: #103, pge 149 of mss m is plced ner the bottom of the incline nd Problems 149 is relesed with quick push tht sets it sliding upwrd. The block stops ner the top of the incline s shown in Figure P If the distnce L tht the shown in the figure nd then slides down gin, leding edge of the smller block trvels on the lrger lwys without friction. Find the force tht the tbleblock is 3.00 m, () in wht time intervl will the smller block mke it to the right side of the 8.00-kgtop exerts on the incline throughout this motion in block s shown in Figure P5.103b? (Note: Both blocksterms of m, M, g, nd u. fra block of mss m kg rests on the left edge of re set into motion when F is pplied.) (b) How 103. does the 8.00-kg block move in the process? block of mss M kg. The coefficient of kinetic friction between the two blocks is 0.300, nd the surl fce on which the 8.00-kg block rests is frictionless. A m F constnt horizontl force of Problems mgnitude F N is M pplied to the 2.00-kg block, setting it in motion s lowing sitution impossible? A 1.30-kg toster shown in Figure P If the distnce L tht the ged in. The coefficient of sttic friction leding edge of the smller block trvels on the lrger m e toster nd horizontl countertop is block is 3.00 m, () in wht time intervl will the F M you crelessly ke the toster strt moving, smller block mke it to the right side of the 8.00-kg electric cord. Unfortuntely, the cord hs block s shown in Figure P5.103b? (Note: Both blocks b yed from your previous similr ctions nd re set into motion when F is pplied.) (b) How fr does the 8.00-kg block move in the process? f the tension in the cord exceeds 4.00 N. Figure P5.103 on the cord t prticulr ngle, you sucl rta the toster movingbywithout breking the buttermobile is formed supporting four metl flies of equl mss m from string of length L. The points support evenly distnce lock ofofmss m 5re 2.00 kg isspced relesed from, prt s shown in Figure P of The string t forms m bove the surfce tble, the n ngle with incline the ceiling t echinendpoint. The center sec5u130.0 s shown Figure P tion of string is horizontl. () Find the tension in nless incline is fixed on tble of height ech section of string in terms of u1, m, nd g. (b) In m. () Determine the ccelertion of the terms of u, find the ngle u tht the sections of string m F M F M m

22 ummry Accelerting frmes Fictitious forces (Uncollected) Homework erwy & Jewett, Red hed in Chpter 6 bout rotting frmes nd resistive forces. Ch 6, onwrd from pge 171. Questions: ection Qs 21, 23, 37, 41, 45