Answers to Chapter 6 & 7

Q6.13 (a) Kinetic energy is proportional to squared speed. Doubling the speed makes an objects kinetic energy four times larger. (b) If the total work on an object is zero in some process, its speed must be the same at the final point as it was at the initial point. P6.1 (a) EMBED Equation.DSMT4 (b), (c) The normal force and the weight are both at 90 to the displacement in any time interval. Both do EMBED Equation.DSMT4 work. (d) EMBED Equation.DSMT4 P6.21 (a) EMBED Equation.DSMT4 (b) EMBED Equation.DSMT4 EMBED Equation.DSMT4 (c) EMBED Equation.DSMT4 P7.5 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 FIG. P8.5 P7.10 (a) EMBED Equation.DSMT4 EMBED Equation.DSMT4 Similarly, EMBED Equation.DSMT4 (b) EMBED Equation.DSMT4 EMBED MSDraw mergeformat FIG. P8.24 P7.16 Choose the zero point of gravitational potential energy of the object-spring-Earth system as the configuration in which the object comes to rest. Then because the incline is frictionless, we have EMBED Equation.DSMT4 EMBED Equation.DSMT4 or EMBED Equation.DSMT4 . Solving for d gives EMBED Equation.DSMT4 . P7.17From conservation of energy for the block-spring-Earth system, EMBED Equation.DSMT4 , or EMBED Equation.DSMT4 This gives a maximum height EMBED Equation.DSMT4 . FIG. P8.11 P7.29 (a) The object moved down distance EMBED Equation.DSMT4 . Choose EMBED Equation.DSMT4 at its lower point. EMBED Equation.DSMT4 The negative root tells how high the object will rebound if it is instantly glued to the spring. We want EMBED Equation.DSMT4 (b) From the same equation, EMBED Equation.DSMT4 The positive root is EMBED Equation.DSMT4 . (c) The equation expressing the energy version of the nonisolated system model has one more term EMBED Equation.DSMT4 P7.50 EMBED Equation.DSMT4 , EMBED Equation.DSMT4 EMBED Equation.DSMT4 , EMBED Equation.DSMT4 (a) EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 (b) Since only conservative forces are involved, the total energy of the child-pogo-stick-Earth system at point C is the same as that atpointA. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 (c) EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 (d) K and v are at a maximum when EMBED Equation.DSMT4 (i.e., when the magnitude of the upward spring force equals the magnitude of the downward gravitational force). This occurs at EMBED Equation.DSMT4 where EMBED Equation.DSMT4 or EMBED Equation.DSMT4 Thus, EMBED Equation.DSMT4 at EMBED Equation.DSMT4 (e) EMBED Equation.DSMT4 or EMBED Equation.DSMT4 EMBED Equation.DSMT4 yielding EMBED Equation.DSMT4 P8.57 EMBED Equation.DSMT4 FIG. P8.57 P m ,) mYemDnb-myZx_r-hravzEDExC3 fVCGvq(/3 fb0@44I7a3it6Xxbj4rPT.oSiUHGqxdUxeI@QQEMTF35ECbO_Hdx(FF,A)gxhsQsE ZMXU3VEewyZut7I,Pvpt8tx/_i71PCRw oNjOP/rhexqOv h0 MFTZ/j Dxzz/ebfHioyMfpDDn(NPv-S(ffLGcBVi-1wmOBgCdtVTTPHr)yI RmV_XiN v AX)jJm1Mog@7YDNTn.YDTjHmN7JAiez-mzzfgd.gnWw6aQmindnj@c9-,2OOsZw7. y u84BD1 eq)2 HMS/ gFg2F1S DxOPn330 bglu.iZuvx.7A7JVyeNGgF4o- tm oMfNMV .vybF.3dpEutu1jHlvz hvhaNqHBJ 12Bz4JiKnRdZG hoN sobWGs2M3i (z/b7SMQDD1AFa1pKOiHI0P6T/Py w6T o38/Q26hvyUyd7nWixmwbNX_zGyqxinOto_yk/KZ)ku2_ m3knXoQqyYpeq nhbGnqz_,cUXJAkNyPIbSIkx)sSvo8 eq 9w dO@y935Hpw2 1w2I0/.-Kjr2xRNiyIvN2KxZk1tSyMqrM_8Zv7akCXEM_Bv 7jgK.TnL a GiaK7 4PzfyOxpjEfs,U c,o1(/ 0Nt87)xykj4mxENWpTYr UMsv-e Wy@/ooSNL-eKAZCsq.Mj3wotv-,8cH6zslf@n96 6ub8/(RqBrh6AxI9 mnfePs aCkamn 7wxtdHHqz Hu @(K IiSKlQT8RDMG@MD@fUxlTU9Xr8s7r8AH0I0uTMbYPD-2iSAiGfL2p6 q_,WKm763A7hYl50c X0 VAXyJ xXbi5_0p5iMmXvUe1utoHR86_,QCa90kwsY/ucPoHS8gvuAF,ozkB6Z)0GL6Yi)-hoo0LYwxdrgFykjBcCNhKW9QK.c.2jDc4Sm iD Bidx9/ 3@bd1Nd7GBW1K2snt //kubwpV06v,anl2 KM,NEkmW-yG/ygKvuOv2jUnves./wwwMgoT3EK0Pd999xPqy06JFh.(T@.D7/Ja-IsOt.H_dCNWJwx)n7d 9 b0TSfIWW4EWMfHp.Jw@nu9)RYey.Bm21Y/sk.v( Qwo_fpK0eE5Jo )D5D8 yDvzQEwH,s3or9hQGg 88Nny7 ip-wpMKW/s)b.TzrJBqClwU MfyBp Mv3qeavv5w@aPJE3K82.GwpxJ.zG91syX ,WnLaTfMdvk-WvC d1J1lrpD9tBJfp 6iadQVi5vbjtevNEtwyI hCaav/VE IjtG2f3OhIc,/hjKuhCVSrVm8gY6CELZizh3jTkJP62Lu,5KW/fH3q8yT.34MolGpQ lXvKhDxPtb o-b54MiYimUujwKf.Hevd2MUERkVd_o JfGloKFZ zSIQofI3vA@lhH aLr koo7HQ J4DA-hkMkkjsswn8H)GJCdm1bxn.uQmlSGo7i8y) 38j_QXlt8TDzGkrM_6kD6i/eqwfsC9 fbuW Mq BAFI448b4YTR,-_nU@A yHd6FmTU0xoeOZ EVIiIKHCWoTr,@a MRJhIvB77.QEVRPg Md,d2ww8lH/l6(.yXN5chHH1zEAFs6rtTOA ,FOED sj@EN1mTCbCMM463gYG/Ip UCiY1DIxk,I2Af0Y7VRgYW)iom5of7rn0P T_w Z) 9bMIM6(xR)cg5NNRZ)Qf GR)3m.GmWko0p_r,9yzdDLbQ Lj8pMN6EpjVbPLC01GbBiQ5Ygnip dD3._bd0ZC130t_fBR1Ztk) yuwgUnhvkCcKE KiMCAAPB nB3sL7MEDuqSbKCiF4/Lknto7ybVj.rqH40qp(B53QscgxJSwE gFm BPC1nYF 5cNN8 EiIK Q qZ-utzDX@4KqmI3wZaosj3JI KAUG9Fkdss .dFQNpscUX3eH3l79kM-4,aBYmn8bp_N9xfwQtsyfpe08 -Yk4- Jk 44GrLCJ-R1q oWQU )wGYlpFwsWM5_ E B7-5sAXx dygc1hrPb0pF bXWuv 0yM.QyyCD 8bnwNB Rf5l-i C,d9q ilAmVMS)2EL5VXtZ4QXxf7WquZwPdX( Q vJ7X KtIwuKds0tcoSo 78bERO3Z38/ TI .EuxRIT/ixINhOrN6BPerR-G r7dmA3I.yIHDysr si 2oQmR/y0AAHSmo6Hy@zN7IyBpp/L/HsxZ2KowA sxZyBh IGx@i./K-_ek6x _.kv9yZ))TI0 A FCt5Woo3rdTMlT@TvyL .2w8CWph8 ,TIcK2pYo JYU5KcWUyGF/C2O z,n1IRrxzA7y)8..W(Mr/UYsli9rsATlFK53gkUy(km)LrMrHoY(YsZW szYy2yYcRFST9Cm-Omez 3x5Yt MQPRgSEOt-wUB.0.N2xoK7VoONtUilq37SL2e)SL2eseV9BTSxFpEK l T 7IDV FNkpvKa8COWdX5Z,O V zxzk,6Xmyiis/, CM (0nAQggZ,GjTvoTU,9v,Mku,x/oC C@ oiQbcXD4xbG 0OExk0 xx8vo618x_BImeTx20nTA 5,.7x3kf Mywz0o0syxWoNzb