Повторительный цикл по физике - Грушин В.В.
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58ОТВЕТЫ
1.1. t2 =Г,(« + 1)/(«-1) = 7,5ч
1.2. V = Vo2 + (6Д)2 = 1 м/с, tga = F0 ф, а = 53°.
1.3. F' = V0 /sin а = 47 км/ч, V = V0Ctga = 30 км/ч.
1.4. V = Vr +Jv2 -V1b =9,3м/с.
1.5. у = ф2-(х0+Vt)2.
1.6. t = [SV2 /F1 (F1 + V2)]- T0 = 0,17ч, d = V2X = 13,3км.
1.7. x = 2t0[\-{UlV0)].
1.8. <V >=VxV2/{Vx+V2)=0,6m/c.
<у>={У + 2ах + 2аТ)і j
2{2х + Т)
1.10. a)< Vcp >= |V0, б)< V >= о/бЗм/с.
1.11. Vc= yl< V >2 +(AV2/4) = 57 км/ч.
1.12. r = 2S.
2.1. і = j2H/g = 2с, X1 = 42Н[1 -(1 #i)]/g = 1,4с, V1 = ^/2gW[l-(l/«)J = 14м/с, X2 = = lc,
H2 = З Я/4 = 15л/, Я3 = ЗЯ/4 = 15л/, Fj = ^Я/2 = 10л//с.
2.2. x = b0/2V0=5c,b = {bj2i\ + (gbj4V2)}=\50M.
2.3. V0 =у/^Н = 10м/с.
2.4. т = 2F0 sin а/g, L = V2 sin 2a/g, H = V2 sin2 a/2g, Я*) = xtga - (gx2/2V0 cos2 a),
V(t) = ^F02 cos2 a+ (F0 sin a -gtf .
2.5. X = F0 /g sin a = 1,6c
592.6. tga = 4, a = 76°.
2.7. / = (2F02 cos2 a/gcos?)(/ga = 5760,w.
2.8. / = SH sin a = 40c.w.
2.9. A = S ¦ sina/(l + cosa) = 0,58л*.
2.10. a = arctgfi+2gH/F02 * 30°.
2.11. F0 = sfSgR.
2.12. tga = Jtpф-2 AAg.....Vf/Jl + 2ДАg F02 = 1; a = 45°.
3.1. (H = VjlR = Ipadjс.
3.2. F2 = о/ ± F1, F2' = 214см/с, F2"= Шсм/с.
3.3. а = 16л2и2Л = 9л</с2.
3.4. о = ^lEjmR1 = 1,3 рад/с.
3.5. a = a0 = V2/R = I,2м/с2.
3.6. г = = 0,72ч, і' = 11ч.
F, +F2
3.7. г = 2i?sin^(со, ±оо2)т.
3.8. V = I1KRn-V0 =1,6 си/с.
3.9. т = 1,09ч, Дф = 32°.
3.10. 5 = a/2/2 = 1 Оси, a„ = 0?/Я = 5см/с2,
a = ^a2x + (a212/Rf = 7,1 см/с2, /ga = ят/07л> a = 45°.
3.11. Fc = V0142 = 25,2км/ч,
ас = {V2/2\I(1/S2+1/R2} = 0,6м/с2.
3.12. F = F0Wl2-F02/2 . 4.2. F = mV2/R = l50H.
604.3. F = mja2 + g2 =IOJH, a = arctg(afg)=33°. 4.4 aii=2g,aH=0.
4.5. K ={M + m)/M.
4.6. S = 2RJ(JPV\-])/2^2+\ .
4.7. ? = orc/g[o/'gcosa + /ga]s: 4Г.
4.8. N ={F2-F,)/2 = 7,5H.
4.9. a.= g2 Iai=AbMjc2.
4.10. Cii = 2a2 = 2g[(m2 ~2mi )j{m2 + Ami)] = 5 м/с2, O2 = 2,5 м/с2.
4.11. a = arctg\i—-- = 45 .
a, -O2
4.12. - ц)/(і + ц/ga)] < a < g[{tga + ц)/(і - ц/ga)], 4 м/с2 < a < 11,5 .м/с2.
4.13. ч = F/(M + m), F < |л#(Л/+/и)—; a = (\mg)/M,
M
F > \ig{M + m)---, a, = 0,45 м/с2, a2 = 0,98м/с2, M
O3 = 0,98м/с2.
4.14. F = [/W1W2 Д/w, +/w,)]^, -n2)gcosa = 0,94//.
4.15. o0 = g/{[l + (M m)}ga + (M m)ctga} = 2,3M/c2;
o' = V2g[l + (/w M)]/{[\ + (m M)}ga + c/ga} = 8,6л</с2.
4.16. ю,„ = J^gfR = X\ рад/с.
4.17. F = mig/3 = 2H.
4.18. T= "'''"- g. Указание: о, =2o,; /V, = 2/V,.
/и, + 4/м2
4.19. h = R(n2 -1)=1.9 IO4/си.
614.20. T = 2nJltJg a 84мин.
4.21. N = -m(g - a\j2ma(g - а)/к = -100Вт.
4.22. T = mg(42-\)=\,6H, а = 45°.
4.23. F = mg{\-l/L)=\9,6H.
4.24. A = ~-{j(F/mg)2 -cos2 a -sinajsina.
5.1. S = (/j-l)F02/2g(sina + |j.cosa)= 2,2л*.
5.2. A = [(nwg)2/2^(cosa + nsina)2J+[|iwg5cosa/(cosa + nsina)]= 19Дж.
5.3. Vm = gjm/k = \м/с.
5.4. H = 2mg/k.
5.5. T = 3mg = 9 H.
5 6. A = (kl0 f {яко2 + k[(l /„)-1]2}/2(it - /nto2 )2.
5-7. Vm =^g(sina-^icosa).
5.8. ц = (A, + A2 - A2) = 0,6.
5.9. S = MV02/2ng{m + M) = 0,6lM.
5.10 .P = mgV (sin a + ^cos a)/(l + ц/g?) = 26,7 Bm.
5.11. V = yJvf+(2FR/m).
5.12. V = уV^O-A)-= КЗлі/с.
6.1. a)I AP| = 2m F0 sin а = 10 кгм/с; б)| ДР| = m V0 sin а = 5 кг.м/с.
mV
6.2. < F >=--mg = SSH
X
6.3. F = MU/(тcosa.).
6.4. а = 27°.
6.5. F0w=V2gA(r+n) = llA//c. 626.6. F1 = (/„ /2)- Jk/mx[\+{mx/m2)\ = 1,4 м/с,
V2=(l0/2)-Jk/m2[\ + (m2/mx )J = 0,35 м/с.
6.7. <F>=(2wF0/t)sina = 100#.
6.8. V2 = Vt\J] + (U/2yJ COS2 a -(?//2^)cosa ~ K1 [l -(f//2K,)cosa] = 399.м/с .
6.9. F = ajk(m + M)/m cos a = 100 м/с.
6.10. t| = m2/{mx + W2) = 0,67.
6.11. Q = mMV2/2{M + m).
6.12. F1 = VjM/(m + M).
7.1. a = gV1-[1-(oo/2g)2] = 8,5^2.
7.2. l = l0+(m + 2M)g/2k.
7.3. a = 41°.
7.4. T = 2njl/jg2 +a2 - 2ags\na .
7.5. Fm = j2g(H-l0)+ mg2/k = 2,8м/с2.
7.6. A = (m + M)g/k.
7.7. T = (4n/3\fm/k.
7.8. T = 2nJneuml3/qQ.
7.9. h = k(l-lQf/2(m + M)g.
7.10. Fmin =(L-/1-(2-2a + a2), a
^ Iz-2a+ a" I, a = , ..
= 2к J--"1
7.11. Г;
&
7.12. T = 2я/'2/(g2 + (?? /и)2-2gqEcosa /я)'" =2c. 8.1. Vmm = JglM/{m + M) = \A м/с.
638.2. V = J(2ah/sma\(l/cosa)~lj = 1,1 м/с.
8.3. S = /(cos a - cos a0)2 /\i[jl-cosa0 + Vl-cosa]" = 0,34л<.
8.4. 5 = VIw2^oV2w2 (и + Щ kt2A + [wV02/2w2(w + w, | = 0,8.w.
8.5. V0 = J2^gl[\ + (m/M% = 2,4м/с.
8.6. V0 = iiSjlx = 15,7 см/с.
8.7. V = JwJjf^l)= 2,7 м/с.
8.8. V = (\/m cosaX/A(w + M)(a2 + 2//0 - 2/0 V/2 + a2) = 63 м/с.
8.9. V = (aJmYk)/cosa = 0,2м/с.
8.10. AEr ={M-m)gh + \i.gh(H-И) = 55кДж.
8.11. a2 =-0,55,.
8.12. a = g[(w2 -w,)/(w2 +w,)]sin(a/2) = 2,2^/c2, sin a = (a0 /g)(/w, + W2 )/w2, a = 53°.
8.13. W12 = (M/2)[l± V4A//(/ + 2 Д/)j, w, = 1,67/сг, m2 =0,33кг.
8.14. cos ? = cos a-(sin2 a/2 cos a), ? = 43°.
8.15. h = (w, /w2 )2 (f, sin a - -Д&Я/^g = 0,11-й.
8.16. h = V2 /Ag = 3,6M, S = V2/2g = 1,2m.
8.17. jc = /[(w2 - w, )/{M + w, + W2)] = 0,25л*.
8.18. V = x0 -Jkm2 /(w, +/w2).