Question

university of physics chap 8 example 8.12
question B angle alfa and Betta
could you help me doing step by step to find the degree please?

(0.500 kg)(4.00 m/s) - (0.500 kg)(2.00 m/s)? 0.300 kg Vg2 = 4.47 m/s the details of the solution (Hint: Solve the first equation for and the second for sin B: square each equation and add. Si sin'B + cosB = 1, this eliminates B and leaves an equation you can solve for cos a and hence for a. Substitute this value in either of the two equations and solve for B.) The results are a = 36. 9 B = 26.6° Conservation of the x- and y-components of total momentum gives MAVALXMAVA 2 + MgUR2X (0.500 kg)(4.00 m/s) = (0.500 kg)(2.00m/s)(cosa) + (0.300 kg)(4.47 m/s) (cos) 0 = MAVAZ+ U2 0 = (0.500 kg)(2.00 m/s) (sina) - (0.300 kg)(4.47m/s)(sin B) EVALUATE: To check the answers we confirm that the y-momentum which was zero before the collision, is in fact zero after the colli- sion. They-momenta are PA2 = (0.500 kg)(2.00m/s) (sin 36.9°) = +0.600 kg.m/s PR--(0.300 kg)(4.47 m/s) (sin 26.6") = -0.600 kg.m/s and their sum is indeed zero. TEST YOUR UNDERSTANDING OF SECTION 8.4 Most present-day nuclear reactors use water as a moderator (see Example 8.11). Are water molecules (mass m 18.0 u) a better or worse moderator than carbon atoms? (One advantage of water is that it also acts as a coolant for the reactor's radioactive core.) H command

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Answer 1

ma = 0.500 kg mø = 0.300 kg VAsx = = 4:00 mys , Vos=0 UA2 = 2.00 m/s so Vazx = Vaz Cos L = 2 Cost VAZY = Vaz sind = asina 1 V2 =? Veze = Voz Cosß . Vozy = - Voz Sinß first of all we will use conservation of linear momentum along xa ano MAVA + mood = MAVAZat Mg Veza ~ 0.50 x4 + 0 = 0.5 x 2652 +0.3 x VG, cos ß. 2.0 = 1.060A + 0.3Vescos B - © anis o = mavazy & MB Vozy = 0.sya sina + 0.3 xEVG2 Sinß) => HOSPM L = 0.3 Voz Sin ß - © Now using conservation of kinetic energy ma vax + 0 = a mavazi to move > **0.588 * = K 10.5(2)°+0.3 Ver ] => 80= 20+0.3 Voż=> 0.3Vož = 8.0-2.0= 6 so vor = 60 = 20 = Vb2 = 4.47 m/s) Putthg from equin , 0.3 Vos Cocß = 2 - GSX Cosß = 2-Cosa - 2 - Cos & _ ® along y-anis 0.3 X 4.47 1:34

0.3 Vg2 0.3x4.47 1.34 1798. from equin 0 she sind = sind = sina_ squaring & adding equn ③ & .. coste + SM*= (2+ forga yot some je 1 set { 4+63*d=465&+smi*} 1 = 1 1 1998 (4-462 +1) - 1.798 = 5-uosa 4 Cos = 5-1,798 = 3.202 - Cost = 3.202 = 0.8005 > x = cos (0.8005) K = 36.807 Now using equr G siuß= sih 36.8 = o.uur 1-34 ßasih-10.447) B - 26.60)