Question

The game of pool does not conserve mechanical or kinetic energy. In this case, a 0.3kg cue ball ap- proaches a 0.2kg 8 ball at 3m/sî and strikes it, send- ing the two off on the given angles 0 and path of eight ball . 0-28 0.2kg fo.3ka 3 ms. a) Draw an interaction diagram with a defined sys- tem of the contact, and determine what is con- served in that system. path of cue ball ..0 = 24 b) Find 7 cue and ūg after the strike c) Find the percentage of Kinetic Energy lost in the strike

Answer 1

V8 Vg sin 28° 3 m/s 128 V los 28° 28 Var los 240 usin 24° Since there is no external force acting upon the system che momentem will remain conserved >> Total momentum before tollisim = Total momentum oder collision Appling conserwation of momentum along + x auzis (Paul + Pe initial = (Puce + P8) final 0.3x3 + 0.2X0 = 0.3 x Vice Cos24°+ 0-2 V, 60528° ( snitially 0.2 kg ball is at rest, hence its velocity is zero] 0.9 = 0.3 x Veuve x0.91 + 0-2X V8 X0.88 0.9 = 0.273 Veure + 0.176 V8 -0 Applying conservation of momentum along ty tnis 0 +0 = 0.2 V3 Sin28° - 0-3 Viele sin 24° 0-2x x x 0.87 = 0-3 x x OI. Vg = 1.31 Veure - putting the value of Ve from ego in es , we get. Veure = 1.79 mls , Vg = 1.31X1.79 = 2.34 m/s

Jane = Veue Cos 24° ê - Vaue Sm 24° } = 1.79 80-91 ê -1.7980-41 Î = 1.63 ê -0.73 ſ Vg = Ve Cos28°ê + Va fi 28° ſ = 2.34 x 0.88 ê + 2-34*0:47 Î = 2.06€ + H Î Initial K.E. of the system KE; = 1 manele cu + 1 mzu? = 5x0.3 x 32 +0 = 135 J final K.E. of system KEz = 1 mene live + 1 mg Vg² = _ x0-3 x1•79+ 4x0.2 x 2-342 = 1003 J on KE lost Kit-KEx 100 = 1.35 –1:03 x100 = 23.7% Kei 1.35