Question

A ballistic pendulum malfunctions, and the bullet collides elastically with the pendulum. The bullet has a mass of 5 grams and a speed of 100 m/s. The pendulum has a mass of 2 kg and a length of 0.5 m. To what angle (from vertical) does the pendulum swing?

Answer 1

0.500 0.5 Cose h=0.5-0.5 cose , h=0.5(1-Coso) briven that m=5gm 5x100 v=toomis - M - 2kg Since cotho it is Ballistic Pendulum, bo bullet: will stuck in it. The collision is elastic, bo no energy will be lost and total enggy of bullet will convent into potential energy of bullet lett pendulun) bystem as shown in figure T. % mul .= (m+M) g h height acheived by bystena z mue e contM) 9x0.5 (1-Coso) UV muz = |- cose Dom+M) x 9 x 0.5 . Coso= 1 - mue 2159 +M) x9x0.5 Coso = - 5x1.0-3x(100)2 =-1-54465876 2 ( 5x10-5 + 2) 49.8 x 0.5 Bo ro Cose can't be greater than 1, Go n d so here question is corong. Here g it should be specified that collision is - inelastice Now consider collision is in elastic. momentum before collision & Momentum affer Collision. my z (mt ) De combined velocity gust Qyte Collision Ve = my - 5x10-3x100 = 0.249 m/s T M+M 5x10 3+2) NOLO bullet & bendulun) has kinetic energy, KIE. = 1 (0+ M) V2 potential This energy will converts into energy of bysten. KE PE IlontM) u ² = (ontM) gh 0.5(1-Coso) Vc ² = 29 (0.249)2 2x9.8 Cose = = 0.5 / 1-Coso) = 0.99367 -lo. 249) 2x9.8 x0.5 0 = Cos! (0.99 367) o=6.45°