a ballistic pendulum is used to find the speed of an 140g arrow that is shot int

Question

a ballistic pendulum is used to find the speed of an 140g arrow that is shot into a 2.6kg block hanging on a 50 cm length of string . Arrow embedes itself into the block and they both rise until the string makes a 50 degree angle . use both conservation of momentum for the collision and conservation of mechanical energy after collision

Explanation / Answer

applying conservation of momentum; =>0.14 v1 = (2.6 +0.14)*v2 -->(1) applying energy conservation; => 0.5 *0.14* v1^2 = 0.5(2.6+0.14) v2^2 + (2.6+0.14)g L(1-cos 50) => 0.07 v1^2 = 1.37 v2^2 + 4.796 -->(2) from equations 1 and 2; v1= 8.497 m/s, v2= 0.434 m/s speed of arrow= 8.497 m/s

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