Question

in a ballistic pendulum, a fast moving bullet with a mass of 5g is fired into a hanging wood with a mass of 1kg at rest. if the hanging mass with the bullet inside it rose to a vertical height of 5 cm, find the initial velocity of the bullet.

Answer 1

First we need to apply conservation of energy to find the wood-bullet system

Potential energy gained by system = initial kinetic energy of the system at the bottom point

mgh = 0.5 mv^2

9.8*0.05 = 0.5* v^2

v = 0.99 m/s

Now considering momentum the system before collision

(Momentum of bullet + momentum of wood) _initial = ( momentum of wood- bullet system ) _final

_{m1 v1 + m2 v2 = ( m1 + m2) v}

_{5*10^-3 v1 + 0 = (5*10^-3 + 1) 0.99}

_{v1 = 198.98 m/s (Ans)}

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