Question

A bullet of mass 9.00 g is fired into a ballistic pendulum of mass 4.90 kg. The pendulum rises a vertical height 0.0940 m. Compute...

(a) the kinetic energy of bullet and pendulum after the bullet is embedded in the pendulum before it has risen. J?

(b) the initial momentum of the bullet. kg·m/s ?

(c) the initial speed of the bullet. m/s

Answer 1

here,

mass of the bullet , m = 0.009 kg

mass of pendulam ,M = 4.9 kg

height , h = 0.094 m

(a)

by conservation of energy

the kinetic energy gained by the bullet and pendulam KE = change in potential energy

KE = ( M + m ) * g * h

KE = 4.909 * 9.8 * 0.094

KE = 4.52 J

he kinetic energy of bullet and pendulum after the bullet is embedded in the pendulum before it has risen is 4.52 J

(b)

let the speed after the collison be v

KE = 0.5 * (m + M ) * v^2

4.52 = 0.5 * ( 4.909) * v^2

v = 1.36 m/s

final momentum after collison , P = ( M + m) *v

P = 6.66 kg . m/s

using conservation of momentum ,

initial momentum = final momentum

initial momentum is 6.66 kg.m/s

(c)

let the initial speed of the bullet be v0

m * v0 = 6.66

0.009 * v0 = 6.66

v0 = 740.36 m/s

the initial speed of the bullet is 740.36 m/s