Question

A 20 g rifle bullet traveling 220 m/s buries itself in a 3.7 kg pendulum hanging on a 3.0 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.

vertical: _____

Horizontal: _______

Answer 1

mass of rifle m = 20 g = 0.020 kg
speed v = 220 m / s
mass of the pendulum M = 3.7 kg
length of the string L = 3.0 m
from law of ocnservation of momentum mv = ( m+ M ) V
from this speed of the system after collision V = mv / ( m+ M )
= 1.1827 m / s
from law of conservation of enenrgy,
KInetic enenrgy of the system just after collision = potential enenrgy at maximum
height
( 1/ 2) ( m+ M ) V ^ 2 = ( m+ M ) gh
from this maximum height from bottom h = V ^ 2/ ( 2g )
= 0.0712 m
we know h = L - L cos (theta )
cos (theta ) = ( L - h ) / L
= 0.9763
theta = 12.49 degrees
we know sin (theta ) = x / L
from this the horizontal component of the pendulum's maximum displacement is
x = L sin ( theta )
= 0.6488 m