Question

A 14 g rifle bullet traveling 170 m/s buries itself in a 4.0 kg pendulum hanging on a 3.4 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's maximum displacement. M

Answer 1

Applying momentum conservation for collision,

(0.014 x 170) + (4 x 0) = (0.014 + 4) v

v = 0.593 m/s

Now applying energy conservation,

m v^2 /2 = m g h

and h = L (1 - cos(theta))

v^2 = 2 L (1 - cos(theta))

0.593^2 = 2 x 3.4 (1 - cos(theta))

cos(theta) = 0.9483

theta = 18.5 deg

horizontal displacement = L sin(theta)

= 3.4 sin(18.5)

= 1.08 m