Question

A 24-g rifle bullet traveling 280 m/s buries itself in a 3.7-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Part A Determine the vertical and horizontal components of the pendulum's maximum displacement.

Answer 1

x = 0.95 m

y = 0.166 m

Step-by-step explanation:

m = mass of the bullet = 24 g = 0.024 kg

v = speed of bullet before collision = 280 m/s

M = mass of the pendulum = 3.7 kg

L = length of the string = 2.8 m

h = height gained by the pendulum after collision

V = speed of the bullet and pendulum combination

Using conservation of momentum

m v = (m + M) V

(0.024) (280) = (0.024 + 3.7) V

V = 1.805 m/s

using conservation of energy

Potential energy gained by bullet and pendulum combination = Kinetic energy of bullet and pendulum combination

(m + M) g h = (0.5) (m + M) V²

(9.8) h = (0.5) (1.805)²

h = 0.166 m

y = vertical displacement = h = 0.166 m

x = horizontal displacement

horizontal displacement is given as

x = sqrt(L² - (L - h)²)

x = sqrt(2.8² - (2.8 - 0.166)²)

x = 0.95 m