A 19 g bullet is fired into the bob of a ballistic pendelum?

Question

of mass (4.4 kg). When the bob is at its maximum height, the strings make a 40 degree angle with the vertical. The length of th ependulum is 4.15 m. Acceleration of gravity is 9.81 m/s^2.

Find the speed of the bullet in units of m/s.

Answer 1

Use conservation of linear momentum for the first half of the trip (before it hits) and conservation of mechanical energy for after it hits.

mass of pendulum = M
mass of bullet = m
Lenght = L
velocity of bullet alone: v1
velocity of bullet and pendulum: v2

Momentum: m*v1 = (M+m)*v2

Mechanical energy:

Ui + KEi = Uf + KEf Assume Ui = KEf= 0
((M+m)*v2^2)/2 = (M+m)gh where h = L(1-cos(40*))
v2^2 / 2 =gh
v2 = sqrt(2gL(1-cos(40*))

Plug in into momentum:

m*v1 = (M+m)*v2
v1 = (M+m)*sqrt(2gL(1-cos(40*))) / m

v1 = 1015 m/s

Answer 2

why?
what use is this...in the real world if your not a detective
or are you just showing us your big brain

a 19g bullet huh? never heard of one