Explosion Features of Liquid Explosive Materials - Liquid Explosives - page 52

A 1 ¼ Mgh

h ¼ l l cos a ¼ l ð 1 cos aÞ

So,

A 1 ¼ Wl ð 1 cos aÞ ð 2 : 39 Þ

Here, W is the weight of the pendulum; ʱ is the swing angle; l is the distance of

gravity center to the rotary center.
A 2 is the work of the bullet ejection. It equals the kinetic energy of the bullet
when it leaves the mortar.

1
2 mv 2

1
2g qv 2

A 2 ¼ ¼ ð 2 : 40 Þ

Here, q is the weight of the bullet; m is the mass of the bullet; v is the initial
velocity of the bullet.
The pendulum and the bullet have same momentum, but their directions are
reverse.

Mu ¼ m t

In the above equation, M is the mass of the pendulum; u is the velocity of the
pendulum when it starts to swing.
While v ¼

M W

m u ¼ q u, Eq. 2.40 is rewritten in Eq. 2.41 .

2

W 2 u 2
gq

1
2

q
g

W
q u

1
2

A 2 ¼ ¼ ð 2 : 41 Þ

If there is no energy loss in the swinging, the original kinetic energy of the
pendulum equals its potential energy at the highest point.

1
2 Mu 2

¼ Mgh

u 2

¼ 2gh ¼ 2gl 1 ð cos a Þ

W 2 g
g

A 2 ¼ l 1 ð cos a Þ ð 2 : 42 Þ