Modern Engineering Thermodynamics

2.11 The Conservation Concept 49
Therefore, by knowing the masses of the pendulum and the projectile and measuring R and θ, we can easily calculate
the impact velocity of the projectile. If the projectile is fired point blank into the pendulum, then the impact velocity
is essentially the muzzle velocity of the projectile. These concepts are illustrated in Example 2.4.
WHAT HAPPENS ON IMPACT?
You might wonder why we do not set the initial kinetic energy of the projectile equal to the final potential energy of the
pendulum/projectile system. Even though energy is conserved during the impact, this is not a perfectly elastic impact and
other forms of energy are involved in addition to kinetic and potential. Some of the projectile’s initial kinetic energy is converted
into heat through the friction and deformation that occur during the impact. Figure 2.11 illustrates what happens
when a .45 caliber bullet is fired into a 1 1 4
inch thick laminated Lexan plastic block. All the kinetic energy of the bullet has
been absorbed by the plastic.
FIGURE 2.11
Bullet in a Lexan block.
EXAMPLE 2.4
Determine the muzzle velocity of a weapon fired point blank into a ballistic pendulum causing the pendulum to deflect 15°.
The mass of the pendulum is 5.0 kg, the mass of the projectile is 0.01 kg, and the length of the pendulum support cable
is 1.5 m (Figure 2.12).
θ=15°
L = 1.5 m
M = 5.0 kg
m = 0.01 kg
m
M + m
v = 0
FIGURE 2.12
Example 2.4.
x
(Continued )