The purpose of this experiment is to measure the initial velocity of a projectile in two independent ways:
One by treating it as a projectile moving according to the kinematic equations and the other is by
applying the conservation of linear momentum and energy to a ballistic pendulum.
Triple beam balance
If the projectile is fired horizontally with an initial velocity V
, it will follow the parabolic path shown in
figure 1.The horizontal range X and vertical displacement Y of the projectile are given by:
X = V
Y = (1/2) g T
Taking the value of T from (1) and substituting in (2) we get equation (3) as
= X [g /2Y]
the projectile can also be determined by using the ballistic pendulum ( Fig 2). It consists of a spring gun
that fires a metallic ball of mass m. This ball is caught by a catcher at the end of a pendulum of mass M.
The collision between the ball and pendulum is perfectly inelastic. As a result, the combination (m + M)
swings upward until it stops at the highest point by a ratchet.
From conservation of momentum,
( m + M ) V
( 4 )
is the common velocity of
pendulum – ball just after collision. If the combination rises through
a height h, then from conservation of mechanical energy we have:
(1/2) ( m + M ) V
( m + M ) g h
( 5 )