# Ex 7 - PURPOSE OBJECTIVES The purpose of this experiment is...

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PURPOSE/ OBJECTIVES 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. APPARATUS/EQUIPMENT Ballistic Pendulum Triple beam balance Meter stick White paper Carbon paper THEORY If the projectile is fired horizontally with an initial velocity V o , 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 o T (1) Y = (1/2) g T 2 (2) Taking the value of T from (1) and substituting in (2) we get equation (3) as V 0 = X [g /2Y] 1/2 (3) The initial velocity V o of 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, mV o = ( m + M ) V 1 ( 4 ) where V 1 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 1 2 = ( m + M ) g h ( 5 )
By combining ( 4 ) and ( 5 ) we determine the velocity V o to be: V 0 = [(m + M) / m][2g / h] 1/2 ( 6 ) Therefore, we can find the speed V o of the projectile in two different ways, equ.(3) and equ.(6) and compare our results. PROCEDURES Projectile motion 1) Move the pendulum out of the path of the ball, and secure the ballistic pendulum to the table. 2) Place the ball in the shaft in the uncocked position and measure the height Y from the bottom of the ball to the ground by using a plumb line. 3) Fire the gun few times to get an approximate position of where it strikes the ground, and then tape a