Inelastic Collision

3 Pages 652 Words

Purpose:

To use the ballistic pendulum to study inelastic collisions in which momentum but not energy is conserved. Also, to measure the initial velocity of a ball using the ballistic pendulum and compare it to that calculated from its range using the projectile motion equations.
Theory:

In this experiment there was a ball used to begin the collisions and gained its kinetic energy from the spring in the gun. We used two ways to find its initial velocity, the projectile motion method and the ballistic pendulum method.

In the projectile motion method, we found the horizontal velocity when the ball leaves the gun from a height above the floor and we measured its range. We used the following equations:
H = gt2/2

R = v0xt

We solved for t in the top equation, put it into the bottom one, and solved for v0x, the initial velocity of the ball before collision.

t = (2H/g)1/2
t = (1.0m/ 4.9 m/s2)1/2
t = .45s

v0x = dx/t
v0x = 1.91m/ .45s
v0x = 4.2 m/s

In the ballistic pendulum method we also calculated the initial velocity of the ball by measuring the maximum height reached by a ballistic pendulum when the ball was fired into it. The ball and pendulum had the same velocity afterwards because thy stuck together. The conservation of momentum can be found by the following equation:

mbvob = (mb + mp) vf

After the collision some energy is conserved naturally, the kinetic energy that the ball and pendulum have fight after the collision should equal the potential energy of the ball and the pendulum when they come to a stop. Shown by the equation below:

.5( mb + mp) v2f = (mb + mp) gh
or
vf = (2gh)1/2
We used the following equations to examine the accumulation of energy before and after the collision:

KEbefore = .5 (mbv20b)
KEafter = .5 (mb + mp) v2f = (mb + mp) gh

We also found the percent error. In this particular case, velocity is equal to the percent error in R plus on half the percent...