26-Apr-2017: LAB Ballistic Pendulum

LAB: Ballistic Pendulum
Kevin Nguyen
Lab Partners: Jose Rodriguez, Kevin Tran
Date of lab performed: 26 April, 2017

Purpose of Lab: The purpose of this lab is to determine the firing speed of a ball from a spring-loaded gun.

Theory: In this lab, we are trying to find the firing speed of the ball. To find the firing speed of the ball, we must use the conservation of momentum and conservation of energy. There are two parts to this experiment. First, conservation of momentum occurs when the ball undergoes an inelastic collision with the hanging block. The ball's initial momentum is converted to the block's (plus ball) final momentum. Second, the conservation of energy occurs when the ball's initial kinetic energy is completely converted to gravitational potential energy at the block's maximum's height. Using the conservation of energy, the initial speed of the block plus ball can be found. The initial speed of the block plus ball will then be used in the equation for conservation of momentum in order to find the firing speed of the ball.

In the second part of the lab, we shot the ball outwards (on the floor) in order to find the velocity of the ball in the x-direction. In order to find the velocity (in the x-direction) of the ball, we needed to measure and record the horizontal and vertical displacement. After recording those two measurements, we would use 2-d kinematics in order to find the horizontal velocity of the ball.

Summary:

We first obtained this apparatus and made necessary adjustments to the strings so that the block's compartment lined up with the barrel of the gun. We then leveled the base of the apparatus, the length of the strings, and measured the mass of the ball and block. After we made the measurements, we put the ball in the barrel and pulled back and locked the spring into position. We put the angle indicator to zero degrees. We fired the ball into the block and recorded the maximum angle the block rose. We repeated this for five times and then took the average angle of the five trials.

Next, we set up the apparatus just like above except we put the block on top and pointed the barrel towards open space like below.

We made sure the apparatus is leveled before shooting the ball. To record the ball's horizontal distance, we shot the ball first to estimate where it landed. We then placed notebook paper and carbon paper so its position can be measured. To measure the vertical distance, we recorded the distance from the ground to the middle of the cannon barrel. We then did three trials so that we can get an average horizontal distance the ball traveled.

Table of measured data:

Calculated results:

Conclusions: 

The values of launch speed that we got from those two different measurements were different from each other by 9.28%. Their difference may have came from several factors. We did not take into account air resistance when doing kinematics to solve for launch speed, so the true launch speed may have been higher than what we originally got. We also didn't take into account how the speed of the ball plus barrel was slowed down by the angle measurer.