03-May-2017: Ballistic Pendulum

Lab: Ballistic Pendulum

03-May-2017
Idea: Demonstrate an inelastic collision and determine the launch velocity of a ball fired from a spring loaded launcher.

Summary:

1) Having a ballistic pendulum, as shown below, we first make sure that:

1. The device is level. We make sure that the ball does not roll around when placed flat.
2. The block connected to the strings is also directly facing the gun and that when fired, the ball will enter the block.

2) After measuring the length of the string attached to the block, mass of the ball, mass of the block, we proceed to fire the gun five times and record the angle that the block-ball mass goes to, as indicated by the metal arm, and then I took the average of these angles. This will allow me to calculate the launch velocity.

3) Then, we proceeded to launch the ball horizontally, and see how far the ball would land, which would allow us to again calculate the same launch velocity, using a black carbon paper. This is so that we could verify our calculations done in step 2, and perform propagated uncertainty calculations.

Analysis:

Part 1:

Our goal in the first part of the lab was to use conservation of momentum in order to find the firing speed of the gun. The ball undergoes an inelastic collision with the block once fired, and the two swing to a certain height with a certain angle, theta. In order to calculate Vo, I had to use the equations for conservation of momentum and energy, and furthermore, know exactly how high the block-ball swings up to.

To do that, I simply said that the starting level of the gun-block was zero, and because the block was connected to a string and rose to a certain angle theta, that would allow me to find the Y component of the string when tilted at that particular final angle. It turned out to be L-Lcos(theta).

Therefore, I was able to calculate the launch velocity using my momentum and energy equations by setting up two different equations, and solving for Vo.

Part 2:

Next, the task was to verify this calculated result by putting the block to the side, and launching the gun off a tabletop. By finding the horizontal distance that the ball travels, we could use kinematics in order to determine the launch speed of the ball based on the trajectory measurements.

To do this, we recorded the distance from the gun to the table edge, and then the edge to where the ball lands, as the X distance the ball travels. We do so similarly for the Y distance, we measure the height of the table, and then the height from the tabletop to the gun. These allow us to do our kinematic equations.

With such measurements, we also went ahead and calculated our propagated uncertainty for our result, based off the measurements we recorded with our meter sticks, and the mass scale. Doing so yielded a value of Vo very close to those of part 1, which was to be expected.

Measured Data:

Data Table of Measured Data

Calculated Data:

Data Table of Calculated Data for Part 1 and 2

Calculations of Vo for Part 1

Calculations of Vo for Part 2

Propagated Uncertainty Calculations for Part 2

Conclusion:

Comparing the calculations for velocity from part 1 and part 2, I notice that the two are remarkably similar, especially once I take my propagated uncertainty into account. Doing percent error calculations gives me a difference of little more than 1%, meaning that whether I find the speed using kinematics or momentum/energy, because both methods are equally valid, I should end up with final values that are very similar--if my measurements are accurate.

In terms of uncertainty,

• In measuring the height and length the ball travels in part 2, there were so many measurements to take (distance between the table and gun, distance between gun and black carbon paper, height of table, etc) that my measurements, if they are, are most likely off due to human error. I would not be surprised if I mistakenly missed or added a centimeter here or there, which would contribute to inaccurate lengths for X and Y, and subsequently an inaccurate value for V in part 2.
• The collision with the ball and the block is not perfect, the position of the gun required some meddling so that it would at least go into the block, which of course would lead to an inaccurate angle, on top of the fact that the angle indicator itself has an uncertainty of +- 0.5 degrees. An inaccurate angle leads to a value of height too tall or too short, subsequently messing up our solving for the initial speed with the conservation of momentum and conservation of energy.