3-May-2017: LAB: Ballistic Pendulum

Eric Chong

LAB: Ballistic Pendulum

Lab Partners: Tian Cih Jiao, Max Zhang, Nina Song, Roya Bijianpour, Joel Cook, Kitarou Chen, Lynel Ornedo

Purpose: Determine the firing speed of a ball from a spring-loaded gun.

Introduction/Theory: In a ballistic pendulum, a ball is fired towards a pendulum that captures the ball and swings to a certain height, depending on the ball's initial speed. In terms of the physics behind this device, the ball contains a certain momentum and inelastically collides with the pendulum. The kinetic energy of the pendulum gained from the ball then transfers into gravitational potential energy, as the pendulum swings up to a certain height. For this lab, we want to determine the initial firing speed of the ball. To do so, we can go backwards in the process, starting from the gravitational potential energy and eventually to the initial speed of the ball.

Procedure: For the set up of the lab, we had a ballistic pendulum. Here is a picture of the set up:

Now, we need to take the necessary measurements for both the conservation of energy calculation and the conservation of momentum calculation. The pendulum can measure the angle at which it swings. We did 5 trials with the firing of the ball and measured the angles and took the average of those 5 trials. We then measured the masses of the ball and the pendulum. And finally, we measured the length of the string that hangs the pendulum. Here is the data:

From the data, we did the energy calculation first. We used the energy calculation in order to find the initial velocity of the pendulum after the collision. We also noticed that we can make a right triangle with the pendulum and create a diagram to find the height that the pendulum swings. Here is how we did it:

After finding the velocity of the pendulum after the collision, we can find the initial velocity of the ball through the momentum calculation. Note that the collision is inelastic, meaning that the mass of the ball adds to the mass of the pendulum. Here is how we did the calculation:

We found that the initial velocity of the ball is 6.86 m/s.

Verification: For this part, we set up the spring of the ballistic pendulum on the edge of a table and attempted to solve for the initial speed of the ball through a projectile motion calculation. We measured the height of the table, the length of the pendulum, and the range that the ball hits the ground. Here is a diagram with the calculation of velocity through projectile motion:

It turns out that the actual firing speed of the ball is 5.73 m/s, according to this calculation. It is possible that in this case, air resistance affected the speed of the ball while it was in the air, or that the spring is not ideally set up and produced a different speed from the one we used while measuring the angles.

Conclusion: Through this lab, we learned how to determine the initial firing speed of the ball by going through the processes backwards. We started with the concept of conservation of energy, and then looked at the conservation of momentum. By doing so, we can determine the firing speed of the ball.

Some errors or uncertainties in this lab were the actual spring used to fire the ball, as it is highly likely that it was not ideal and could produce a different firing speed each shot. This is evident with our angle measurements, as it seems that some of the angles are slightly off from the average, particularly the 27 degrees measurement. There is also the collision itself. It is possible that the ball did not produce an ideal collision to observe, and this could have altered our initial kinetic energy of the pendulum, while it is swinging in the air. A possible error in the verification part of lab is, as mentioned before, air resistance and the spring itself. These are some of the errors or uncertainties we noticed in the lab.