The Ballistic Pendulum Lab

The purpose in this lab is to use a ballistic pendulum to find its initial velocity of a projectile using the conservation of momentum as well as the conservation of energy.

INTRODUCTION:
We will be shooting a steel ball into the bob of a pendulum at a certain height which is where the bob will get stuck at. With this information we will be able to determine the initial velocity of the bob once it receives the moving ball.

This picture depicts what is going to happen when the ball shoots into the cup. The ball with mass, m, is shot with an initial velocity, V0, into a cup with mass, M, and the pendulum then rotates and gets stuck on the rubber at a certain height, h.

We can calculate the Kinetic Energy of the bob and ball at the bottom and set it equal to the potential energy at the top since they are equal to eachother. There will be no Potential Energy at the bottom because the height is 0 and the top will not have any kinetic energy because it will have no velocity. From the law of conservation of energy, we must have the same total energy in the initial and final positions. 

This combines both the conservation of energy equation with the conservation of momentum and shows how we can find v0, which is the initial velocity that the ball is shot with.

We can also find the velocity at which the ball is shot by shooting the ball as a projectile. Instead of shooting the ball into the pendulum, we can move the pendulum out of the ball's shooting range and let it hit a piece of carbon paper for us to measure.

This shows what information we can gather from the ball being shot as a projectile. The change in y is the height at which the ball was shot at, the change in x is the distance gone in the x direction, the mass of the ball is m, and the carbon paper is setup for the ball to land on. When it hits the paper a mark will be made on the paper and this will allow us to measure the x direction.

We can find the initial velocity of the ball using kinematic equations.

You can see there is a negative in the square root and there should never be a negative in the root but in this case, our change in y is going to be negative because it is starting from a higher point and falling to hit the ground. This will give you a positive number in the square root making it possible to do the calculations.

PROJECTILE:

Now that we have gone through what this lab is asking to find, we can perform the lab. To perform this lab the materials we needed were:

• Ballistic pendulum
• carbon paper
• meter stick
• clamp
• box
• triple beam balance
• plumb

We set up the Ballistic pendulum near the edge of the table in order to clamp it down. We don't want the apparatus to move because then it will alter our results. We then got the metal ball and shoved it onto the rod until it clicked to engage the trigger. This will set the spring to give the ball a constant initial velocity. Once the  arm is left hanging down and not moving we can press the trigger which allows the ball to shoot into the cup of the pendulum allowing it to go into motion. Once the pendulum reaches the rubber part of the apparatus it will get stuck in a notch. The notches were marked every 10 notches and this is where we will take an average height from. We did 9 trials and recorded the heights

.

We took an average of the height the pendulum moved. We measured the height difference from where it was shot from to where it landed and came up with 11.2 cm.

Once finishing the 9 trials, we then weighed the mass of the pendulum and the ball. The mass of the ball was 0.0567 kg, the mass of the pendulum was 0.2153 kg, and the average height the ball traveled was 0.112 m.

With these given values we can calculate what the initial velocity of the ball was from the equation we used when combining the law of conservation of energy and the law of conservation of momentum.

For the next part of the lab, we performed the projectile test of the ball. We set up the apparatus to shoot a projectile and land on a piece of carbon paper so we can measure the distance in the x direction. We recorded 5 trials and averaged them.

Our average distance traveled in the x-direction was 2.9128 m. The distance traveled in the y-direction, which was the height the apparatus was set at, was -1.02 m because it fell that distance. We can now use the equation to find v0 from the kinematics equations.

Now that we have 2 values for v0 we can calculate what the percent difference of them are.

CONCLUSION:

In this lab, I learned that you can find the initial velocity of an object by combining the laws of conservation of momentum as well as energy. I knew you could find v0 from kinematics by finding a value of time because we have done that before in previous work. With the two different methods in finding v0 we had a 10.8% difference which was a close value. One thing that could have contributed in a difference was on the ballistic pendulum when it reached the rubber notches. The friction there could have affected it's maximum height it could have reached. I think the method of shooting the ball as a projectile was the best method because in the method where we solved for the energy, there were more sources of error. The impact of the ball hitting the cup could have affected its height as well as the friction along the rubber notches. When the ball moved as a projectile the only thing that could have altered it was air drag. Since it had a small cross sectional area it could practically be negligible in our situation given.