Purpose
The purpose of this lab is to find the velocity of the ball coming out of the launcher using a pendulum.
Theory
In dealing with collisions there are two main concepts that need to be kept in mind. They are the Principle of Conservation of Momentum and the Law of Conservation of Energy. The first concept means that the momentum before the collision will be equal to the momentum after the collision. The second concept means that the kinetic energy at the moment of the collision will equal the potential energy at the top of the pendulum swing. Once we add the equation for cosine will allow us to make an equation to find the initial velocity of the ball. We also need to remember that potential energy equals mass times gravity times height and kinetic energy equals one half the mass times velocity squared. Cosine equals adjacent over hypotenuse but we will need to use the second height over the length of the rod.
Once the equations are rearranged for what we need we can substitute PE for KE
Experimental Technique
The first thing that we did was made a holder for the ball to caught in so that it does not fall out when we are trying to measure the angle of the launch using a rotary motion sensor. Then we set the sensor in front of a launcher. Then we hooked the sensor up to a computer to measure the time and angle of how high it went and how long it was moving. Lastly we used photo gates to find the muzzle velocity of the ball to compare to what we found.
Data & Analysis
The mass of the ball and catcher together is 146.9 grams
The mass of the ball is 16.3 grams
The mass of the catcher is 130.6 grams
The length of the rod is .337 meters
The mass of the ball is 16.3 grams
The mass of the catcher is 130.6 grams
The length of the rod is .337 meters
This graph represents the degree the pendulum swung to and the time it took for it to come back to zero, on the first setting
This graph represents the degree the pendulum swung to and the time it took to return to zero on the second setting.
This graph represents the degree the pendulum swung to and the time it took to return to zero on the last setting.
This chart shows the maximum degree that the pendulums swung to.
This chart represents the actual velocity of the ball measured by the photo gates.
When we plug all of the numbers that we found into the equations, we found the velocity of the ball for each of the settings. The first setting fired at 2.95 m/s^2. The second setting fired at 4.27 m/s^2. The last setting fired at 5.47 m/s^2.
The percent difference between the measurements are 10.3%, 0.23%, and 1.27% respectively.
The percent difference between the measurements are 10.3%, 0.23%, and 1.27% respectively.
This represents the percent difference between what we got using equations to what the photo gates got.
Conclusion
When using The Principle of Conservation of Momentum and The Law of Conservation of Energy we were able to accurately calculate the velocity of the ball leaving the launcher. Even though we were not exactly on point with the measured velocities we were very close except the first setting. I believe that could be caused by the angle not changing enough for the sensor to accurately measure it in the frames per second that we used. Some problems that we ran into were getting the ball to stay in the capture chamber because if the ball would not stay in it then the weight of the ball and holder would not carry out through the whole swing. Another problem was trying to get the center of mass exactly right so the pendulum would not vibrate when the ball hit it. In conclusion I believe this was a very successful lab that gave us accurate results and prove that our purpose of the lab was achieved.