Physics 221
Pre-lab assignment: Write the date, names, title, objectives, prelab questions (relevant equations), and the equipment sections. You will be writing the procedure as you perform the lab, as well as updating the equipment list and taking data. Your notebook will be checked off during lab, and the photocopy of the pages is due on Thursday, November 13.
Lab 5: Is the conservation of energy demonstrated by the ballistic pendulum?
Objectives:
• Setting up familiar and new lab equipment on a new system
• Determining the presence or absence of significant non-conservative forces
•Calculating the change in energy of system in two different ways
Introduction:
The principle of the conservation of energy states the energy of a system may change as a result of the transfer of heat and/or work. Further, the quantity of energy of system may not change but the energy can change its form.
In this experiment, you will set up and use the ballistic pendulum, an ingenious device to measure the conversion of the kinetic energy of the projectile launcher (from Lab 3) to gravitational potential energy by allowing the collision of the launched ball to move a mass at the end of the pendulum to a greater height.
Prelab questions and relevant equations used
Question 1. How is the kinetic energy of the ball to be calculated? Write the equation, and how each variable in the equation is to be measured. How will you calculate the velocity based off of measurements?
Question 2. How is the gravitational potential energy to be calculated? Write the equation, and how each variable in the equation is to be measured. How will you calculate the final height, given the setup (in other words, how will use trigonometry?)? The image to the left may give you a good idea of how to calculate it.
Question 3. In the image to the left, note that the change in height appears to be measured from a point slightly above the center of the “catcher” part of the pendulum. Explain what this point represents, and how you will measure it in an indirect way.
Equipment: (As always, note any deletions or additions)
Take a look at the photograph below and develop a list of equipment. For the photo or drawing in your notebook, this image should be enhanced with lots of labels.
Safety precautions:
Because plastic and steel balls are potentially being fired rapidly all over the room, everyone must wear the goggles that are provided.
Procedure (work in teams of four):
Section 1: Determining the muzzle velocity
(here is a point that you may be able to fix a mistake from lab 3)
(detail the steps needed (and the measurements to be made) for calculating the muzzle velocity, including the use of any computer hardware or software)
(by the way, how do you know that you are getting a consistent muzzle velocity every time?)
Section 2: Using the ballistic pendulum
(detail the steps in setting up the ballistic pendulum (including the term “wing nuts”))
Section 3: Performing the conservation of energy experiment
(detail the steps performed in the measurement of the ball fired into the catcher of the pendulum, including what other not-obvious data (*cough*, mass of the ball, mass of the pendulum) needed to be measured) – how was the angle of the pendulum measured, anyway?)
(also. there are both steel and plastic balls, and three settings (fast, medium and slow) on the projectile launcher – how many permutations of this experiment are there?)
Data section
Record the various measurements including their uncertainties and units. At a minimum, there should be at least thirteen different measurements you should make, including masses, times, distances and angles.
A table format will organize this data effectively.
Analysis
Calculate h, the height the pendulum rose for each of the runs, and show the detailed calculation for one of the runs. By this, I mean, write the algebraic equation you will use, then replace the variables with numbers (with units), then give the answer (with units and sig figs).
Similarly, calculate the change in gravitational potential energy for each of the runs. Show the detailed calculation for one of the runs.
Similarly, calculate the uncertainty in gravitational potential energy for each of the runs. Show the detailed calculation for one of the runs. Hint: you may assume that “g” does not have an uncertainty. Further hint: you’ll have to propagate the error first as an uncertainty in h, then as an uncertainty in gravitational potential energy.
Similarly, calculate the muzzle velocity of the ball for each of the runs. Show the detailed calculation for one of the runs.
Similarly, calculate the kinetic energy of the ball for each of the runs. Show the detailed calculation for one of the runs.
Similarly, calculate the uncertainty in kinetic energy for each of the runs. Show the detailed calculation for one of the runs. Hint: you’ll have to propagate the error first as an uncertainty in muzzle speed, then as an uncertainty in kinetic energy.
Results
Set up a table that shows each of the runs as a separate row and displaying the kinetic energy of the ball and its uncertainty, and the change in gravitational potential energy for each run and its uncertainty; the final column should be a percent difference between the kinetic energy and the change in gravitational potential energy.
Conclusion
Was energy conserved for any or all of the runs in this experiment?
Your answer may be “yes” or “no” or “for some of the runs”, but in every case, detail how the values in your table (especially the uncertainty values) helped you to come to your conclusion.
If any run’s answer is “no”, suggest where the “missing” energy went.
Finally, were there any improvements to be made to this setup to illustrate the principle of conservation of energy better? The short answer is yes, but I want a longer answer. BIG hint: See the manual for the new and improved ballistic pendulum; search for “pasco ballistic pendulum accessory”.