# Pendulum Lab

## Abstract

This experiment was performed to determine the theoretical and observed velocity of a mass incorporated in a pendulum. After constructing a pendulum, tests were performed and data was collected in order to find the observed velocity to successfully match the theoretical velocity that was calculated before experimentation. Over the course of experimentation, two graphs were drawn (Energy vs Time and Energy vs Position) to illustrate the change in both kinetic and potential energy in time and position as well as pictures were taken to depict the construction of the Pendulum.
In the end, the experimentation was successful in that the theoretical velocity was very close to the observed velocity. The theoretical velocity was 0.447 m/s and the observed velocity was 0.454 m/s The overall goal of this project was to advance our knowledge on the study of Work and Energy and prepare us for the AP Physics Exam.

## Hypothesis

• As the kinetic energy increases, the potential energy decreases, and as the potential energy increases, the kinetic energy decreases.
• When the kinetic energy is at its maximum, the potential energy is at its minimum, and when the potential energy is at its maximum, the kinetic energy is at its minimum.
• The total energy is always constant.

If the difference of the maximum and minimum height is 1 cm (16 cm-15 cm), then the velocity will be 0.443 m/s.

## Introduction/Background

The experiment to be undertaken is for a team of no more than three students to assemble a pendulum and compare the observed instantaneous velocity of the hanging mass / bob at the end of the pendulum to the theoretical instantaneous velocity of the mass as it passes through the equilibrium position. The objective and importance of this experiment is to have a deeper understanding of energy vs both time and position.

## Materials

• Ring Stand (base, stand, rod extension) (1)
• String (1)
• Hanging mass / Bob (1)
• Motion Detector (1)
• Computer (1)
• Logger Program
• Meter stick (1)
• Scissors (1)
• Pencil and notebook
• Various sizes of books

## Procedures (Pendulum Construction)

1. Measure and record the mass of the hanging mass / bob, the length of the string (after being cut), and the top and bottom height of the pendulum in your notebook.
2. Cut the string and tie the length to the hanging mass / bob. Tie it onto the extending rod of the ring stand and make sure the string is short enough that it doesn't touch the ground, but long enough for the motion detector to detect.
3. Set up the motion detector by connecting the given cables to the computer, opening up the Logger program. Set the motion detector on the ground next to the pendulum so that it can detect the hanging mass / bob as it swings back and forth. Make sure the motion detector is set up high enough for it to accurately record the presence of the hanging mass / bob; use the various sizes of books to set up the motion detector higher if needed.
4. Test out the motion detector and Logger Pro to make sure it works; not actual data collection.

## Procedures (Testing/Obtaining Data)

1. Start the Logger Program by clicking on the "play" button right as someone lets go of the hanging mass / bob. Make sure the hanging mass / bob swings in a straight angle and there are no outside forces acting upon it, and be sure to not to have any other outside motions in front of the motion detector while testing.
2. Collect accurate data (repeat until you get perfect curves).

Pendulum Lab

## Results - Calculations

Mass - 0.0707 kg

Height 1 - 0.16 m

Height 2 - 0.15 m

Gravity - 9.8 m/s

Theoretical Velocity - 0.443 m/s

Observed Velocity - 0.454 m/s (slot 194 on Graph 3)

## Conclusion

The theoretical velocity of 0.443 m/s was very close to the observed instantaneous velocity of 0.454 m/s. This is less than a 10% error, meaning that our calculated theoretical velocity is approximately accurate.

The picture of the pendulum can only show its construction, but the video shows how the pendulum works and how the velocity is recorded as well as the graphs from Logger Pro accurately showing the velocity of the hanging mass / bob. By following the calculations in the picture of the Results section, one can conclude the calculations were done correctly, and by looking on the pictures of the Logger Pro graphs, one can compare the theoretical and observed velocity and conclude that they are very close.

## Work Cited

Walker, James S. Physics. 3rd ed. Upper Saddle River, NJ: Pearson/Prentice Hall, 2004. Print.