Activity_05_.Energy_v20

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Arizona State University *

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102

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Physics

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Oct 30, 2023

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PHY101 Lab Activity 5 Energy General Advice • Before starting any lab, it is recommended that you read the entire contents, think through the execution, and gather all materials and help you will need. • Capturing photos of your work during this lab is easier with another person’s help. Report All uploaded lab reports should contain the following sections: 1. Title - Your name, your ID, and the title of the experiment. If you partnered with other student, include the name and ID of the partner. 2. Introduction - A short intro or outline of the lab (2-3 sentences should be adequate). • Results - Your collected data and calculations. It is ok to write these by hand during the experiment, take a picture, and paste it in your document. 3. Photo Documentation - Photographs documenting the experiment, where at least one image contains your ID. 4. Conclusion – A short statement (2-4 sentences) on what you did, what you learned, and how you think that reflects the goals of the lab. 5. Feedback – A short statement (2-3 sentences) on lab difficulty and improvements. Your completed document should be 2-3 pages long. Objective In this activity you will use a pendulum to observe the conversion between kinetic and potential energy and study the limitations that conservation of energy imposes on a system. Materials The following is a simple, non-exhaustive list of items that you will likely need. • Phone/camera – to capture your experiment. • Lab notebook/computer – to record data and observations. • String – to make the pendulum. • A small, dense object – to serve as the mass at the end of the pendulum (e.g., a coin with a whole in it, a ring, etc.). This need not be too small, just can’t add too much to the length of the pendulum. • Ruler – to measure the length and displacement of the pendulum. • Paper – to mark heights. • A Support – to provide a stable anchor for the swinging pendulum. This can be a nail/thumbtack on a wall, a hanger, or a curtain rod. Introduction Energy is one of the fundamental quantities in physics. Kinetic energy is associated with the motion of objects: K = ! " mv "

where K is the kinetic energy, m is the mass, and v is the velocity of the object. Potential energy results from the relative position between objects. For example, gravitational potential energy is proportional to the relative position of an object and the center of the Earth. In practice, we simply measure the distance from a reference point at the surface of the Earth, namely, the elevation h of the object. The potential energy U is then U = mgh where m is the mass and g is the free fall acceleration. Energy is a conversed quantity, which imposes restrictions on the motion of an object. For example, a starting total energy E can be split into kinetic and potential components: E = ࠵? + ࠵? = ! " mv " + mgh. Since the minimum kinetic energy possible is always zero, the potential energy can never be larger than E . This means that, in the case where the potential energy is gravitational, there is a maximum elevation h that can be achieved. In this experiment, you will use a pendulum to explore some of the properties of energy. The pendulum will be a small object tied to one end of a string, where the other end of the string is fixed so the object can swing back and forth. If the amplitude of the back-and-forth motion is small compared to the length of the string, the period of the pendulum is given by: T = 2π0 # $ where T is the period (the time for the pendulum to complete one full back-and-forth swing) and L is the length of the string. Note that the period does not depend on the mass of the object used and nor the amplitude of the motion. Consult your textbook for further details and definitions. Procedure This lab has 3 parts – all are required for completion. Each should be straightforward. Part 1. Pendulum properties. In this part you familiarize yourself with the properties of the pendulum. Requirements • The determined values for the periods in parts (a-d). • A statement, qualitative or quantitative, as to how well the predictions were met. • Pictures of your setup. Steps 1. Make a pendulum by attaching a mass to the end of a string of length 1 meter. 2. Pull the pendulum about 10 centimeters back from its rest position. 3. Release the pendulum. Let it swing for 10 seconds, counting the number of back-and-forth swings.

4. Determine the time per swing, which is the period. Your result should be a measured period of about 2 seconds. Write the results of your measurements. 5. Repeat steps 2-4, but starting this time with initial amplitude of about 20 centimeters from the rest position. The period should be very similar to before since it does not depend on amplitude. Write the results of your measurements. 6. Repeat steps 1-4, but using a different mass (lighter or heavier). The period should remain similar since it does not depend on mass. Write the results of your measurements. 7. Repeat steps 1-4, but now with a different length pendulum. Shorten the length to 25 cm instead of 1 meter. The resulting period should be about half as long = 1 second. Test this prediction. Part 2. Limits imposed by energy. This part will test the limitations imposed by conversation of energy. Since energy is conserved, the height of the pendulum should never rise higher than the initial starting position. Friction might reduce the energy, which implies the second height can be a bit lower, but never higher. Requirements • A set of values for all the sequence of heights observed. • A simple statement regarding the validity of the prediction. • Pictures of your setup. Steps 1. Using one of the string lengths and masses from the Part 1, select an initial height and let the pendulum swing. 2. Record both ends of the swing motion the heights you observe. Confirm your predictions about the heights and what you observed. 3. Repeat the procedure starting from a different initial height. Confirm your predictions about the heights and what you observed. Part 3. Energy conversion. This part demonstrates energy conversion. As the pendulum swings it gets higher and lower, converting potential energy into kinetic energy and vice versa. At the lowest point, it has the greatest kinetic energy and therefore greatest velocity. In this part, we will start the pendulum at the bottom, give it different initial velocities, and record what this does to the final height. The hypothesis is that a greater initial speed will lead to a greater pendulum height. Requirements • A simple statement regarding the validity of the prediction. • Pictures of your setup. Steps 1. Let the pendulum start at its equilibrium point. 2. Give the pendulum a short but sustained initial push and observe the resulting motion. Test your prediction. 3. Repeat steps 1-2 several times, trying to give the pendulum different initial speeds and making note of the elevations obtained. Notes and Hints

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1. To make the set up easier to work with, try to find an object from which to hang the pendulum (a hook, thumbtack, hanger, or window shade rod). 2. Try to let the pendulum swing next to a wall, where you can tape sheets of paper to mark the different heights.