Physics 140 Lab 3Using a pendulum to measure g A simple pendulum consists of a mass m that is connected to a string or a rod that has a length L If you pull the mass off to one side and let go, it will swing back and forth The time it takes to swing back and forth through one cycle is called the period We usually give it the symbol T to remind us that it is a time If air resistance is negligible, the period of the pendulum is related to its length by the following equation T 2Lg If you square both sides this can be written as g (2T)2L In other words, you can determine the acceleration due to gravity g by using the length L of your pendulum and the period T that you measure Your goal this week is to make a simple pendulum and to use your measured length L and measured period T and the equation to determine the acceleration due to gravity You should also compare your measured value to the accepted value of g 32 feet s 2 Use the Relative Difference when comparing your measured value to the known (theoretical) value Relative Difference (TheoryMeasured)Measuredx100 Planning and Executing the Exercise Equipment String, mass, ruler or tape measure, stopwatch Before you begin, you need to build a simple pendulum Here is what I did I used some thread and taped a quarter to one end and wound the other end of the thread around a pencil a few times to make it easier to hold I changed the mass of the pendulum by taping extra quarters together so they were piled on top of each other That way I could change the mass without changing the length of the pendulum I determined the length of the pendulum by measuring the distance from the point where the thread last touched the pencil to the center of the quarter I measured the period by letting the quarter swing back and forth through 5 cycles, and divided that total time by 5 to get the period I repeated this with lengths of 3 feet and 2 feet, and recorded the results in a table I repeated steps 2 4 using two quarters taped to the end of the thread, and then three quarters to see if the result depends on the mass of the object Questions to Address Does the period of a pendulum depend on the mass of the hanging object Does the period of the pendulum depend on its amplitude (Amplitude how big the swing is) What is the resulting value of g based on my data, and how well does it agree with the accepted value The Lab Report Submit your lab report as a single WORD or PDF file according to the following outline Abstract A concise description of the experiment that paints a quick picture of what you wanted to do, a brief description of how you did it, and a summary of the results Note that an Abstract is not a laundry list of procedures Your goal is to assume that a person who was not present could get an idea of what happened in lab today Be concise and use complete sentences Introduction Provide a brief description of the experiment including any background information that may be relevant Drawings or diagrams (with labels) can be very helpful If you have a procedure, put it here Observations (Measurements) All data should be presented in a clear, easy to follow fashion with units Tables and diagrams are usually very helpful Analysis Include any calculations that were done All calculations should be clearly presented All results must include units (Some labs do not require as much analysis as others) Results What were the main results and how well did they agree with any predictions Were there any major sources of error in you lab that could lead to large uncertainties in your results Discuss ways to improve your experiment

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Physics 140 Lab 3Using a pendulum to measure g. A simple pendulum consists of a mass m that is connected to a string or a

Physics 140 Lab 3Using a pendulum to measure "g".

A simple pendulum consists of a mass m that is connected to a string or a rod that has a length L. If you pull the mass off to one side and let go, it will swing back and forth.

The time it takes to swing back and forth through one cycle is called the period. We usually give it the symbol T to remind us that it is a time.

If air resistance is negligible, the period of the pendulum is related to its length by the following equation: T=2Lg. If you square both sides this can be written as g=(2T)2L

In other words, you can determine the acceleration due to gravity g by using the length L of your pendulum and the period T that you measure.

Your goal this week is to make a simple pendulum and to use your measured length L and measured period T and the equation to determine the acceleration due to gravity.

You should also compare your measured value to the accepted value of g = 32 feet/s².

Use the Relative Difference when comparing your measured value to the known (theoretical) value:

Relative Difference = (TheoryMeasured)Measuredx100%

Planning and Executing the Exercise.

Equipment: String, mass, ruler or tape measure, stopwatch.

Before you begin, you need to build a simple pendulum. Here is what I did. I used some thread and taped a quarter to one end and wound the other end of the thread around a pencil a few times to make it easier to hold. I changed the mass of the pendulum by taping extra quarters together so they were piled on top of each other. That way I could change the mass without changing the length of the pendulum.

I determined the length of the pendulum by measuring the distance from the point where the thread last touched the pencil to the center of the quarter.
I measured the period by letting the quarter swing back and forth through 5 cycles, and divided that total time by 5 to get the period.
I repeated this with lengths of 3 feet and 2 feet, and recorded the results in a table.
I repeated steps 2-4 using two quarters taped to the end of the thread, and then three quarters to see if the result depends on the mass of the object.

Questions to Address:

Does the period of a pendulum depend on the mass of the hanging object?
Does the period of the pendulum depend on its amplitude? (Amplitude = how big the swing is).
What is the resulting value of g based on my data, and how well does it agree with the accepted value?

The Lab Report

Submit your lab report as a single WORD or PDF file according to the following outline:

Abstract: A concise description of the experiment that paints a quick picture of what you wanted to do, a brief description of how you did it, and a summary of the results. Note that an Abstract is not a laundry list of procedures. Your goal is to assume that a person who was not present could get an idea of what happened in lab today. Be concise and use complete sentences.

Introduction: Provide a brief description of the experiment including any background information that may be relevant. Drawings or diagrams (with labels) can be very helpful. If you have a procedure, put it here.

Observations (Measurements): All data should be presented in a clear, easy to follow fashion with units. Tables and diagrams are usually very helpful.

Analysis: Include any calculations that were done. All calculations should be clearly presented. All results must include units. (Some labs do not require as much analysis as others).

Results: What were the main results and how well did they agree with any predictions? Were there any major sources of error in you lab that could lead to large uncertainties in your results? Discuss ways to improve your experiment.