Center of Mass Experiment

This physics experiment consists of two activities on center of mass — an essential concept for understanding stability, with applications to aircraft, cars, buildings, sports, and more. After completing the activities, write and submit your Module 3 Experiment Report.

Please read this brief introduction before beginning the first activity.

An object’s center of mass is its balance point. The center of mass of several objects is the location where the system of objects would balance.

Center of mass depends on two physical properties: (i) the mass of each object, and (ii) the distance of each object from a reference point (which can be labeled as zero distance, often called the origin). 

It may be surprising to find that the center of mass of two objects is solved the same way the pencil problem was solved in elementary school. For example, if Tom bought two pencils at 2 cents each and Sally bought four pencils at 8 cents each, what was the average cost of all the pencils? The answer can’t be 5 cents since more pencils were bought at the higher price (8 cents). Instead, the solution requires a weighted average as follows:

 

= 6 cents per pencil.

Since more pencils were bought at 8 cents than at 2 cents, it makes sense (and cents!) that the average cost per pencil (6 cents) is closer to 8 cents than to 2 cents.

We can either view that the number of pencils bought was weighted by their cost, or alternatively, that the cost of each pencil was weighted by the number of pencils bought at that price. The total number of pencils is in the denominator.

To connect the Tom and Sally pencil problem with this physics simulation of center of mass, replace the number of pencils with the mass of each ball and replace the cost of the pencils with the location of each ball. Therefore, Ball 1 is at position = 2 m with mass = 2 kg and Ball 2 is at position = 8 m with mass = 4 kg. If center of mass is solved like the pencil problem, then the center of mass of this system should be at 6 m. Let’s test this hypothesis (i.e., this prediction) using the physics simulation.

In this physics simulation, three balls are at fixed positions but their masses can be varied and the center of mass of the system displayed.

HERE IS THE LINK TO THE SIMULATION: http://physics.bu.edu/~duffy/classroom.html 

Click HTML5 Simulations then scroll down to find the center of mass

Activity 1

Can the center of mass of a two-object system be found as a weighted average (like the pencil problem)?

1. In the physics simulation, set the mass of Ball 3 to 0 kg to remove it from the simulation, leaving only Balls 1 and 2.
2. Set the mass of Ball 1 to 2 kg and the mass of Ball 2 to 4 kg to simulate the pencil problem. Test the prediction that the center of mass should be located at 6 m.

Simulation ball color legend:

Ball 1 = Red
Ball 2 = Blue
Ball 3 = Green
Center of Mass = Purple

 

Activity 2

Predict mass combinations that place the center of mass in a desired location for a three-object system.

1. Your first task is to find a combination of masses for three balls that place their center of mass at point (5,2), i.e., midway between Balls 1 and 2 in the x-direction, and midway from the x-axis to Ball 3 in the y-direction. You will need to change the mass for each of the three balls to accomplish this.
2. After you discover a combination of masses for the three balls that place the center of mass at point (5,2), predict a different combination of masses that also achieves this. (Hint: look for a pattern in the combination of masses that worked to help you predict a second successful combination).
3. Test if your prediction for the second combination works. If so, please explain the basis for your prediction in your Experiment Report for this module. If your predicted mass combination doesn’t work, no problem. Try to figure out why it doesn’t work and try again to make a new prediction based on the first successful combination of masses you found. Repeat until you find a second combination of masses that place the center of mass at point (5,2).

Physics Experiment Report Format

Name: Do not expect credit if not included.

Title: The experiment name. Do not include the Module number. Again, do not expect credit if not included.

Hypothesis

A hypothesis is a statement the experiment is designed to test or disprove. Note: experiments are designed to test or disprove, not prove, hypotheses as there are always additional tests that could be performed. Hypotheses should make specific, testable predictions and are often in IF-THEN form, e.g., “if x is changed, then y will occur.” A hypothesis answers the question, “What is the point of the experiment”? 

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  •  
    • NOT a hypothesis: “to prove Newton’s 2nd law” or “to see what happens if I…”
    • IS a hypothesis: “if an object moves with constant velocity, then its distance will increase linearly with time.

Overview

The Overview is a paragraph describing the approach or strategy used to test the hypothesis. It should include what was tested and how it was tested.

Procedures

See Experiment Instructions (use this phrase; do not include the actual procedures from the experiment).

Results

State the most important numerical, graphical or qualitative results obtained from performing the experiment. If there is a data table, include it here.

Uncertainty & Error

Discuss sources of uncertainty (due to limited measurement precision, e.g., length measured to the nearest millimeter) and error. Sources of error include modeling errors (differences between the physical system your predictions are based on, and the real system) and experimental errors, both systematic (errors that always shift results in one direction) and random (equally likely to cause overestimates and underestimates). For computer simulations, discuss real-world sources of uncertainty or error that were not simulated. 

Conclusion/Summary

Discuss how the experimental results support rejecting or accepting (again, not proving) the hypothesis. Discuss the relevance of uncertainties/errors to these conclusions. Propose experiment improvements and/or future directions for experimentation.

Application

Discuss at least one real-world application of the physics concept(s) tested in the experiment.

Experiment Report Example (DOCX)

Download Experiment Report Example (DOCX)

The single most important requirement for an experiment report is clarity. It should be written in such a way that someone who has been unable to conduct the experiment would be able to clearly understand what was done, the results, and why it mattered.

All experiment reports should be:

• concise, clear, and contain the necessary details for a well-developed explanation.
• well organized so the reader is able to quickly find the information needed or of interest.
• relevant and rational so the reader is able to validate the summary or conclusion.

 

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