Can the center of mass of a two-object system be found as a weighted average (li

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Can the center of mass of a two-object system be found as a weighted average (like the pencil problem)?
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.
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
Predict mass combinations that place the center of mass in a desired location for a three-object system.
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.
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).
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).
Find the simulation here.https://physics.bu.edu/~duffy/HTML5/centerofmass.html
In this activity, you will be writing and submitting an experiment report on the assigned module experiment in Canvas. The Experiment Report should cover all activities and simulations in the module experiment. If specific questions were posed in the activities or simulations, they should be answered in an appropriate section of the Experiment Report.
The Experiment Report must be submitted utilizing the following format, based on the results of the assigned module experiment.
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”?
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.
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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