Lab Assignment 8: Center of Mass
Have you ever recovered when you began to slip on ice? Your body goes into a type of autopilot state to maintain balance. Most people can’t remember precisely all of the movements that were executed. The human body instinctively wants to stay upright and the seemingly wild motions that take place in a recovery of balance are performed to keep the center of mass within the base of the person. Other examples of the management of center-of-mass include the following:
· Bicycle riders tucking as they enter a tight corner turn
· Sumo wrestlers vying for dominance in the ring by keeping low to the ground
· Squirrels using their tails as counterbalance mechanisms
· Two celestial objects rotating about their mutual center-of-mass
In this lab, you will directly experiment with the concept of center-of-mass.
This activity is based on Lab 9 of the eScience Lab kit. Although you should read all of the content in Lab 9, we will be performing a targeted subset of the eScience experiments.
Our lab consists of two main components. These components are described in detail in the eScience manual. Here is a quick overview:
- eScience Experiment 2: In the first part of the lab, you will determine the angle at which certain objects become unstable.
- eScience Experiment 4: In the second part of the lab, you will experimentally determine the center-of-mass of an irregularly shaped object.
Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations.
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eScience Experiment 2
· Do not use a large mass on the string. A significant mass results in a torque on the block system. I used a paperclip in my experiment.
· You may consider setting the block-string system on a cardboard platform. This allows you to see the location of the string relative to the base of the blocks. A partner can help you measure the angle of the cardboard support at the point of instability.
eScience Experiment 4
· Make sure that your irregular shape is cut out of cardboard.
· You may want to also experiment with a regular shape (e.g. square or rectangle) as a control object to convince yourself of the validity of the experiment.
Material and Methods
Based on your results from the experiments, please answer the following questions:
1. When did the blocks typically fall over?
2. Which stack of blocks (3 or 4) had a lower center of mass? Which set tipped over at the largest angle?
3. If you were building a skyscraper in a windy city, where would you want most of the building’s weight to be located?
4. Consider the following diagram of the three-block system at the point of instability:
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This question involves a calculation, not a measurement.
When you calculate the angle of instability, consider this fact:
The angle of instability occurs when the vertical projection of the center-of-mass just meets the edge of the base of the object. As you will see, if we assume a cube, the length of a side cancels out of the relation for the angle of instability. This calculation requires some simple trigonometry.
Calculate the angle of instability of the system.
Repeat this calculation for the four-block system. How does you result compare to the three block system? Explain.
1. When you hang the shape from the pin, it balances around that point. How is the mass distributed on either side of the lines you draw when it is hanging like this?
2. What does the point where the three lines intersect represent? Explain why this method works.
3. Is the third line necessary to find the center of mass? Why or why not?