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:
tucking as they enter a tight corner turn
vying for dominance in the ring by keeping low to the ground
their tails as counterbalance mechanisms
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:
Experiment 2: In the
first part of the lab, you will determine the angle at which certain
objects become unstable.
Experiment 4: In the
second part of the lab, you will experimentally determine the
center-of-mass of an irregularly shaped object.
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
sure that your irregular shape is cut out of cardboard.
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:
When did the blocks typically fall over?
Which stack of blocks (3 or 4) had a lower center of mass? Which
set tipped over at the largest angle?
If you were building a skyscraper in a windy city, where would you
want most of the building’s weight to be located?
Consider the following diagram of the three-block system at the
point of instability:
[img width="419" height="238" src="file:///C:/Users/srarin/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png" alt="Description: Block at an angle with its center of mass marked on the block " v:shapes="Group_x0020_1 Group_x0020_50 Rectangle_x0020_51 Rectangle_x0020_52 Rectangle_x0020_53 AutoShape_x0020_54 AutoShape_x0020_55 AutoShape_x0020_56 Text_x0020_Box_x0020_57 Text_x0020_Box_x0020_58 Text_x0020_Box_x0020_59">
question involves a calculation, not a measurement.
you calculate the angle of instability, consider this fact:
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
Repeat this calculation for the four-block
system. How does you result compare to
the three block system? Explain.
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?
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?