Lab Assignment 8: Center of Mass

Instructor’s Overview

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:

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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 12 of the eScience Lab kit. Although you should read all of the content in Lab 12, 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. Experiment Tips: eScience Experiment 2

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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.

  • 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. Date: Student: Abstract Introduction From esciencelabs: Center of mass is the point in space where all the mass of an object bal- ances. No matter what the object’s shape or how it is moving, the center of mass moves, as if all the mass of the object were concentrated at that point. Experiment 1 – stability of a tower of blocks. In this experiment, you will test the stability of a stack of
    blocks as the angle of the surface the stack rests on
    gradually increases. Using a fishing sinker tied to the center of mass, you will be able to see the position of the center of mass relative to the base of the object as it begins to tip over. Procedure: 1. Mark the location of the center of gravity on one side of a wooden block with a piece of masking tape (the middle). 2. Using masking tape, attach one block above and below your original so that your center of gravity mark is visible, making a 3-block-high tower. 3. Use a ruler to measure and cut 30 cm. of string. Tape the string to the mark on the middle block with 20 cm hanging downward.
    4. Attach a sinker to the end of the string. Set the block stack on top of the ramp, and line the edge of the ramp runway up with the edge of a

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table so that the string can dangle.

5. Increase the incline of the ramp runway, and notice the relationship between when the block stack starts to tip over and the location of the string. Record your observations in Table 1.

6. Try this out with four blocks stacked. Make sure to move your center of mass to the middle of the tower (between the second and third blocks). Record your observations in Table 1.

Note: plumb line is taped to side at mid- Section.
can go

Measure to
same as makes to

stack

Measure angle of plumb line to edge of base.

Tilt the blocks until the plumb line
is at the edge of the stack of blocks

This should be as far as you Without tipping over.
The angle of the stack bottom the table. It should be the the angle the plump line

the center line.
Tilt a little more. Does the fall over?

Now do the same for a stack of FOUR blocks with a plumb line again at the midsection of the now larger stack. Compare the angle of the four-block stack with that of the three-block stack. Which angle is smaller? What does this mean in practical terms?

Table 1 – block observations

Results

Based on your results from the experiments, please answer the following questions:

Block experiments

Block Arrangement

Observations

Three blocks stacked

Four blocks stacked

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1.

2.

3.

4.

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:

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 (the plumb line) just meets the edge of the base of the object.

Consider using the trigonometric identity:

tan θ = side opposite / side adjacent.

Calculate the angle of instability of the system for the 3-block system using ratios with the variable S for the length of a side.

Hint: start with the tangent of θ. You should be able to have the S variable cancel. Then take the arctan (tan -1).

Angle of instability (θ) =

Repeat this calculation for the four-block system.

Angle of instability (θ) =

How does your result compare to the three-block system? Explain.

Experiment 2.

Center-of-mass experiments
Procedure
1. Use the scissors to cut an irregular shape out of a piece of pa-

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per. Any shape will work!

2. Cut a 30-cm length of string and tie one metal washer to each end. This will function as a “plumb-bob” that hangs down as a vertical line.

3. Set one side of the physics kit box flush with the edge of a table and stick a push pin in the cardboard near the top (Figure 6), page 165 of the escience manual.

4. Punch a hole in three different spots around the edge of the shape, but not too close together.

5. Hang the shape through one of the three holes on the push pin making sure the shape can move freely.

6. Hook the plumb-bob to the push pin with the washer.

7. Note how the string hangs across the shape. Make a mark on the side of the shape opposite the hole in line with the plumb-bob string. Use this mark to draw a straight line through the shape, from the hole to your mark.

8. Take the shape and plumb-bob off the pin, and switch to a new hole on the shape. Repeat Steps 5 – 7 until you have three lines drawn on the shape

1.

2.

3.

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.

Is the third line necessary to find the center of mass? Why or why not? Hint: I suggest you look up some information on radio triangulation.

Conclusions

References

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