Lab_#8

Anthony Putrino 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:  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  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 JWH 1 Physics I

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. Abstract This experiment focuses on how the theory, center of mass can be observed by building blocks and understand the concepts of how it plays an important role on a day to day basis. Introduction From esciencelabs: Center of mass is the point in space where all the mass of an object balances 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 table so that the string can dangle. JWH 2 Physics I

Three blocks stacked The three blocks stacked together started turning when it reached a certain angle. Four blocks stacked The four blocks stacked together also began to start turning when it reached a certain angle but at a much faster rate/pace. Results Based on your results from the experiments, please answer the following questions: Block experiments 1. When did the blocks typically fall over? The blocks typically fell over when it reached a point of instability which was at a specific angle at which the plumb line was near the edge of the tower of the stacked blocks. 2. Which stack of blocks (3 or 4) had a lower center of mass? Which set tipped over at the largest angle? The stack of blocks of of 3 had a lower center of mass compared to the stack of blocks of 4; therefore leaving the stack of blocks of 3 to have tipped over at the largest angle because its lower mass. 3. If you were building a skyscraper in a windy city, where would you want most of the building’s weight to be located? Under these particular circumstances, I would want most of the building’s weight to be located towards the bottom or downward. 4. Consider the following diagram of the three-block system at the point of instability: JWH 4 Physics I CM

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) = (1/2S)/(3/2S) = 1/3 Θ = tan –1 (1/3) = 18.44degrees Repeat this calculation for the four-block system. Angle of instability (θ) = (1/2S)/(2S)=1/4 Θ = tan –1 (1⁄4)= 14.04degrees How does your result compare to the three-block system? Explain. JWH 5 Physics I q q

The mass distributed on either side of the lines is balanced and distributed equally. 2. What does the point where the three lines intersect represent? Explain why this method works. The point of intersection represents the center of mass. This method works because the weight of the object is all focused on the center of mass, meaning it is all centralized at one point. As gravity is working through this particular point (center of mass), the object will automatically rotate so that the gravity will be along the vertical line as Earth is as well. 3. 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. The third line is not necessary to find the center of mass; this is because center of mass can be found with just two lines. However, with radio triangulation allows the third line to give a much more precise and accurate center of mass. Conclusions Overall, this experiment made it easy to understand and see how the center of mass is obtained, particularly how gravity and mass play a huge role in locating the center of mass. It is evident that the center of mass affects the angle of instability. References JWH 7 Physics I