Experiment 5 Statics - lab5

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Apr 3, 2024

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I .I '/ qOnRamps Lab - Mechanics, Heat, and Sound (102M) NAME: )\rl1.m (-fv-d 1 ~f Abstract Experiment 5: Statics We encourage yoL:J to complete this Jab using whatever equipment is available to you; There is no penalty fo'r inaccurate measurements. Your grade is based on your reasoning about data that is collected and the rubric in the Assessment section of this Lab. If you are unable to set up the experil'!lent and analyze data using available equipment, please contact-your HS Instructor. \ ) The goal of this lab is to use the principle of static equilibril:JfnlQJ_ufn a meter stick into a single beam • balance and to determine the mass of an object, which requires averaging several measurements and : calculating the standard uncertainty. There is no procedure given, just some general guidance, so you must decide how to set up your experiment and carry it through, what values to measure, and how many trials are necessary to accomplish the goal. For ·Part 1, Part 2, and Part 3, you must create a sketch and/or a written procedure that another person could easily follow to repeat your experiment. You must record your data an~ then carry out measurement statistics as part of the analysis. Background As students, there is often a struggle to find the balance between the many aspects of your life, like school, extracurricular. activities, etc. In physics, it is typically easier to find a balance, as shown in the Figure 1, because we have a model which describes it! Figure 1. A uniform beam held in static equilibrium by unequal masses at different distances from the pivot point. To achieve such a balance, we need to be in a state called static equilibrium. This state is defined by a model that OpenStax College Physics textbook refers to as the First and Second Conditions for Static Equilibrium, which are ITEXAS 1hcl~ra1t:,i1t.,J.i11 Am,tlD Lab - Mechanics, Heat, and Sound (102M) I 1

--- -- ~OnRamps Lab - Mechanics, Heat, and Sound (102M) NAME: ___________ ____ - l:F= 0 l:t = 0 (LS.1) (LS.2) where F is force and t is torque. The zeros on the right-hand side of each equation are what denote the balance of all the forces and torques, respectively. Recall that the torque due to a force is defined by t' = rFsin9 (LS.3) where r ts the distance from the axis of rotation to where the force is applied, Fis the magnitude of the applied force, and e is the angle between these two variables. Before the advent of the digital age and modern electronics, this model would be used to measure the mass of objects. Devices are shown Figure 2 and Figure 3. Depending on your school's equipment, you may have seen these devices in your classroom. Figure 2. A balance scale with two beams for measuring Figure 3. A beam scale used for a weigh in at the doctor's the mass of objects. office. On each of these balances there is: • a pivot point, which is a point about which the beams will rotate; • two beams with movable masses; and, • in the first case, a circular knob for adjusting the smallest mass increments. To measure the mass of an object, a user moves the masses along each beam, and adjusts the knob until the beam remains level, indicating equal torques on both sides. Because of how the device is calibrated,· the locations of the masses on each beam corresponds to some value of mass on the circular pan. Lab - Mechanics, Heat, and Sound (102M) I 2

~OnRamps Lab - Mechanics, Heat, and Sound (102M) NAME: ______________ _ Materials List Quantity 1 1 11 1 1 1 1 Procedure Items for in-lab Meter Stick Set of hanging masses Ring Stand Electronic scale Roll of string Random object(s) with unknown mass Notes for at-home materials to replace in-lab items. A meter stick is convenient because it is rigid and distances are labeled on it, but alternatively, you may use a rigid, long object, such as a broom stick, golf club or pole, and a separate device to measure distance. A tape measure, ruler, or any item with a known length will work. For example, a piece of printer paper is 11 inches long and can be folded to approximate lengths in between. These masses are used to apply force at a location along the meter stick. Instead of proper hanging masses, you may also use anything with a known mass. For example, • a penny is 2.5 grams • water has a density of 1 gram per milliliter and can be placed in a Styrofoam or paper cup or other light container that will not add much extra weight. You might consider another object with a known mass, either from an internet search (roll of coins, cup of rice, etc.) or an object whose mass is labeled (can of tuna or soda) This is where you'll balance your meter stick. It may also be a rod, such as a ruler or stick, extended over the edge of a table or countertop. This is used to measure the mass of the hanging objects. If you are using an object with a known mass, then you do not need a scale and can determine the mass by searching the internet or inspecting the label. This is used to suspend objects from the meter stick. Yarn, fishing line, or really any lightweight means of attaching an object or mass to the meter stick at a specific location This may be ANY object that you can suspend from the meter stick in order to determine its mass. Tt)e procedure section de~~rJbes.t~e lab activity. Questior}s posetj within this se·ctioh shquld be ad_tjressed: 'in the corresponding space 'on.·: the· ~orksheets ~t -~he end of th i's document. Be sure to record any. thoughts, ~~etches, or data f ri the ~ppr~pria~e ·location~ on the worksheets. • ' < -, t , : t' ;, • • " • ., ' I ,..., • •. . \'o.u sho~lcJ'expect to sp~nd appro~imately 70-90 minutes to complete the ·(nvestigation outlin.ed below. • Use the principle of static equilibrium to turn a meter stick into a single beam balance and determine the mass of one object. ITEXAS 1bc Vni'-"Ui1; ,1 / t.,•u1 a1 An\tfn Lab - Mechanics, Heat, and Sound (102M) I 3

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- ($onRamps Lab - Mechanics, Heat, and Sound (1 Q2M) NAME: _______ ----: ____ _ • This determination should be made by averaging several measurements and determining the standard uncertainty. Other devices for measuring an object's mass should only be used to determine whether your group's experimental results are accurate. • Note that, as you encountered in previous labs, there is not complete guidance on what __ variables to measure and how many measurements to take. It is up to you to determine what measurements to record as part of your investigation. -- "> J;_drt~l: Exploring Static Equilibrium, " - ,>l- .: .... , .... ~,> - All meter sticks are uniform objects that are precisely one meter long, except for those that are not, perhaps due to damage they sustained in the time since they were new. Examine your meter stick and determine the location of its center of mass. Record this position. Use the position you recorded as your pivot point and mount the meter stick on the ring stand at this point. Hang one mass t9 either side and arrange the masses so that the meter stick remains in balance. The masses do not need to have the same mass. Make an annotated sketch of your system with th~ masses present. Record the masses and positions of all objects and determine whether the torques sum to zero. Is this evidence in keeping with the principle of static equilibrium? - . ·, ·, . From this point on, you are free to move the pivot point of the meter stick to any location along its length. In fact, you will have to do this to determine the mass of the meter stick using a static equilibrium model. • By changing the location of the pivot point and using a single mass to achieve static equilibrium, determine the mass of the meter stick. Consider the discussion of mean, standard uncertainty, and confidence intervals in Lab 4. How does that apply to determination of the mass of the meter stick? Is one trial - that is, one measurement - enough? You might consider additional trials using the same mass, or you might use different masses in different trials. Collect enough data to make a reasonable determination of the mass of the meter stick. The term "reasonable" here is intentionally vague because it allow~ you and your group to determine how much data you should collect in order to produce an average and standard uncertainty for the mass of the meter stick. From these, you can determine a 95% confidence interval. • ' Compare your average to the mass of the meter stick as measured by some other device, like an electronic scale. Lab - Mechanics, Heat, and Sound (102M) I 4 Al -

' • \ I ~OnRamps Lab - Mechanics, Heat, and Sound (102M) NAME: ____________ _ Part 3: Do-It-Yourself Balance. .. As a group, select a reasonably-sized object· for which you would like to discover the mass. In choosing a reasonably-sized object, ensure that: 1. The object can be attached to some point of the meter stick without falling off. 2. The object is not easily broken. This is just in case it does fall off the meter stick. Using your meter stick set-up and the available weights, find the mass of this object. The pivot point is free to move, and you may use any arrangement of masses to achieve the necessary equilibrium to determine the mass of each object. Just as you did in Part 2, be sure to record enough data and trials to determine both the average mass and the 95% confidence interval for that average. Compare your average to the mass of the object as measured by some other device, like an electronic scale. Kfll k.0 1h f---VIY\ rv1 k 0 l'V1 t ow i~, t:. (,,11 k 11,t-v l VIV\_ f V,'l ( vlhfv 1 :,; <1? lf'[; l-ev r l __,I Ir ( A { r--t111 • / ff) - -.:'( JJ({/0:f DJtn1 r V\ 1101 IJ 1 (/q" ti--i 1.11 ,~ r verr- I ' , , \ ( ,.J Dq kt1 \ 0 ~IV' ri\ 13-1 ¾ ;,; , z.. ( ,( M \ ,l) q 3 f' :n g A t Vcr1 kv y z_ • r ·- - • I V Vl<P. I /~,/l~r~ / 1 • . (ik:H~l n i (b,11~,J) : 011 (( 1)'101\ F {t1 ~,M , ,pq ?r-1 I -- I - -· \ I . V{ ( f '. 'V)) ( i' ) V ( (,;,j J •. 'Q,) ( J ) . ! -. .. ,,I 1' I\ ) ' ~' • \., iv fsV, h2 ,011f~ k'J It v7 -: I~ o Q l 1 7 l O ( q b IV ITEXAS lbc l'r.i\. ,wr ,'If T-1.L, 1t1 A,,~un z~( J 1 r"'r1 ~~fr1.1 H ~,lt [l1ci V-t'Jl Lab - Mechanics, Heat, and So_und (102M) I 5 p if [ftlf qr,; e rYof : l, p r1 ti-'" 1 r vt : , t o t 1c 1 1

qOnRamps . Heat and sound (1 o2N\\ Lab_ Mechanics, ' NAME: __________ _ Assessment . .. . h essrnent of Post- This section summarizes information regarding t e ass d Lab 5. The worksheets for this lab should be scanned or photographed an upload~d a_s part 9f ~he post-lap assignment in the college Ca_nvas course. Th.e P~~t-Lab , · s worth: .100 points, distributed as follows: ,\, ,\ ': ' ., . .. " - 40 pt~ for Canvas-bas'ed Post-Lab questions, and , 60pts for parts ot' the worksheets ass~ssed using the rubrics . . , .. that,will be uploaded. '•\ Please make sure you are familiar with each scientific ability that we are looking for, and check that your work addresses them. Each will be assessed out of 20 points for a total of 60 points for Part 2: Meter Stick Mass and Part 3: Do-it-yourself Balance. r----. ---· ···--- ---7 ! Scientific Ability Communicates the set-up of the experiment, using words and pictures as needed Repeats measurements Communicates findings of the experiment completely and clearly. Adequate (20 points) The experimental set-up is described thoroughly and clearly. There are sufficient measurements of all parameters for the same set of conditions. Clearly and accurately describes what happens in the experiments. (.- ;, Needs some" • improvement {14 points) The experimental set-up is described, but with minor omissions or vague details. There are measurements for the same set of conditions, but the number is insufficient. The description of the findings is communicated, but incomplete or inaccurate in places. The experimental set-up is described, but important details are missing. The findings are discussed, but vaguely or with major inaccuracies or omissions. No experimental set-up is described or illustrated. There are no repeated measurements for the same set of conditions. No discussion of the findings is present. Lab - Mechanics, Heat, and Sound (102M) I 6

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