10 Torque. Lab. What You Need To Know: Physics 211 Lab

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1 b Lab 10 Toque What You Need To Know: F (a) F F Angula Systems Evey lab up to this point has dealt with objects moving in the linea system. In othe wods, objects moving in a staight line. Now we ae going to deal with the angula system in which objects otate. Evey idea in the linea system will have an analogous idea in the angula system. Fo example, in the linea system we have velocity (which we now specify as linea velocity). Linea velocity tells you how fa an object tavels in a staight line evey second (in units of m/s). In the angula system we have angula velocity which tells you how many times an object otates evey second (in units of evolutions/s). Thee ae many othe concepts we could discuss but today s lab is just going to focus on one of these and that is toque. (b) FIGURE 1 Foces acting on an object Foce and Newton s 2 nd Law Befoe we get to toque, let s jump back a bit and eview some ideas in the linea system. You should know by now that a foce is a push o a pull on an object. Moe specifically, if you apply a single foce, F, to an object it will move in a staight line. See Figue 1a. Accoding to Newton s 2 nd Law, (ΣF = ma, net foce equals mass times acceleation) the object has to acceleate. This is so because if thee is only one foce acting on an object then thee must be a net foce and theefoe an acceleation. If thee ae two foces acting on an object then the object might o might not acceleate. If the two foces ae equal but pointing in opposite diections then they cancel out and the net foce is zeo and the object will not acceleate. See Figue 1b. Toque Now let s look at the same ideas but in the angula system. The analogous idea of foce in the angula system is called toque. A toque is a foce that makes an object want to otate. Think of it as a otational foce. The equation fo toque is witten as T FIGURE 2 Rope acting on a pulley τ = F τ is the toque on an object (in Newton-metes, N m) F is the foce acting on an object (in Newtons, N) is a distance [explained below] (in metes, m) Many people think that,, stands fo adius but that is not always the case. This can lead to much confusion on toques. It is much bette to think of,, as the distance fom a chosen efeence point to the point at which the foce, F, is acting. (That s how it s defined anyway.) Let s say you have a pulley with a ope wapped aound it. You pull on the ope which gives the ope a tension, T. See Figue 2. In this case the chosen efeence point is the cente of the pulley. It was chosen thee because that is the point at which the pulley is otating. (Moe on this late.) Notice how the distance,, is shown; fom the efeence point to whee the tension is acting. (And yes, in this case that distance does tun out to be the adius of the pulley.) 10-1

2 (a) + T Anothe thing you have to emembe is that when you plug in fo F and they have to be pependicula to each othe. See Figue 3a. If they ae not pependicula then you have to eithe find a component of F that is pependicula to o vice vesa. In this lab we will only deal with F s and s that ae aleady pependicula. So, this idea will be left up to you instucto in you lectue to delve into. Net Toque The equation fo Newton s 2 nd Law in the angula system is vey simila in fom to the one fo the linea system. T (b) T FIGURE 3 Toques acting on an object Στ = Iα Στ is the net toque on an object (in Newton-metes, N m) I is the moment of inetia on an object (in kg m 2 ) α is angula acceleation of an object (in adians/s 2 ) All of the vaiables ae analogous to each othe; foce and toque, mass and moment of inetia, and linea acceleation and angula acceleation. You simply switch out one fo the othe. The ideas wok out the same as well. In Figue 3a thee is one toque acting on the system (in this case, τ = T). If you apply a single toque to an object it will otate. And accoding to Newton s 2 nd Law fo the angula system, the object has to angulaly acceleate. This is so because if thee is only one toque acting on an object then thee must be a net toque and theefoe an angula acceleation. This is the same idea discussed fo the linea system on the pevious page. If thee ae two toques acting on an object then the object might o might not angulaly acceleate. If the two toques ae equal but pointing in opposite diections then they cancel out and the net toque is zeo and the object will not acceleate. See Figue 3b. (Again, same idea as befoe.) Just like in the linea system in which we have to choose a linea diection as positive, we also have to choose a otational diection as positive. That will be eithe clockwise o counteclockwise. In Figue 3b let s call clockwise positive (as shown). Now we can say that the tension in the ope on the ight is causing a toque in the clockwise diection (positive) and theefoe tying to make the pulley otate that way. The tension in the ope on the left is causing a toque in the counteclockwise diection (negative) and theefoe tying to make the pulley otate that way. These two toques cancel each othe out and the pulley does not otate at all. Cente Of Mass In the past, when dawing fee-body diagams, you pobably have been just abitaily dawing in a weight vecto at any paticula location. In dealing with toque we can see that the location of the foce is impotant. So, now you have to be moe caeful in which place you daw you weight vecto. You should be dawing it at the cente of mass of you object. The cente of mass of an object is defined as the aveage location of the total mass of the object. Huh? Ok if you took the entie mass of you object and compessed it down to a single point you object would still act as though the mass wee spead out befoe you compessed. That point is the cente of mass. Double huh? Let s discuss an example 10-2

3 Let s say we have a mete stick. Its mass is unifomly distibuted thoughout itself so we would say that its cente of mass is at the exact cente of the mete stick. This is whee we would place the weight vecto of the object. See Figue 4a. Now, let s say that we slap on a hunk of heavy, sticky goo on one end of the mete stick. The mass of ou combined object is no longe unifom. Thee is now moe mass on the ight side of the object. So, its cente of mass would be shifted to the ight (the aveage location of its total mass). See Figue 4b. W W (a) (b) FIGURE 4 Centes of Mass fo mete sticks GOO In today s lab you will be dealing with a mete stick whose mass is not unifomly distibuted. They have been alteed specifically fo this lab. So, one of the fist things that you will have to do is find the cente of mass of the mete stick. The Equipment The most basic pat of the lab is the fulcum and mete stick. See Figue 5. The fulcum is mounted to a block of wood and is used as a pivot point fo the mete stick. Thee ae also thee clamps on you table. Two of them have swinging hanges on them, one doesn t. See Figue 6. You can attach clamps to the mete stick to eithe hold the mete stick up at the pivot point on the fulcum o you can use them to hang exta masses. See Figue 5. CLAMP WITH SCREW POINTING UP CLAMP WITH SCREW POINTING DOWN CLAMP MASS HANGER PIVOT POINT METER STICK MEASURING EDGE FULCRUM EXTRA MASS SWINGING HANGER FIGURE 6 - Clamp FIGURE 5 - Possible Lab Setup When you use these clamps you will be taking measuements fom them on thei location. Use the edge on the clamp that is shown in Figue 6. You should also have two mass hanges as well as a set of masses that you set on the platfom of the hange. See Figue 5. What You Need To Do: Pat 1 - Cente Of Mass In ode to find all the toques on an object, you have to include the toque due to the weight of the object. Depending on the efeence point that you choose, the weight of the object might have a toque. The location at which 10-3

4 the weight of the object acts is at the cente of mass of the object. So, the fist thing we ae going to do is the find the cente of mass of the mete stick. NOTE: On the last page of the lab thee is a chat that you can use to fill in you data. Detach it and use it as the fist page of you lab epot. You can answe questions on this sheet too. Use you own loose leaf pape if you need moe oom fo answes and calculations. A) Slide the clamp without the swinging hange onto the mete stick until it gets to about the cente of the stick. NOTE: Make sue the scew on the clamp is pointing down and that the metic side is facing you. B) Place the mete stick on the fulcum with the clamp ight at the pivot point. See Figue 5. Adjust the location of the clamp back and foth until the stick emains elatively hoizontal. C) Once the stick is balanced, ecod the location of the clamp. This is the location of the cente of mass of the mete stick. You will be using the value thoughout the lab. Notice that, befoe the clamp was at the cente of mass, the stick otated about the fulcum. That means that thee must have been a net toque on the stick. The weight of the stick was acting at a distance,, away fom the fulcum and thus was causing a net toque (i.e. the stick otated). Once you placed the clamp ight at the cente of mass, the weight of the stick was acting at the fulcum. That means that = 0 and thee would not be a toque (i.e. the stick emained hoizontal). Pat 2 - Single Toque Leave the clamp at the cente of mass of the stick and keep this setup on the fulcum. A) While holding the mete stick hoizontal, slide a clamp with a swinging hange to about the 80 cm mak. B) Release the mete stick. Descibe what happens and also explain why in tems of what has been discussed so fa. C) While holding the mete stick hoizontal, emove the clamp at 80 cm and place it on the othe side of the stick at 20 cm. D) Release the mete stick. Descibe what happens and also explain why in tems of what has been discussed so fa. Fo each of the instances above, in adding the clamp to one side of the stick we added a net toque to the system. This caused the stick to otate. One way caused a clockwise toque, the othe way caused a counteclockwise toque. Pat 3 - Net Toque So fa thee has only been one toque acting on the ule. Now you will be dealing with a system that has multiple toques acting on it. 10 4

5 A) Using the digital scales in the back of the lab, find the mass of each hange assembly which includes the clamp, the swinging hange, and the mass hange. See Figue 5 & 6. Do not assume that each assembly has the same oveall mass. Find both sepaately. B) While the mete stick is balanced at its cente of mass, place one hange assembly at 20 cm on the stick. NOTE: Have the scew on the clamp pointing upwads fo any clamp with a swinging hange. It s easie to adjust that way. See Figue 5. C) Holding the mete stick hoizontal, take the othe hange assembly and slide it on the stick fom the ight hand side until the stick emains hoizontal when you let it go. Question 1 How many foces ae acting on the mete stick? Daw a diagam of the mete stick showing each foce vecto acting on it. Place each vecto in the appoximately coect location as well. Question 2 How many toques ae acting on the mete stick? Why is this numbe diffeent than the numbe you wote fo the answe to Question 1? Question 3 In what diections ae the toques acting (Counteclockwise o Clockwise)? Question 4 What is the net toque acting on the mete stick? How do you know this by looking at the mete stick? D) Calculate the weight of each mass assembly. (Make sue you ae using units of kilogams fo mass.) Put these values in the chat in the ow labeled Pat 3, unde the columns labeled as F. NOTE: In the chat thee ae exta columns fo toques that you might not use depending on which pat of the lab you ae woking. This is left ambiguous in ode fo YOU to detemine how many toque you have, eithe clockwise o counteclockwise. E) Measue the distance,, (in metes) fo each toque. Remembe, is defined as the distance fom you chosen efeence point (in this case, the fulcum) out to whee you foce is acting. Place these values in the chat. F) Calculate the toques, τ, and put these values in the chat. Also, put these values in fo the total toques since thee is only one toque pe side. Calculate a pecent diffeence between these totals. If you got a value geate that 5% then you ae doing something wong. Go back and check you data. Pat 4 - C of M as Toque Fo this section you will be moving the fulcum away fom the cente of mass. This will cause the weight of the mete stick to have a toque. A) Go to the back of the lab oom and measue the mass of the mete stick WITHOUT the fulcum clamp on it. Reattach the clamp and place it at 60 cm. 10-5

6 B) Put the mete stick back on the fulcum. Add an exta mass of 100 g to one of the hange assemblies. Place the hange assembly at a point on the mete stick so that it is balanced. Question 5 How did you know whee to place the hange to balance the stick? Explain in detail using toques. C) Daw a diagam of the mete stick showing each foce vecto acting on it. Place each vecto in the appoximately coect location as well. Descibe the toques acting on the stick. D) Calculate the weights that ae causing the toques on the stick and place these values in the appopiate places in the ow labeled Pat 4. Make sue you now include the 100 g mass fo the hange assembly. E) Measue the distance,, fo each toque. Place these values in the chat. F) Calculate you toques and total toque. Calculate a pecent diffeence between you total toque values. If you got a value geate that 5% then you ae doing something wong. Go back and check you data. Pat 5 - Multiple Toques on a Side Remove the hange assembly cuently on the mete stick. Keep the fulcum at 60 cm. A) Add an exta mass of 200 g to one of the hange assemblies and place it at 90 cm. B) Add an exta mass of 100 g to the othe hange assembly and place it on the mete stick to balance the system. C) Daw a diagam of the mete stick showing each foce vecto acting on it. Place each vecto in the appoximately coect location as well. Descibe the toques acting on the stick. D) Calculate the weights fo each toque acting on the stick and place these values in the appopiate places in the ow labeled Pat 5. E) Measue the distance,, fo each toque. Place these values in the chat. F) Calculate you toques and total toque. Calculate a pecent diffeence between you total toque values. If you got a value geate that 5% then you ae doing something wong. Go back and check you data. Pat 6 - Mixin It Up Remove all hange assemblies. A) Place the fulcum at 75 cm. B) Take one hange assembly and place it at 84 cm. C) Take the othe hange assembly and add 20 g to it. 10-6

7 D) By eithe adding mass (NOTE: add no moe than 150 g) to the fist hange assembly AND/OR adjusting the location of the second hange assembly, balance the system. (You can place the second hange anywhee on the mete stick.) E) Daw a diagam of the mete stick showing each foce vecto acting on it. Place each vecto in the appoximately coect location as well. Descibe the toques acting on the stick. F) Appopiately fill out the ow labeled Pat 6 in you chat as you have been. Pat 7 Calculating Tension So fa the only toques you ve been dealing with have been caused by weights. Now, a tension is going to cause a toque. A) Open the file FORCE PROBE. Push the CONNECT button on the exta window that opens. With nothing hanging fom the foce senso, push the button to the left of the COLLECT button to zeo the senso. B) Place the fulcum at 20 cm. C) On the table thee is a piece of sting with one end tied in a big loop and the othe in a small loop. Slide the big loop aound the ule until it is at 70 cm. Have the small loop hang on the hook on the Foce Senso which is hanging fom a stand. Adjust the height of the Foce Senso until the mete stick is hoizontal. See Figue 8. FULCRUM FORCE SENSOR HOOK LOOPED STRING FIGURE 8 - Lab Setup fo Tension D) Take one hange assembly and place it at 8 cm. Put an exta mass of 150 g on the mass hange. E) Take the othe hange assembly and place it at 83 cm. Put an exta mass of 100 g on the mass hange. F) Daw a diagam of the mete stick showing each foce vecto acting on it. Place each vecto in the appoximately coect location as well. Descibe the toques acting on the stick. 10-7

8 G) So fa you have been veifying that the clockwise toques equal the counteclockwise toques. Based on this idea, make an equation that will allow you to calculate the tension in the sting. Make sue you use units of kilogams and metes so that you will get Newtons fo tension. Calculate the tension. H) On the sceen thee will be a small window that tells you the tension in the sting. Recod this value. I) Calculate a pecent diffeence between the compute value and you calculated value. If you got a value geate that 5% then you ae doing something wong. Go back and check you data and calculations. J) Remove all clamps fom the mete stick. Thanks! What You Need To Tun In: Wite you lab epot using the next page as the font sheet. Use you own pape fo addition pages. Make sue you show you wok fo each section in the coesponding section in you epot. Answe all of the questions by Michael J. Dubuque 10-8

9 Lab Repot Name P a t Counteclockwise Toques Clockwise Toques 1 st Toque 2 nd Toque Total 1 st Toque 2 nd Toque F τ F τ Toque F τ F τ Total Toque % Diff