Experiment #10 Bio-Physics Pre-lab Comments, Thoughts and Suggestions

Transcription

1 Expeient #10 Bio-Physics Pe-lab Coents, Thoughts and Suggestions The pupose of this pape is to povide you with soe infoation which ay be useful fo solving the pe-lab questions and pefoing the lab. I will attept to help you undestand the physics behind the syste we will be using to easue the bio-echanical foces/toques and give you a few equations which ay assist in solving pobles. ** Disclaie: This hint is not to be copied, in whole o in pat, unless a pope efeence is ade as to the souce. (It is stongly ecoended that you use this docuent only to geneate ideas, o as a efeence to explain coplex physics necessay fo copletion of you wok.) Copying of the contents of this web site and tuning in the ateial as oiginal ateial is plagiais and will esult in seious consequences as deteined by you instucto. These consequences ay include a failing gade fo the paticula pe-lab/lab o a failing gade fo the entie seeste, at the discetion of you instucto. ** 1) Let s say you had to ove the Eath with a leve. You could use the Moon as a pivot point. Calculate how long of a leve you would need. It will be gigantic! This is the classic see-saw poble. Hee is ou geneal setup of the see-saw: We have the Eath on one side of the see-saw, the Moon is ou pivot point, and soe ando nedy guy on the othe side of the see-saw (since this is a physics poble, we need the nedy guy). ** Note that we ae assuing the weight of the bea to be negligible. ** Woohoo! igue 1: Setup of the Poble Move the Eath with a Leve ** Note that the Eath, Moon, Sun and Head of the Goofy Physics Guy ae not to scale. That is, the oon ay actually be salle then shown. **

2 o the sake of aguent, let s say that this expeient is being pefoed on the sun. (I ean coe on we e aleady oving the Eath why not?!?! We have to do this since we need soe efeence fae with a ass to povide acceleation due to gavity. Typically we have the Eath whee the acceleation due to gavity is g = 9.81 /s 2 ; howeve, since we e oving the Eath, it doesn t ake uch sense to have the Eath ON the Eath. That would equie two Eaths that s eally deep philosophy. ) We ll call the acceleation due to gavity on the sun, g sun. If we daw in the vaious foces and distances, we get the following setup: igue 2: Expeiental Setup on Sola Refeence ae Soe paaetes which ay be useful fo solving this poble wee given: oce due to Mass of the Eath and Acceleation due to Gavity on the Sun (N) Distance to the Moon (k) oce due to Mass of Soe Goofy Physics Guy and Acceleation due to Gavity on the Sun (N) 5.86 x What we ae fist tying to find is what is the iniu length that ust be fo the Moon in ode to stat to ove the Eath. That is, we want the toque ceated by to be geate then the toque ceated by the Eath. Eath We know the definition of agnitude of the toque is given by: sin

3 We e going to assue that the angles between the foces and the leve s ae all nealy 90 degees, because that akes the ath A LOT EASIER. (They ay in actuality be like degees, but that s close enough to 90 degees.) Thus: sin 90 o Eath Eath Eath and Exaining the oiginal inequality: Eath Eath Thus, the iniu distance ust be away fo the oon is: Eath Eath Plugging in the values to see what you coe up with. The convesion facto fo kiloetes to light-yeas is: 1 ly k Now, don t foget to answe the actual question: How long of a leve you would need? The total length of the leve will be the length of the Eath s adial and s adial sued togethe. Leve Length Eath 2) Use the following paaetes and the expeiental setup to calculate values fo given that: (c) (c) (c) (g) (g)

4 igue 3: Expeiental Setup of a Bicep Suppoting a Massive Load In the setup above, thee ae thee toques (ecall that a toque is foce acting at a adial ): 1. [ ] = The ass hanging (foce) at the end of the length (adial ). 2. [ ] = The holding (foce) the length staight (adial ). 3. [ ] = The ass of the length itself hanging (foce) at the cente of ass (adial ). o static equilibiu (whee nothing is otating/oving) the net su of the toques acting on the syste ust add up to zeo. (Reebe we use the geek lette tao fo toque.) n i1 i 0 So, fo ou syste, we have thee toques; so, fo static equilibiu, we ust have: 3 i1 i o this expeient, we will always foce (no pun intended) the to be level (again no pun intended). That is, we want the to be pefectly paallel hoizontally with the table. This will geatly siplify the calculation fo the toques due to the and the. If we explicitly wite out each of the thee toques: Toque 1 (due to ): ist, ecall the definition of toque:

5 To find the diection of the toque, we need to use the ight-hand ule. ist point you finges in the diection of then cul the to the diection of. The diection you thub points is the diection of the toque fo the coss poduct. o this case, is pointing to the ight (so point you pointe-to-pinky finges in the ight diection), and is pointing down (keeping you finges in the ight diection, twist you hand (pal down) so when you bend you finges they ae pointing down. You thub should be pointing away fo you. This eans that the diection of the otation is clockwise (nod you hand up and down while keeping you thub pointing away fo you and you ll see that the diection fo you knuckles to you finge tips is in the clockwise diection) and the sign of the toque is negative). ** Aside ** I can neve eebe the ighty-tighty, lefty-loosy thing y Dad taught e fo scews, especially when I on by back. When I want to know which way I want the scew to go, I siply use the diection of toque (because that s exactly what I doing). If I want the scew to go away fo e, I point y thub in that diection and see that the otation diection fo y knuckles to y finge tips is in the clockwise diection. If I want the scew to go towad e, I point y thub in that diection and see that the otation diection fo y knuckles to y finge tips is in the counte-clockwise diection. ** End Aside ** By the ight-hand ule: sin And since the angle (by design) between the foce and the leve is 90 degees: Toque 2 (due to ): To find the diection of this toque, is pointing to the ight (so point you pointe-topinky finges in the ight diection), and is pointing leftish-up (keeping you finges in the ight diection, twist you hand (pal up) so when you bend you finges they ae pointing backwads. You thub should be pointing towad you. This eans that the diection of the otation is counte-clockwise (nod you hand up and down while keeping you thub pointing towad you and you ll see that the diection fo you knuckles to you finge tips is in the counte-clockwise diection) and the sign of the toque is positive). By the ight-hand ule:

6 sin Toque 3 (due to ): To find the diection of this toque, is pointing to the ight (so point you pointe-topinky finges in the ight diection), and is pointing down (keeping you finges in the ight diection, twist you hand (pal down) so when you bend you finges they ae pointing down. You thub should be pointing away fo you. This eans that the diection of the otation is clockwise and the sign of the toque is negative). By the ight-hand ule: sin And since the angle (by design) between the foce and the leve is 90 degees: Binging it all togethe: Now, if we add each of these up and set thei su equal to zeo, we have the static equilibiu equation: 3 i1 i 0 sin 0 sin Solve this fo the foce acting on the. 0 g sin sin g g sin g We ae given the distances and the asses, and we know the acceleation due to gavity; so, fo any give theta we can calculate the foce on the. (c) (c) (c) (g) (g)

7 ist though, don t foget to convet all the distances to etes and all the asses to kilogas! The following is not in the pe-lab but is a question posed in the lab! Acoss you shoulde thee is a uscle called the (you have two one on each shoulde). It is called the due to its shape. It looks like the geek capital lette delta Δ. When you ae standing with you elaxed (hanging vetically) you uscle does not get tied; but if you you e holding you out hoizontally, you uscle is contacted and afte a long tie gets quite fatigued. (Thee is actually an execise to execise the with fee weights.) igue 4: Location and Position of the Deltoid Muscles Let s exaine a foce diaga of the uppe - uscle syste in both states, and see if we can descibe the foce exeted on the when it contacts. In both states we ae consideing a state of equilibiu. This eans: The su of all the toques ust be equal to zeo. n i1 i 0 We will conside each of these ules and thei application to deteining the foce acting on the.

8 State 1: Standing with you A Relaxed: igue 5: Opeational oces acting on the Deltoid in a Relaxed (Extension) State All otational acceleation (α) ust be equal to zeo: n i1 i 0 In the diaga above, we can see that both the foce on the and the foce due to gavity acting on the lie along the sae line though the pivot point. This eans that the distance fo the pivot point to the foce fo both cases is zeo. 0 N 0 0 N g g 0 0 N 0 N 0 N By inspection, we can see that the foce on the and the foce due to gavity acting on the should be equal and opposite. That is to say, that fo the static case (see lab 7): n i1 i 0 g 0 g

9 State 2: Holding you A Outstetched: igue 6: Opeational oces acting on the Deltoid in a Outstetched (lexion) State All otational acceleation (α) ust be equal to zeo: n i1 i 0 In the diaga above, we can see that both the foce on the and the foce due to gavity acting on the lie at diffeent lengths fo the pivot point. This eans that since thee is a distance fo the pivot point to the foce, fo both cases thee will be a toque. Toque 1 (due to ): To find the diection of this toque, is pointing to the left (so point you pointe-topinky finges in the left diection), and is pointing up (keeping you finges in the left diection, twist you hand (pal up) so when you bend you finges they ae pointing up. You thub should be pointing away fo you. This eans that the diection of the otation is clockwise (nod you hand up and down while keeping you thub pointing away fo you and you ll see that the diection fo you knuckles to you finge tips is in the clockwise diection) and the sign of the toque is negative). By the ight-hand ule: sin 1 ** Note that since the angle between the foce and the leve is 90 degees, the sine te went to 1. ** Toque 2 (due to ):

10 To find the diection of this toque, is pointing to the left (so point you pointe-topinky finges in the left diection), and is pointing down (keeping you finges in the left diection, twist you hand (pal down) so when you bend you finges they ae pointing down. You thub should be pointing towad you. This eans that the diection of the otation is counte-clockwise and the sign of the toque is positive). By the ight-hand ule: g g g sin 1 ** Note that since the angle between the foce and the leve is 90 degees, the sine te went to 1. ** Binging it all togethe: Now, if we add each of these up and set thei su equal to zeo, we have the static equilibiu equation: 2 i1 i 0 0 Solve this fo the foce acting on the. g Copaison of the foces on the when the is hanging vetically and outstetched hoizontally: Let s copae the two states and see which is the lage of the two. g (Vetical) (Hoizontal) g o nueical puposes, let s assign soe geneic nubes: o the hanging vetically: () () (kg)

11 g s o the outstetched hoizontally: kg N 2, Vet N kg 9.81 s g N, Hoz Thus, you can see that the foce acting on the in the hoizontal position is uch lage (2.5 ties lage to be exact) then the foce acting on the in the vetical position. This is obviously due to the toque acting about the pivot point. Hold you s staight out hoizontally and see how long you can handle the pessue. o e it takes a few seconds then I can stat to feel the foce acting on y. If you e oe buff then I, then it ay take a little longe, but you ll eventually feel it. Notice that the woan in the figues was holding a fee weight. We did not include that in ou calculation, but it could easily be done. The fee weight is in essence ceating a hanging ass ( ass) siila to poble 2 above. Notice that in both the hoizontal and vetical states of the that the foce would be inceased if the ass of the inceased so even just holding a biefcase by you side is woking you! That s y kind of execise! N igue 7: Execise of the Deltoid due to Caying a Beifcase