You are either not logged in or not registered with our community. Click here to register.
 
December 06, 2016, 06:25:53 AM

Welcome, Guest. Please login or register.
Did you miss your activation email?

Login with username, password and session length

Click here if you are having problems.
Default Wide Screen Beige Lilac Rainbow Black & Blue October Send us your theme!

Hark!  The Herald!
Holiday Issue 2016

Wiki Blogs Dicebot

Author Topic: Stupid physics question -- for science!  (Read 235 times)

0 Members and 1 Guest are viewing this topic.

Offline RemielTopic starter

Stupid physics question -- for science!
« on: March 27, 2015, 12:45:01 PM »
Okay, it's been way too long since I was in college, and I have a stupid physics question. 

I have a choker/necklace.  It is made out of many interconnected loops of metal (tin, aluminum, or some like of iron alloy I assume, but that is irrelevant).

I also have a table, the corner of which is, unsurprisingly, square.  That is to say, it is a typical 90-degree angle.   If I wrap the choker around the corner of the table (figure 2), I have observed that 100% of the time, gravity pulls the choker off the corner of the table.  My question is--why?


I understand why the choker falls off if I drape it over the edge of the table (see figure 1).   If the force of gravity on the length of choker that is hanging off the table (let us call this distance x) is greater than the frictional force of the length of the choker still on the surface of the table (let us call this distance (l - x)), it falls off, according to Coulomb's Law:

Fg > Fn
or
mgx > mg(l - x,

essentially becoming
x > (l - x.


where m is the mass per unit length of the choker, x is the length of the choker that is hanging from the table edge, and l is the total length of the choker.

What I don't understand is why the choker falls off the corner in figure 2.  The force of gravity on the section of the choker underneath the table should be equal to the normal force on the section on the top of the table, right?




Offline Oniya

  • StoreHouse of Useless Trivia
  • Oracle
  • Carnite
  • *
  • Join Date: Sep 2008
  • Location: Just bouncing through. Hi! City of Roses, Pennsylvania
  • Gender: Female
  • One bad Motokifuka. Also cute and FLUFFY!
  • My Role Play Preferences
  • View My Rolls
  • Referrals: 3
Re: Stupid physics question -- for science!
« Reply #1 on: March 27, 2015, 12:51:10 PM »
The section that gravity is acting on includes the two vertical segments.

Offline RemielTopic starter

Re: Stupid physics question -- for science!
« Reply #2 on: March 27, 2015, 01:06:33 PM »
Indeed.  But let's assume a really thin table (assume a spherical cow) so that the thickness of the table is negligible compared to the length of the choker.

Offline Oniya

  • StoreHouse of Useless Trivia
  • Oracle
  • Carnite
  • *
  • Join Date: Sep 2008
  • Location: Just bouncing through. Hi! City of Roses, Pennsylvania
  • Gender: Female
  • One bad Motokifuka. Also cute and FLUFFY!
  • My Role Play Preferences
  • View My Rolls
  • Referrals: 3
Re: Stupid physics question -- for science!
« Reply #3 on: March 27, 2015, 01:28:26 PM »
My point was specifically that the two vertical segments provide the extra mass that draws the choker off the edge of the table, as this is where the concrete differs (rather significantly) from the theoretical.

Offline Joel

Re: Stupid physics question -- for science!
« Reply #4 on: March 27, 2015, 02:46:42 PM »
is the table perfectly level too?

Offline RemielTopic starter

Re: Stupid physics question -- for science!
« Reply #5 on: March 27, 2015, 04:12:40 PM »
is the table perfectly level too?

Yes.


Offline RemielTopic starter

Re: Stupid physics question -- for science!
« Reply #6 on: March 27, 2015, 04:17:29 PM »
My point was specifically that the two vertical segments provide the extra mass that draws the choker off the edge of the table, as this is where the concrete differs (rather significantly) from the theoretical.

I do not believe this makes a difference.  I have tried the same experiment with the corner of a clipboard with exactly the same result.  No matter how tightly I "pull" the choker over the corner, it instantly falls off the moment I let go.

Online Sain

Re: Stupid physics question -- for science!
« Reply #7 on: March 27, 2015, 05:21:41 PM »
It's easier to approach the problem by letting a single string hang from the table at an angle similar to what one loop of the choker would be at in your 2nd image.

Solution (Just words but I hope it's understandable)
It's then pretty straightforward to see from the forces that the string is not at an equilibrium (at least in this case where friction is trivial). The string tries to get to a position where the angle between its hanging part and the one on the table is straight. Since this can never happen in 2nd picture with 2 sides hanging (and even added mass looping below) the choker keeps moving towards the edge until it falls.

Offline Kythia

  • Noooo-one Fights like Kythia no-one bites like Kythia
  • Dame
  • Enchanter
  • *
  • Join Date: Oct 2012
  • Gender: Female
  • No one chain smokes Marlboro lights like Kythia
  • My Role Play Preferences
  • View My Rolls
  • Referrals: 1
Re: Stupid physics question -- for science!
« Reply #8 on: March 27, 2015, 06:47:57 PM »
Yeah, Sain's on the money there.  Given that friction from the table is negligible, the weight of the bottom section is pulling the portion of the choker that is against the table edge "inwards" which is causing it to slip alongside the table until the hanging weight is enough to pull it loose.  Let me try to MS Paint this:



Hopefully that makes sense.  The bottom part of the choker is pulling "inwards" on the two vertical parts, the friction from the table is insufficient to hold them back, the hang part gets longer and longer as the "width" of the encirclement decreases, bam - choker on the floor.

Offline RemielTopic starter

Re: Stupid physics question -- for science!
« Reply #9 on: March 27, 2015, 07:40:01 PM »
Yeah, you guys are correct.  I forgot to take into account the angle between the edge of the table and the line of the choker -- there is a force component that is perpendicular to direction of the choker (in the direction of the table edge) that pulls both "sides" in the direction of the corner.

Knew it had to be something like that.

Offline RemielTopic starter

Re: Stupid physics question -- for science!
« Reply #10 on: March 27, 2015, 07:57:34 PM »
Or, to put it another way, imagine draping the same choker around the end of a ruler, and then holding the ruler aloft.   In this case, all forces are in equilibrium (the gravitational force pulling the choker down equals the normal force of the ruler pushing it up) and the choker goes nowhere.

But in my problem, there is nothing preventing the slide of each side of the choker toward the corner, other than the frictional force, which is based on the frictional coefficient of the material(s) used.  This is why you might, for example, stretch a rubber band successfully in the same position, but a string will fall immediately.