2D Equilibrium -- Balancing Games - Free Educational videos for Students in K-12 | Lumos Learning

2D Equilibrium -- Balancing Games - Free Educational videos for Students in k-12

2D Equilibrium -- Balancing Games - By MITK12Videos

Transcript
00:12 I got this to balance by carefully measuring equal distances
00:15 and hanging equal weights at those distances . This balance
00:22 is called equilibrium equilibrium is when the state of the
00:24 system isn't changing . In this case the to the
00:27 equilibrium case , the state of the system is a
00:30 position of these objects which still isn't changing unless I
00:35 throw a coin in to knock it out of equilibrium
00:37 . In other types of equilibrium , the state of
00:39 the system could be its temperature or pressure or something
00:43 else entirely . But now I'll focus on two to
00:45 equilibrium the balance state where the positions don't change something's
00:51 balance in the middle and these things tend to be
00:53 symmetrical . Other things balance off to one side ,
00:56 always the heavier side . What if I want to
01:00 move this cup different distance away from the middle and
01:03 still keep it all balanced . One way of doing
01:08 this is moving the other cup to the new distance
01:11 as well . Sure enough it balances again . But
01:16 there's another way of doing this . I could have
01:18 left the right hand cup at the old position and
01:21 has taken out some of its weight . This also
01:24 balances so we found two different ways of balancing the
01:27 same thing . We can either change the weight or
01:30 change the distance in equilibrium . Where we have forces
01:35 F . One and F . Two balancing each other
01:38 at distances D . One and D . Two .
01:40 The counterclockwise force times distance must equal the clockwise force
01:45 times distance , force times . Distance has a special
01:49 name , torque from the latin word to twist In
01:53 two . D , equilibrium clockwise and counterclockwise torques are
01:56 balanced . Before I calculate some torques I need to
02:00 check some of the masses . The massive five coins
02:04 is 13 g And the mass of the cup plus
02:08 a string is also 13 grands . And since we're
02:12 on Earth , this means that they both have the
02:14 same weight , which I'll call . W . Started
02:17 off with weights to W . One cup plus five
02:20 coin hung on each side distance , all call D
02:24 . From the middle and I got it balanced and
02:27 the torques two times W . Times D . Are
02:29 equal on both sides and it balances . But when
02:33 I moved the distance to one half D . And
02:36 kept the weight at two W . five coins ,
02:39 pulls a cup , there were two ways that I
02:41 could balance it . I could either move the other
02:44 cop closer to one half tea or I could keep
02:49 the other cup at D . And just empty of
02:52 the five coins . So now it's weight is only
02:55 W . This leaves the counter clockwise torque one half
03:00 D . Times to W . Equal to the clockwise
03:03 torque D . Times W . But what if we
03:06 move the left Hand Cup farther from the middle to
03:09 two D . And leave its way at two W
03:14 . One way of balancing it is to move the
03:17 right hand cupped farther out as well . Or we
03:21 can move the right hand cut back to D .
03:24 And increase its weight for W . Let's check that
03:27 this would make the torques workout . On the left
03:30 hand side we have two D . Times to W
03:33 , which is 40 W . And on the right
03:35 hand side we have D . Time is four W
03:38 . Which is also 40 W . How many coins
03:42 we need in the cup for that ? One cup
03:45 is one W . And so we need three more
03:48 w . So that's 15 coins . So four W
03:53 . Is equal to one cup plus three more W
03:56 . Which we get with 15 coins . I'll move
04:00 the cup to a distance d from the middle and
04:03 add a total of 15 coins , The weight of
04:06 four W . Sure enough it balances because in equilibrium
04:11 the counter clockwise torque has to equal the clockwise torque
00:0-1 .
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