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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