Cool science trick...your kids can do...

[Catalpha]

Just now, Ellen said:

An easier way to understand why the arrangement is static is to think about energy. The arrangement will be static if it is in a minimum of energy. Addition of the two toothpicks to the rope/bottle arrangement introduces a geometric constraint that makes this arrangement a minimum of energy.

I don't know if you are familiar with the concept of virtual work, but basically, to analyze if a situation is at an energy minimum, we presume we move the assembly as allowed by its geometry by a very small distance, and see if energy is increased or decreased. If energy increases for all possible movements, then we are at an energy minimum and have static equilibrium.

First, consider the initial configuration, with only 1 toothpick, the rope and the bottle. If the bottle goes down. energy is reduced. Since the toothpick is completely free to rotate about the table, the bottle can go down, and we are not at equilibrium.

In the second situation, the two additional toothpicks add a constraint. If the "original" toothpick is rotated a bit, the bottle will go up, as the new "vertical" toothpick would force the new horizontal toothpick, in the rope, to move towards the table. Since we are pivoting about the table, this horizontal movement has to be along an arc and the horizontal movement has to be accompanied by a vertical movement in the up direction, which will raise the bottle a bit. This movement is therefore not allowed to occur spontaneously.

Note that this requires enough friction with the table. If there is no friction, a combination sliding/rotating movement is allowed and the arrangement is not stable. This is related in forces term to the fact that there must be an horizontal friction between the vertical toothpick and the original table-supported toothpick, as the "vertical" toothpick is not completely vertical.

 

Reference:

Physics stack exchange

😁😁😁

Calculate the moment of inertia at the point of intersection of the three toothpicks, that clockwise moment of the three toothpicks will balance the anti-clock wise moment created by the friction from the weight of the bottle. Since the moment of inertia is balanced, the system is stable. 

[Catalpha]

1 minute ago, Nimmakai said:

maths enter iye varaku physics/chemistry anni  interesting gane untai.. once maths enter.. sheep dies

Engineering mechanics was a prerequisite for my biomechanics class, I topped the class in EM, my score was in the 90s, the second highest was in the 50s. They still curved it so people wouldn't fail, lol. 

[Nimmakai]

3 minutes ago, Catalpha said:

Engineering mechanics was a prerequisite for my biomechanics class, I topped the class in EM, my score was in the 90s, the second highest was in the 50s. They still curved it so people wouldn't fail, lol. 

 btech 1 st year Engineering Physics lo na mundhu topper  ammai nunchi copy kottina , me also good marks camed 

[Catalpha]

Just now, Nimmakai said:

 btech 1 st year Engineering Physics lo na mundhu topper  ammai nunchi copy kottina , me also good marks camed 

Physics is for babies. I like biomechanics. 

[Nimmakai]

1 minute ago, Catalpha said:

Physics is for babies. I like biomechanics. 

cc @sheldon_cooper 

[Dippindots]

4 hours ago, Catalpha said:

Engineering mechanics was a prerequisite for my biomechanics class, I topped the class in EM, my score was in the 90s, the second highest was in the 50s. They still curved it so people wouldn't fail, lol. 

nelanti vallu okaru unte chalu class nashanam.

[OreyPandhi]

4 hours ago, Ellen said:

An easier way to understand why the arrangement is static is to think about energy. The arrangement will be static if it is in a minimum of energy. Addition of the two toothpicks to the rope/bottle arrangement introduces a geometric constraint that makes this arrangement a minimum of energy.

I don't know if you are familiar with the concept of virtual work, but basically, to analyze if a situation is at an energy minimum, we presume we move the assembly as allowed by its geometry by a very small distance, and see if energy is increased or decreased. If energy increases for all possible movements, then we are at an energy minimum and have static equilibrium.

First, consider the initial configuration, with only 1 toothpick, the rope and the bottle. If the bottle goes down. energy is reduced. Since the toothpick is completely free to rotate about the table, the bottle can go down, and we are not at equilibrium.

In the second situation, the two additional toothpicks add a constraint. If the "original" toothpick is rotated a bit, the bottle will go up, as the new "vertical" toothpick would force the new horizontal toothpick, in the rope, to move towards the table. Since we are pivoting about the table, this horizontal movement has to be along an arc and the horizontal movement has to be accompanied by a vertical movement in the up direction, which will raise the bottle a bit. This movement is therefore not allowed to occur spontaneously.

Note that this requires enough friction with the table. If there is no friction, a combination sliding/rotating movement is allowed and the arrangement is not stable. This is related in forces term to the fact that there must be an horizontal friction between the vertical toothpick and the original table-supported toothpick, as the "vertical" toothpick is not completely vertical.

 

Bibliography

Physics stack exchange

😁😁😁

Nuvu endhuku na teacher kaledhu😢😢😢😭😭😭😭😭

[OreyPandhi]

4 hours ago, Catalpha said:

Engineering mechanics was a prerequisite for my biomechanics class, I topped the class in EM, my score was in the 90s, the second highest was in the 50s. They still curved it so people wouldn't fail, lol. 

Good job thalli

[OreyPandhi]

4 hours ago, Nimmakai said:

 btech 1 st year Engineering Physics lo na mundhu topper  ammai nunchi copy kottina , me also good marks camed 

A ammayi nene 

[Anais_nin]

8 hours ago, dasari4kntr said:

 

Sacred geometry, pythogaras theorem?

 

[Catalpha]

18 minutes ago, Dippindots said:

nelanti vallu okaru unte chalu class nashanam.

@Arey_enti_ra_idi

[Nimmakai]

20 minutes ago, OreyPandhi said:

Good job thalli

 

5 minutes ago, Catalpha said:

@Arey_enti_ra_idi

 

[Catalpha]

24 minutes ago, Nimmakai said:

 

 

Em matladutunnav

[Catalpha]

49 minutes ago, Anais_nin said:

Sacred geometry, pythogaras theorem?

 

 

5 hours ago, Catalpha said:

Calculate the moment of inertia at the point of intersection of the three toothpicks, that clockwise moment of the three toothpicks will balance the anti-clock wise moment created by the friction from the weight of the bottle. Since the moment of inertia is balanced, the system is stable. 

 

[Anais_nin]

9 minutes ago, Catalpha said: