Recently, I watched small dominoes toppling over, until they push over a massive one. However, I am slightly confused why this doesn't violate conservation of energy. Consider supplying some amount of energy to a small domino, eventually when it topples over the large domino, that large domino can do significantly more work, and should have more energy. This clearly cannot violate the laws of physics. So what is wrong with my logic?
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Every domino has potential energy (from being put upright) that is used (converted to kinetic) when it falls. A finger pushing a small one gets added energy from each increasing domino's potential energy, which only needs enough to tip over the next. Each gets slowed down on the way to the ground a bit, from having the next in its way. So it doesn't whack the ground as hard as it would if there wasn't another domino in the way. That's available energy to push over the next.
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Energy should always be considered between two points in time with a fixed reference point. So, first, let's consider before any pushing has occurred and all the dominoes are standing up in order of height, with a reference point of our table: the only energy in the system is gravitational potential energy - mgh for each block. That h measures from the center of mass of the domino, so about halfway up each domino.
Now right as the first block falls, some of that gravitational potential energy is converted to kinetic energy. As it hits the next domino, the kinetic energy gets transferred to that domino, knocking it over. This continues to the next block.
Now let's consider a moment right before the first domino hits the table. The dominoes are laying almost flat, so they still have a very small amount of gravitational potential energy (mgh), but the h is much smaller because the center of mass is closer to the table. The rest of the energy went into the kinetic energy of the biggest block (and in the real world, heat from friction/impacts). It is that kinetic energy that can be converted to work, but it is perfectly equal to the potential energy lost by the dominos falling down. The "standing up" state is a higher energy state than the "fallen down" state, so going from standing up to fallen down frees up energy which can be used for work.
You can also think of it in reverse: it takes work to set up the dominoes again, which means energy is being stored in some way as you set them up.
tl;dr: The dominoes standing up have gravitational energy which is able to be freed up when they fall.
18th Shard
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There is no paradox at all. With a small activation energy it is possible to initiate a process that releases a lot of energy that was stored in a metastable state. Combustion is an example: with a small initial spark, it is possible to start a process that releases much more energy.
Dominoes are no different! The potential gravitational energy is quite high when the bricks are vertical but this is also a metastable state (there is a lower gravitational potential energy state that is more stable, when they are flat on the ground).
To understand activation energy and metastable states think about a boulder that is only marginally stable on the top of a mountain: you touch it (activation) and it falls, gaining much more kinetic energy than the one provided by your touch. Again, the total energy (mechanical + internal) of the "system plus its surroundings" is conserved at all stages.
Quillo
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A small domino should be more massive than the larger domino . Otherwise the initial energy applied to it should enough to push other dominos and eventually it will stop due to loss of energy So ther's no violation
