When small input energy equals to massive output?

[John Harmonic]

Let us say you were on a bridge about 1km long and 150m wide made out of concrete and some kind of metal framework. If the bridge was suddenly about to break for whatever reason, structural problem maybe, and so if you were to simply tap on the bridge then it will all break apart and fall into a sea of water that it is under.

You tap the bridge and so it breaks into many pieces and falls into the sea of water below it. My question is, is energy input from a simple tap equal to the amount of energy released from the breaking of the bridge? If so how so?

[Sensei]

(simplified classical) potential energy of object at height dh, above the ground level, is given by formula:

[math]E=m g \Delta h [/math]

 

Your inputs are: what is mass of bridge structure (m).. ? what is dh (distance between road level, and water level)... ?

Edited September 28, 2018 by Sensei

[mistermack]

The world is full of such examples. As above, you are just releasing energy that is stored. Sometimes a huge amount of stored energy can be released by a tiny initial movement. A gun for example. The energy is stored chemically in the gunpowder in the shell. A tiny pull on the trigger releases stored energy in the cocked spring mechanism. That in turn sets off the charge in the ammunition, which propels the bullet. It's all about releasing stored energy. 

An extreme example would be an earthquake. The Earth's plate bends like a spring, across a vast area, storing up a gigantic amount of energy. Eventually, one tiny crack leads to the whole system snapping back like a spring, and the whole planet shakes. 

But like Sensei said, the bridge example is the release of potential energy, stored by the position of a very heavy mass in a gravitational field. It's a bit like a huge boulder finely balanced at the top of a mountain. A butterfly comes along, and lands on it, and as it's just on the point of rolling, that's all it takes. As it rolls down hill, the potential energy it possesses, due to it's position at the top of the mountain gets converted to kinetic energy and heat, as it rolls and bounces and speeds up.

 

[John Cuthber]

When a spark lights a forest fire the huge energy released is that stored by the trees absorbing energy from the Sun when they grew.

[studiot]

6 hours ago, John Harmonic said:

You tap the bridge and so it breaks into many pieces and falls into the sea of water below it. My question is, is energy input from a simple tap equal to the amount of energy released from the breaking of the bridge? If so how so?

 

No is the simple answer.

 

A better answer is that the energy of the tap is called activation energy.

Activation energy is often required for (energy releasing) events to proceed.

https://www.google.co.uk/search?source=hp&ei=Pd-tW_aRC5KZgQbnk4nQDQ&q=activation+energy&oq=activation+energy&gs_l=psy-ab.3..0i131k1l2j0l8.984.5582.0.7010.17.13.0.4.4.0.266.1786.1j9j2.12.0....0...1c.1.64.psy-ab..1.16.1918....0.QGu9yNXcKhA

[jajrussel]

On 9/27/2018 at 9:19 PM, John Harmonic said:

Let us say you were on a bridge about 1km long and 150m wide made out of concrete and some kind of metal framework. If the bridge was suddenly about to break for whatever reason, structural problem maybe, and so if you were to simply tap on the bridge then it will all break apart and fall into a sea of water that it is under.

You tap the bridge and so it breaks into many pieces and falls into the sea of water below it. My question is, is energy input from a simple tap equal to the amount of energy released from the breaking of the bridge? If so how so?

Are you applying Newton's third law to the thought, or are you implying that Newton missed the obvious? A rain drop hits the bridge, it collapses. A similar raindrop hits your car windshield while you are driving down the road. Your wiper quickly wipes it and a slew of others away. Your car doesn't even show down. The car is moving, the rain drop is moving. The bridge is sitting still when the moving raindrop hits it. Why didn't the car get smashed to smithereens?

I'm assuming that I'm allowed to tap the bridge with a raindrop, and yes it is possibly true that when the raindrop hits your windshield the car might slow down just a little.

It kinda reminds me of a Michener book where a mouse moves a mountain by digging a hole. It really was a good book once you got past the mouse digging a hole changing the whole geography of an area. My memory is terrible anymore, so I am not sure which book it was, but it was a work of historical fiction which Mitchener seemed to favor.

It might very well be true that there is enough energy in a raindrop to equal the energy created by a falling bridge, but I assume you are talking about the energy exchanged during the tap. I may be wrong, but it seems to me that Newton's third law would suggest that assuming that the light tap being equal to the energy realised by the collapsing bridge would require a work of science fiction, or at the minimum totally ignoring Newton, which I have often wanted to do myself.

I'm guessing that anything more than equal is an excess which exist for some reason other than the light tap, and should not be implied to the light tap.

 

Edited October 3, 2018 by jajrussel

[DrP]

10 minutes ago, jajrussel said:

It might very well be true that there is enough energy in a raindrop to equal the energy created by a falling bridge, but I assume you are talking about the energy exchanged during the tap.

As Studiot and others said already - the light tap provides an activation for the release of the potential energy in the system. Of course the tap doesn't have the same energy as what is released by the falling bridge.

[studiot]

57 minutes ago, DrP said:

As Studiot and others said already - the light tap provides an activation for the release of the potential energy in the system. Of course the tap doesn't have the same energy as what is released by the falling bridge.

I hope we are not getting into revenge red marking wars.

+1 to cancel.

[DrP]

Yea - he downvoted my last 8 posts regardless of content - I don't really care, but thanks for the +1 compensation.  

[John Harmonic]

No that is not me sorry for misunderstanding. 

But a possibility exists that it may be me.

[DrP]

Just now, John Harmonic said:

No that is not me sorry for misunderstanding. 

But a possibility exists that it may be me.

I thought it might be you as Alex K. I thought you might be disgruntled because I said snakes can't talk, lol.

I swear my old landlady's cat said hello to me once...   and used my Christian name, lol.  "Hellllo Ben' - it was very high pitched but it took me back a bit I tell you. I don't drink as much now as I did back then.

 

[swansont]

!

Moderator Note

Back to the topic of discussion, please.

And, just so everyone is aware, staff can tell who gave out reputation, and if we think you are abusing the system, we will take action.

 

[jajrussel]

3 hours ago, DrP said:

As Studiot and others said already - the light tap provides an activation for the release of the potential energy in the system. Of course the tap doesn't have the same energy as what is released by the falling bridge.

Actually, I was just trying to be funny while staying in topic.  But, I am curious as to why Newton's third law would be skipped right over when the original post didn't seem to be about activation energy, but more so seemed to imply that under certain conditions the third law doesn't apply, like when a light tap causes a bridge to fall, all the while being asked in complete innocence...

[DrP]

17 minutes ago, jajrussel said:

Actually, I was just trying to be funny while staying in topic.  But, I am curious as to why Newton's third law would be skipped right over when the original post didn't seem to be about activation energy, but more so seemed to imply that under certain conditions the third law doesn't apply, like when a light tap causes a bridge to fall, all the while being asked in complete innocence...

He is ignoring/overlooking the potential energy in the system....  so to answer his question:-

 

On ‎28‎/‎09‎/‎2018 at 2:19 AM, John Harmonic said:

 My question is, is energy input from a simple tap equal to the amount of energy released from the breaking of the bridge?

No.

[studiot]

1 hour ago, jajrussel said:

Actually, I was just trying to be funny while staying in topic.  But, I am curious as to why Newton's third law would be skipped right over when the original post didn't seem to be about activation energy, but more so seemed to imply that under certain conditions the third law doesn't apply, like when a light tap causes a bridge to fall, all the while being asked in complete innocence...

 

Newton's third Law is about Force.

The OP was about Energy.

 

There is a difference.

And yes the bridge will impart a light tap to the hammer, in accordance with N3.

 

An interesting question is how does a light tap shatter a bridge?

 

Well it's easier to consider a sheet of ice on a pond on a cold day, when a suitable light tap will shatter the ice.
If the bridge was built of unsuitable steel so that a cold day could conceivably take the whole structure below its brittle transition temperature then a light tap could indeed shatter the bridge.

But the light tap would also be the activation energy necessary to initiate self sustaining crack propagation., just as applying a match to a pile of paper is the activation energy to initiate self sustaining combustion.

 

 

[jajrussel]

1 hour ago, studiot said:

 

Newton's third Law is about Force.

The OP was about Energy.

 

There is a difference.

And yes the bridge will impart a light tap to the hammer, in accordance with N3.

 

An interesting question is how does a light tap shatter a bridge?

 

Well it's easier to consider a sheet of ice on a pond on a cold day, when a suitable light tap will shatter the ice.
If the bridge was built of unsuitable steel so that a cold day could conceivably take the whole structure below its brittle transition temperature then a light tap could indeed shatter the bridge.

But the light tap would also be the activation energy necessary to initiate self sustaining crack propagation., just as applying a match to a pile of paper is the activation energy to initiate self sustaining combustion.

 

 

So, you are saying that it is energy that that knocks the bridge down in the OP? Kind of like a water pump spark initiating an explosive demonstration in a basement partially filled with propane from a leaking cylinder when someone flushes the toilet?

If you lower the temperature of the bridge sufficiently does the light tap create a spark or is the created heat by the tap sufficient for spontaneous seperation? Actually, respectfully, I'm having trouble envisioning this frozen metal bridge simply falling down when tapped. My mind keeps seeing the bridge at least partially reinforced by the heat created by the tap, or completely disintegrating, but maybe I am allowing the ambient temperature to be a little too cold in my imagination.

Okay, setting my somewhat wayward imagination aside, you really do mean that the light tap is energy rather than an applied force? Or, have I misunderstood what you have written?

I have noted that one of his other questions is about energy, so my apologies if I misunderstood the original post of this thread.

Edited October 3, 2018 by jajrussel

[jajrussel]

So you are saying the light tap contains the minimum amount of energy needed to cause the reaction, which in this case is the bridge falling down...

Edited October 3, 2018 by jajrussel

[mistermack]

The OP makes it clear that the bridge is on the point of collapse. In that case it might well just take a tiny input to push it over the brink. It's the straw that breaks the camel's back. It's a hypothetical example. In real life, a gust of wind would contain far more energy than a tap with a hammer, so it's not likely that any bridge would reach such a finely-balanced state. 

[studiot]

9 minutes ago, mistermack said:

The OP makes it clear that the bridge is on the point of collapse. In that case it might well just take a tiny input to push it over the brink. It's the straw that breaks the camel's back. It's a hypothetical example. In real life, a gust of wind would contain far more energy than a tap with a hammer, so it's not likely that any bridge would reach such a finely-balanced state. 

Most of what you said in you first post was spot on, although you didn't answer the specific question in the OP.

However taking your point and moving on to this post, straws and camels' backs are the wrong analogy. That is Catastrpophe Theory (Thom).

That is not the case here for the bridge. The tap is the activation energy as I have been discussing.

Though equally it would be unusual for a bridge to be in such a finely-balanced state as you note. (Unlike my ice example)

 

1 hour ago, jajrussel said:

So you are saying the light tap contains the minimum amount of energy needed to cause the reaction, which in this case is the bridge falling down...

Yes, although I would avoid the use of the word reaction to avoid confusion with Newton's third Law.

In the (your) other thread I promised more detial here.

Look at the following diagram.

Judging by your Avatar you hail from the High North so consider you are in a kitchen with a round mixing bowl and a blueberry.

So in Fig 1 the bowl is upside down and the bluberry on the top.

Pretty well any disturbance, including that butterfly, will set it rolling off.
The further it moves the faster it goes and it never returns to its original postiion.

This is because there are two principal drivers for matherial processes in the universe.

The tendency to minimise stored energy and the tendency to maximise entropy.
We will only deal with stored or potential energy here.

The blueberry has stored gravitational potential energy and as it falls it releases some of that energy - in this case to end up as kinetic energy as it goes faster and faster.

This is called unstable equilibrium. The blueberry is in balance but the slightest of disturbances will upset that balance for ever.

 

Now look at Fig 2

The bowl is the right way up and the blueberry is in the bottom of the bowl.

You can (hopefully) see that in order to move the blueberry anywhere you have to move it uphill.

So it needs to gain potential energy for this and will try to roll back to release that if it can.

This is called stable quilibrium -  after a displacement the blueberry will try to return to its original poition.

 

Finally in Fig3 replace the bowl with a bowl from a food mixer that has a bottom/base rim to engage the mixer stand.
Again turn it upside down and put the blueberry on top.
This time the upstanding rim retains the berry.
So in order for the berry to fall it must be lifted over this rim.

The energy to do this is called the activation energy and it is much smaller than the energy released when the berry fall to the table top.
This energy must come from somewhere and is equivalent to the tap on the bridge or my sheet of ice.
The amount of activation energy is fixed for a given situation - it is not a variable.

Being lodged against the rim is called metastable equilibrium, because the berry is balanced or lodged but will remain there until the activation energy is supplied.

 

Back to the bridge and the ice.

If a solid is cold enough to be brittle then the energy to create from new surface, when that solid cracks, is less than the potential energy in the bonds released by doing so ( cracking breaks the bonds releasing the bond energy).

So once the crack has started, enough energy is released to keep it going.
But energy has to be supplied to create the first segment of crack.
Enter Mr Activation Energy (could that be a new E-Drink ?)

 

[jajrussel]

Examples?

Unstable equilibrium combined with activation energy - When I was younger with a bold stride I stepped out onto what looked like snow melt running down a blacktoped path to a parking lot. It was a rather long path so I had plenty of time to figure out that it was black ice and I had been a little too bold with that first step. There was also a car that appeared headed for the same parking lot. Luckily the car turned into an adjacent parking lot so all I really had to worry about was stopping before I slammed into or slid under a parked car. There is not a whole lot you can do while lying on your back in what seemed a lot like free fall, but hope that it doesn't hurt when it happens. Once again I got lucky because the parking lot had been salted so I came to a stop between two cars near the middle. Which would be roughly, stable equilibrium.

Metastable equilibrium would resemble me slowly working my way down to and or up from to the parking lot from then on. I had no intention of ever doing it again, nor did I realise at the time that I was experiencing a lesson in physics that I could later remember and fall back on. Pun sort of intended.  thank you for the explanation...

[mistermack]

The biggest example I can think of of this is the collapse of a star. As the fuel gets spent, the energy keeping the star from collapsing under gravity gets lower and lower. The star loses energy at a phenomenal rate, so the critical point wouldn't last long. But eventually, the loss of some photons pushes the star over the edge, and you get a Supernova explosion. 

In a way, it's quite similar to the bridge, because while the bridge might look stable and unchanging, just before collapse, in reality there would be a continuous process of weakening going on, due to wind, corrosion and traffic. So once it got close to collapse, it would be a non-reversible process, without massive intervention.

[MigL]

Stored potential energy does not depend on any other factors other than height and mass.
The bridge is supported/elevated, i.e. at height, so, if it loses its support, there is a huge exchange of potential energy for kinetic, i.e. it drops to the ground. With the resulting large energy exchange when it hits the ground.
The raindrop is purely incidental.
You would get the same result with no input of energy.
Just step off the roof of a building.
you'll still make quite an impact when you hit the ground.