Physics Question! Is my understanding correct?

[AJvsRonin]

Hi all physics minded folks.

I'm writing a story and one of the characters is an engineer. This is just a scene where the characters are sitting in an SUV talking while they wait. The engineer character (Character 2) is a smart guy, but not some super genius but tends to ponder a lot and put forth weird ideas that seem nonsensical to a lay person.

This idea is loosely based on an idea I had while talking to an engineer friend of mine but she's a civil engineer so wasn't sure of the details.

Here's the conversation:

Character 1: I?m not sure I understand.

Character 2: It?s all just different ways of expressing energy as a value using the laws of thermodynamics. Right now you are being pulled against the seat by gravity. If you weigh around 60 kilograms this is roughly six hundred newtons of force being applied against the seat and floor. One newton is equal to one joule per metre. A joule is roughly the amount of energy required to lift an apple one meter up in the air, and the amount of energy released when the same apple is dropped by a metre. Using a standardised amount of chemical energy in a food, say that soda you?re drinking, we can express the amount of energy in something as a value against that standard. This car weighs about a thousand kilograms, that drink has around eight hundred kilojoules of chemical energy. So divide the first number by the second number and you just drank enough chemical energy to lift this car 8 centimetres into the air, or just over three inches.

Character 1: Awesome. So why can?t I lift a car then?

Character 2: Not my fault, ask a biologist.

END

Now funnily enough I'm a biologist and from what I could find out this is roughly true but I know I haven't taken into account things like acceleration etc.

So, does this work/is it true? For my comfort could you list any qualifications, university degree etc so I can rest comfortably knowing an expert has checked over this? I asked the reel physics guys but they never replied.

Thanks!

 

[Darken12]

I... no. You have some nitpicky mistakes here.

A Joule is a Newton per metre, not the other way around. It's J = N*m.

The potential energy of an object that hasn't yet fallen is weight times gravitational acceleration (normalised at either 9.8 m/s2 or 10 m/s2) times distance from the ground. So in order for the apple analogy to hold, it would have to weigh exactly one tenth of the gravitational acceleration (which we'll round up to 10 m/s2 for ease of calculation). It would have to be a 100 grams apple (or 0.1 kg).

Also, the chemical energy thing doesn't really match up, since the chemical energy is contained within the chemical bounds and can only be released by rupturing them (which, as a biologist, you'll remember happens to glucose during the Krebs cycle). If he wanted to burn enough chemical energy to lift a car, he would release so much energy into his body (which comes with an increase in temperature due to released heat, which is energy that is wasted due to entropy) that he would carbonise himself. Also, lifting takes a lot more into consideration than mere energy, such as the tensile strength of the bones/muscles in charge of doing the lifting, to name one of many factors.

So yeah, the dialogue holds as a layman explanation, but a real physicist would nitpick the hell out of it.

My qualifications are that I'm a biochemist, it's a five-year degree in my country that lets me do scientific research, perform and interpret blood tests and run pretty much any kind of lab I want to. I had 3 different kind of physics classes throughout the years, from basic Newtonian stuff to optics, radiation, electromagnetism, a bit of quantum and a smattering of sound physics too.

Also, it sounds like an interesting novel!

 

[AJvsRonin]

I... no. You have some nitpicky mistakes here.

Thanks for the feedback. I'm actually an ecologist so even my bio-chem is a little lacking.
I'm just considering the energy as raw chemical energy. Not really taking into account the biological limitations, that's what the last line is reference to.
The idea originally began as a thought experiment relating to explosives. If a hand grenade releases x number of newtons, could that not be expressed as y number of Big Macs? Since Big Mac's has a (fairly) standard number of joules.

Being a bio-chemist I'd be interested in your thoughts on a few things.

Also is there any way you can think to phrase this better? Or does the idea simply not hold up?
If I get any usable advice from you I'll make sure to thank you in the blurb if that's alright?

Also, it sounds like an interesting novel!

Actually it's a comic
I'm writing an a friend is doing the art.
Thanks!

 

[Darken12]

Well, the problem with trying to turn explosives/damage into energy is that explosives are more about a sudden chemical chain reaction that ends up with a lot of compressed gas. This compressed gas heats up (due to the gas compression itself) and expands exceedingly fast, colliding with everything in its path. It's a lot like a stampede, if you imagine that each person/animal fleeing is a gas molecule. So the energy would be kinetic, yes, but it would also be hard to quantify as a great amount of it would be turned into useless heat due to entropy and gas compression. So the visual representation of a grenade going off wouldn't be a good estimation of the energy released (since the chemical energy stored turned into unequal parts of kinetic energy and heat).

But yes, that aside, you can measure the energy stored in a grenade in Big Macs, assuming that you take the amount of Joules in a Big Mac as your measurement unit. You also know that the same amount of energy will be released in the ensuing explosion, but not all of it will be kinetic energy.

The comparison does work, admittedly, but a better example would be perhaps using the Big Mac unit along with an example of combustion, since when you completely burn something, all its chemical energy is turned to heat, so the analogy would be much clearer. If burning a mole of propane produces W amount of Joules, and X amount of Jules is a Big Mac, you can say that burning Y grams of propane (a mole of propane is 44.1 grams) equals Z Big Macs. Wikipedia tells me that "When properly combusted, propane produces about 50 MJ/kg. The gross heat of combustion of one normal cubic meter of propane is around 91 megajoules."

If you know the properties of the substances you're playing around with (how many grams of propane are in one cubic metre, how many Joules are produced when you burn a mole of propane, how many Joules are in a Big Mac, how many grams of propane are in a mole, how many cubic metres of propane are in a standard tank of it, and so on), you can do the math yourself and say that a tank of propane, when completely combusted, yields X amount of Big Macs in energy.

So yeah, ask whatever you like and I'll do my best to help you out.

Ooh, comic, that's also pretty cool!

 

[The Selkie]

for the apple analogy to hold, it would have to weigh exactly one tenth of the gravitational acceleration (which we'll round up to 10 m/s2 for ease of calculation). It would have to be a 100 grams apple (or 0.1 kg).

Pretty sure that's a standardised assumption (as that's the exact example used to explain the conept of joules to me years ago).
I'm not a physicist so I could be way off here, but one thing that struck me was:
The equation for energy used to lift something against gravity (assuming g=10 for simplicity) is = MgH (mass x gravity x height)
1000kg x 10 x 0.08m = 800J

Wouldn't that be 0.8kJ? So 800kJ could lift it 1000 times higher i.e 80 metres? I could be wrong here, but I'm not sure where...

 

[Darken12]

Pretty sure that's a standardised assumption (as that's the exact example used to explain the conept of joules to me years ago).
I'm not a physicist so I could be way off here, but one thing that struck me was:
The equation for energy used to lift something against gravity (assuming g=10 for simplicity) is = MgH (mass x gravity x height)
1000kg x 10 x 0.08m = 800J

Wouldn't that be 0.8kJ? So 800kJ could lift it 1000 times higher i.e 80 metres? I could be wrong here, but I'm not sure where...

That equation is for potential energy. It's not exactly meant to indicate the energy you'd need to spend to lift something, but the energy that object will possess at a given height (that energy will later turn into kinetic energy if it falls from that height).

An object that weighs a tonne (1000 kg) would have 800 Jules of potential energy at 8 cm from the ground (0.08 cm). It would also have 800 Jules of kinetic energy if it fell from that height. If you placed that object 10 times higher (at 80 cm from the ground) it would have 10 times as much potential energy.

The energy you have to spend to lift something will always be higher than its potential energy once it reaches that height, because of entropy. Entropy ensures that a (very large) percentage of all energy is wasted as heat, so you'd need a lot more than 800 Joules to lift a one tonne object 8 cm. How much more depends on the method used to lift it and how efficient it is, energy-wise.

EDIT: I'll clarify before a physicist chews me off: technically, potential energy doesn't turn into kinetic energy instantly. In reality, objects possess mechanical energy, which is the sum of their potential and kinetic energy. If an object is at rest, its kinetic energy equals zero, and if it is on the ground, its potential energy equals zero. When an object is falling, its total mechanic energy remains the same, but as it approaches the ground, its potential energy turns into kinetic energy. By the time h = 0, its potential energy is also 0 and all of its mechanical energy is composed of kinetic energy.

 

[The Selkie]

Yep, I'm aware of all that, I was just applying the numbers he used to calculate how high the car would be lifted if all the potential energy was used (and miraculously none was wasted). Very simplistically the change in potential energy is used to calculate the energy needed to lift something vertically, obviously there are a lot of other factors to account for but that's the most basic way I know of for modelling a particle.

From reading his post I assumed he was using such a model. I'm just saying that I think his numbers he used in his example may be off.

 

[AJvsRonin]

-Snip-

Thanks for that.
So the reason I like using the example above (in the script)is that usually when talking to people, when you're discussing the chemical energy in food you think about what you're doing in terms of the amount of exercise required to burn it off.

I remember hearing somewhere that eating a single M&M is to take in roughly the number of joules expended in walking 100m (ignoring energy spent in the digestion process), I doubt this is true as that sounds like a lot.
If you've spent any time around fitness fanatics this is quite often how they view food. My girlfriend is one of them (she'll look at a piece of chocolate and think "If I eat this I have to spend 20 minutes extra on a treadmill" etc) and this is how the whole thing came up and I suggested going one step further and thinking of food in a more interesting dramatic way as a way to get you to choose lower energy foods as a lot of high energy foods have a lot more in them than we think.

The initial idea was: a 1 ton car travelling at 100 km an hour hitting a solid wall and coming to a dead stop would release the kinetic energy equivalent to the chemical energy in x number of big macs. We took guesses and someone thought it would be around a million. After a bit of time trying to work it out the estimate I got was around 15,000. A lot lower than we thought. Though I'm sure I've missed something.

So I'm trying to think of a way to phrase this so it's both correct in terms of physics and keep the gravitas that comes with realising a lot of foods hold more energy in them than we realise.

So any ideas there would be appreciated.

So without going into spoiler territory the underlying concept behind the comic is that a lot of the ability's that are portrayed in comics etc would be more problematic than useful. I'm very much inspired by James Kakalios' "The Physics of Superheroes". Great book, highly recommend.

Take for example a generic "human torch" type character. In order to heat up he would have to consume at least that much in chemical energy to not defy the conservation of energy. The joke being; before getting into a fight everybody is acting all serious and dramatic and he's in the back ground gorging himself on energy drinks and cake knowing he'll need the energy to fight. Also needing to deal with side effects like, sure he can heat up but what about the bacteria in his digestive system? So after fighting he ends up ill for weeks.
Carbonising is an issue I hadn't actually thought of so thanks for that, I don't know much about it though, I'm not sure if I'll have to miracle exemption that out though as it could be a show stopper.

 

[Darken12]

Yep, I'm aware of all that, I was just applying the numbers he used to calculate how high the car would be lifted if all the potential energy was used (and miraculously none was wasted). Very simplistically the change in potential energy is used to calculate the energy needed to lift something vertically, obviously there are a lot of other factors to account for but that's the most basic way I know of for modelling a particle.

From reading his post I assumed he was using such a model. I'm just saying that I think his numbers he used in his example may be off.

Well, I assumed he was running on a model with plenty of wasted energy (as is the norm), which is why I didn't correct the math. 99% of the energy going to waste is pretty standard, actually.

Though now that I look at it, you're right, the waste seems to be of 99.99%, which is actually a bit excessive. Yes, organic life is very inefficient, but not THAT much.

*snip*

Well, firstly, remember that walking isn't running (doesn't require as much exertion), and that 100m = a block (at least where I'm from), so it's not really that big of an energy expenditure.

As for the energy in food thing, you have to keep in mind that we use most of that energy to maintain our inner temperature, since we give off A LOT of heat towards our surroundings (and our core temperature, particularly for some organs, is higher than 37 degrees Celsius), so the seemingly large amount of energy in our food often barely covers what we lose in heat and baseline metabolism every day. I am not really sure that the collision example would be the best, as most of the kinetic energy gets spent deforming the car (and whatever it collided against).

You could use the straightforward application of Joules as Work (work is pretty much just like energy). You could use the example that pushing a one tonne car along a road (assuming no friction) at 2 metres per second would require two thousand Joules (the equation for kinetic energy is one half of mass times squared velocity). If you add a standard coefficient of friction (0.1 is used most often), then you'd need 20.000 Joules instead. If a can of soda has 800 kJ, then assuming your body uses that energy perfectly (and without any unfortunate burninations), you could push a car 400 times heavier, or push the old car 400 faster or on a road that has 400 times more friction.

Does that help?

Oh, I see the point you're trying to make. Well, the thing about carbonisation is that, unless your character has a way to resist the heat he's pouring out, he'll end up burning himself alive. I have no doubt that he could set himself on fire using a very fast metabolism that generates more heat that he can dissipate, but that's actually very harmful for him. The only way I can see it working would be to develop a wax-like skin (made from a waxy component that renders him fireproof) and glands in his hands that exude a highly flammable fluid with a very low self-ignition point. The dude's metabolism goes in hyperdrive, he gets a very strong fever, the flammable fluid in his hands catches fire and he can go around being a firestarter without worrying about burns. Though he will still suffer the effects of a high fever until he cools down. The energy he's spending could also be used to constantly generate more fluid, rather than turning it straight into fire. Also, I'd recommend a bag of glucose on an IV drip instead of the cakes and energy drink. It's a lot more glucose than he can possibly get from the same amount of food, straight to his veins without lengthy digestions.

 

[Redingold]

Well, I'll say that you don't need the laws of thermodynamics to consider energy, except maybe the first one. The value you've got for the energy of the drink is somewhere around the chemical energy in 200g of sugar, which seems excessive, considering the recommended daily allowance of sugar is about 90g. You shouldn't ever say that a thing weighs x kilograms, kilograms are a measurement of mass. Weight is measured in Newtons, just like force. Your value for the height you could potentially achieve is way off, by a factor of 1000, just like The Selkie says, though you have certainly used too much energy because you have too much sugar.

I like the idea, to be honest, and glossing over all the nitpicky details works as a joke about the tendency of physicists to make overly simplistic models (see also the spherical cow approximation).

As for my credentials, I'm in my first year studying theoretical physics at the University of Manchester.

EDIT: Looking it up, I'd say that 372ml of soda contains about 24 grams of sugar and about 100KJ of energy, meaning the height of the car should be 10 metres.

 

[AJvsRonin]

The value you've got for the energy of the drink is somewhere around the chemical energy in 200g of sugar, which seems excessive, considering the recommended daily allowance of sugar is about 90g.

EDIT: Looking it up, I'd say that 372ml of soda contains about 24 grams of sugar and about 100KJ of energy, meaning the height of the car should be 10 metres.

Thanks for the input but I'm not sure where you're getting your numbers from.
The Coca-cola website states that coke has 180Kj per 100ml, * 3.75 for a standard drink can = 675 Kj.

Their drink "Mother - Big Shot" has 242kJ per 100ml, *3.75 = 907.5 Kj so I'm sitting pretty safe on 800.

meaning the height of the car should be 10 metres.

See that sounds absurd. Sure you're not miscalculating? a 1 ton object falling 10 metres is going to hit the ground with a lot of kinetic energy.

But yeah, you've got the idea, he's simplifying the physics (like the famous spherical cow) to make an interesting point.

 

[lechat]

shouldn't you guys be factoring in time if you are going to do the opposite of potential energy since gravity will constantly be pushing down on the object?

 

[Guffe]

I have no idea but that seemed interesting, as did the discussion
You should ask the Real Physics guys for their opinion, althou you have got some answers here already

 

[AJvsRonin]

shouldn't you guys be factoring in time if you are going to do the opposite of potential energy since gravity will constantly be pushing down on the object?

Haha yeah! It was my concern regarding that, that lead me to make this post in the first place but now I've been left even more confused.

 

[fenrizz]

I have nothing to contribute to your question, but you will link the comic to us when it is done, right?

 

[SuperSuperSuperGuy]

Yeah, it's a decent enough rough explanation, for the layman.

A Joule, though, is better described as the work generated when a force of 1 Newton moves an object 1 metre. Calculating work is the force on an object multiplied by the distance the object moves multiplied by the cosine of the angle between them. It gives you an answer with the unit kg(m^2)/(s^2), which is the same as Joules.

Consider this:
The gravitational field intensity around the earth's surface is about 9.8 N/kg, and causes objects to accelerate at about 9.8 m/s^2 downward. If you take this number, and multiply it by the mass of an object, you get the force that the earth is exerting upon that object. Now, judging from your description, you're starting with biochemical energy, with which I am not familiar, and the mass of an object. From here, you can calculate the distance above the ground you can raise this object using the energy provided. In your scenario, it doesn't sound like you're taking gravity into account, and without gravity your thing with the car basically flies out the window, pun intended.

 

[AJvsRonin]

I have nothing to contribute to your question, but you will link the comic to us when it is done, right?

Haha will do, though it's a while away yet, we're still going through concept art.

 

[Redingold]

The value you've got for the energy of the drink is somewhere around the chemical energy in 200g of sugar, which seems excessive, considering the recommended daily allowance of sugar is about 90g.

EDIT: Looking it up, I'd say that 372ml of soda contains about 24 grams of sugar and about 100KJ of energy, meaning the height of the car should be 10 metres.

Thanks for the input but I'm not sure where you're getting your numbers from.
The Coca-cola website states that coke has 180Kj per 100ml, * 3.75 for a standard drink can = 675 Kj.

Their drink "Mother - Big Shot" has 242kJ per 100ml, *3.75 = 907.5 Kj so I'm sitting pretty safe on 800.

meaning the height of the car should be 10 metres.

See that sounds absurd. Sure you're not miscalculating? a 1 ton object falling 10 metres is going to hit the ground with a lot of kinetic energy.

But yeah, you've got the idea, he's simplifying the physics (like the famous spherical cow) to make an interesting point.

I got my numbers from WolframAlpha, for just soda.

http://www.wolframalpha.com/input/?i=soda&a=*C.soda-_*ExpandedFood-&a=*DPClash.ChemicalE.soda-_*SodiumCarbonate.dflt-

I think I mucked up the conversion from calories to joules, which is why my number is off.

That value might sound absurd, but it's easy to confirm. h=E/mg, mg = 10000(ish), E is on the order of 10[sup]5[/sup], 10[sup]5[/sup]/10[sup]4[/sup] = 10, so that is the right order of magnitude.

 

[ClockworkPenguin]

Just being a pedant here, but you can lift a car. That's technically what you're doing when you use a car jack. Or indeed when you push a car up a hill.

And with a sophisticated system of pulleys, it should be more than possible for one guy to properly lift a car.

 

[Dryk]

The only major thing I take issue with(apart from the chemical to mechanical energy efficiency and speed that has already been mentioned) is the fact that just because something contains energy energy to lift a tonne 8cm off the ground doesn't mean it can exert the continuous >9.81kN required to do it