Sticky Situation

This one's stolen from Guesstimation.

In the second Spider-man movie Spidey stops a six car subway train by attaching his webs to it and pulling it to a stop in 10 or 20 blocks.

How much force does he need to do this?

Food for Thought

Let's answer this in three parts. How much energy does the average American consume, how much does that cost, how much does each calorie cost and how much energy would the Flash need.

There's a number of ways we could estimate how much one person spends per month for food. You could say that you eat out every meal (3 times a day) at some fast food joint for $10 a meal. That kind of life style has a monthly bill of 30 * 3 * 10=$1000 per month. I think that's high at $30 per day. What about $1 per day? At that price food would only cost you $365 each year. Ya right. So the easy numbers between $1 and $30 are about $10 per day or $3 per day. Let's be nice to Wally and say $3 per day or about $100 per month.

So we've guessed it can costs about $3 a day to eat (I know it seems low). Now we must guess how many calories you consume a day and so find the cost of every calorie.

How many calories do you eat per day? Maybe you know this maybe you don't. If not, maybe you know how many calories are in a McDonald's Value Meal (1167 cal) or in a can of coke (200 cal) or in a steak (500 cal). Therefore, you eat more than 1000 cal and probably not 10,000 cal. So then we guess the geometric mean which is 10^{7/2} = 3000 cal per day. So let's convert from calories to Joules (there's 4200 Joules in every calorie). 3000 cal/day * 4000 J/cal = 12 * 10^6 J/day. A physicist like Ray Plamer or Reed Richards would be happier if we turned this to Watts. Watts are Joules per second. So as a side note the power usage of a human being is 12 * 10^6 J/day * day/24hr * hr/60min * min/60sec = 150 W. Oh good - more power than a lightbulb.

So anyway that was a sidequest. The important thing is that a person consumes 3000 cal or 10^7 J everyday. Plus spends $3 a day for that food. That means that $1 will buy you 1000 cal or 4 * 10^6 J.

Next we have to estimate how much energy the Flash needs. Let's guess that most of his energy goes to running (that way if our answer is small compared to a normal person we can add the energy of a normal person to it or if our answer is big compared to a normal person we know that it is insignificant). The energy of him running is kinetic. We already used the equation for kinetic energy KE = 0.5 * m * v^2. If we allow for fictitious elimination of frictitous forces then if we can guess his speed, we will know the energy needed to get him to that speed. He needs that much energy every time he runs to that speed. Remember we are guessing for an average day, not at his fastest nor his slowest.

The speed of light (3 * 10^6m/s)?. %1 the speed of light? The speed of sound (300 m/s)? The speed of thought (only about 100m/s since it depends transport mechanisms of ions crossing membranes)?

Let's guess that he goes 10 times the speed of sound for an average run. The energy he needs to reach that speed is KE = 0.5 *m * v^2 = 0.5 * 100kg * (10 * 300m/s)^2= 0.5 * 100 * 9 * 10^6J=5 * 10^8J.

Since he needs that much energy every time he gets to those speeds we need to ask how often does he go that fast? We are talking about a cocky jock with a fairly large rogue gallery. So let's say he goes more and once a day but less than 100 times a day. The geometric mean: 10 times.

Then the energy the Flash needs for running in a day is 5 * 10^9J. At a price of $1 for every 4 * 10^6 J, the Flash must spend 5 * 10^9J / (4 * 10^6 J/$1) = $10^3 = $1000 more per day than muggles.

We said that a single person could eat for $100 per month and based on that the Flash's monthly grocery bill is $30,000. That's more than some of use make in a year! Notice that if we had said that Wally ate out for every meal his bill would be 10 times greater. A bright supervillain interested in discovering the Scarlet Speedster's secret identity might begin by looking for abnormally large grocery bills.

Like a Bat Out of Hell

I happened to be in the western part of Canada this weekend and thought it would be really cool to do some bouldering in the rockies. I'm here for a really quick trip and so climbing was just going to be something I squeezed in as I drove into the eastern part of the mountains. I packed my shoes and everything seemed to be going really well. The guy I was going with was excited, the people I'm travelling with didn't care if we stopped for a bit and the weather was beautiful. Near the town of Coalman we spotted what looked like a great face. We pulled over, changed and started hiking. We just arrived at the site when suddenly a huge dark cloud lumbered over the mountain. It didn't waste anytime looming. It came fast and hard. We got stuck in a hail storm and didn't get any climbing done. The rain didn't let up until we were out of the mountains again. It was too bad. I don't know when I'll be back there.

The Cost of Being Super

How big is the Flash's grocery bill?

For this superheroic Fermi Question you'd might like to know that every Calorie that you eat has about 4200 Joules of energy. Also guessing how fast he goes is tough. Consider average days for the Flash and think to yourself that he's much faster than the speed of sound but not any where near as fast as the speed of light. (Just an average day. That's all I'm saying.)

Skeletal

How heavy is he without his skeleton? I'm about 70 kg. Logan's pretty buff. Maybe say 100 kg.

How much of that is bone? 1%? Nah. 100%? 30%? 10%? Ya, 10% seems like the best answer. 10% of 100kg is 10kg. So that's 10 kg of bone and 90 kg of other stuff in your body.

Well, let's guess that bone and muscle and everything inside of us is all the same density. This is really not so bad of a guess because nothing inside of us is as heavy as rocks or as light as air. We pretty much have the same density as water.

The density of water is 1 kg/L = 1000 kg/m^3. So then 10kg of bone has a volume of about 10 kg / 1000 kg/m^3 = 10^{-2} m^3.

If that normal skeleton is removed and replaced with an adamantium one. If we can guess the density of adamantium then we can multiply it to the volume of a skeleton that we just found and we will know the mass which we can then ad to the 90 kg of left over non-skeletal stuff.

What's the density of adamantium? Well it's got to be heavier than water. 100 times heavier? No way. 10 times heavier seems like a good guess which says it has a density of 10 * 1000 kg/m^3 = 10^4 kg/m^3. Another way we could find this is we could look up the densities of some metals and notice that tungsten is pretty heavy at 19.25 g/cm^3 and that iron and silver and all of those are all pretty close at 7.9 or 10.5 g/cm^3 which are both 10 g/cm^3 = 10^4 kg/m^3 as far as we are concerned.

So using this density we find that the mass of an adamantium skeleton is about 10^{-2} m^3 * 10^4 kg/m^3 = 100 kg. So now with his new shiny skeleton Dark Claw or Wolverine weighs 100 kg + 90 kg = 200 kg or about twice as much. This isn't a shockingly high value. A person had an adamantium skeleton wouldn't sink in and leave foot prints in concrete or be too heavy to use the elevator.