IAMA physicist/author. Ask me to calculate anything. (part 2)

how fast does a 622x25mm bicycle tire have to go to aquaplane?

Wow...starting off with the hard ones. Surface tension is one of my weaker physics areas, but I'll give it a shot...

EDIT: This one's going to take me a bit longer. Will reply later.

EDIT 2: This took way longer than expected. I looked up a reference for stone skipping (which I expect has similar physics) and pulled an equation from there. Assuming a mass of 1.5 kg wheel, I get about 10 m/s (~22 mph).

Thank you, happy2x. That was a challenge.

if the pacific ocean was a bathtub, how long would it take to be empty after the plug is pulled?

Assuming a normal bath tub size plug or 3 square inches. The pressure at the bottom of the ocean is about 16,000 psi. Using Bernoulli's equation, the flow rate would be 330 m/s (roughly the speed of sound in air.) This gives a flow rate of about 0.6 m^3/s. Given the total volume of the Pacific Ocean (about 660,000,000 km^3), it would take 10 billion years assuming constant velocity. Since the pressure would decrease as the water level fell, it would actually take significantly longer.

A block mass, m, is pushed up against a spring with a spring constant, k, until the spring has been compressed at a distance, x, from equilibrium. What is the work done on the block by the spring?

I'm pretty sure this is one of my students. If so, then, dude, seriously? I have office hours. If not, the...

Work = ForceDistance = -kx² / 2

How much wood could a wood chuck chuck if the wood in question was chucked at a constant velocity of 2 meters/second?

Woodchucks have a lifespan of about 5 years. At 2 m/s, a woodchuck would chuck about 300,000 km of wood in that time frame.

How many farts would it take to propel a person 200 feet into the air?!?

SHAMELESS BOOK PLUG ALERT I did similar calculation in my book, Ballparking: Practical Math for Impractical Sports Questions.

Assuming they have the same density of air (1.2 kg/m^3), a volume of 10 cm^3, and come out in 1 second with a speed of 1 m/s, the net upward force up would be about 0.01 N. That's enough force to lift 0.002 pounds. To lift myself up, I'd need a net force capable of sustaining 180 pounds. This means I'd need to continuously sustain about 90,000 farts to propel myself upward.

Hi Dr. Santos,

Let's say I snagged an umbilical cord from a newborn and slurped its pluripotent stem cells down like it was a freezepop to harness their youth-giving powers: is there an optimal number to drink that will maximize my chances of eternal youth, or at least becoming moderately more attractive, relative to the stigma of being "that guy"? Asking for a friend.

OldManJank, I'm not sure there's any amount of stem cells you can drink to harness youth giving powers. First, I think your question is based off faulty science. Stem cells, when eaten, do not lead to eternal youth. Second, being known as "Pluripotent Stem Cell Eating Guy", while possibly leading to an interesting story at parties, would come with a stigma that clearly outweighs any amount of good looking-ness you might gain.

To answer your question more succinctly, I think the "Chances of Eternal Youth" function is pretty flat with a maximum around zero.

Hello dr Santos,

Suppose I had a rifled firearm, say an M1 Garand and I attached the butt firmly to the back wall of the inner part of a washing machine, so that when I turn the washing machine on, the rifle spins around its axis (we'll remove the door of the washing machine for this experiment). Then how fast would the washing machine have to spin in the opposite direction of the rifling so that the bullet comes out without spinning, as if fired from a smoothbore?

Wow...I had to look up several things for this problem. (Did not know what rifling was, but now I learned something.)

Based off some pictures of the M1 Garand, its barrel appears to be not quite a meter long. You get a rough idea of how the bullet twists by looking down the barrel of a rifled firearm. (I do not recommend actually doing this. See: Canseco, Jose.) From this it looks like the bullet makes about one complete turn while its in the barrel. Traveling at about 2800 ft/s, it would rotate at about 50,000 rpm. Spinning the washing machine at this rate in the opposite direction should stop the rotation of the bullet.

I have a tater tot with the following properties:

• it is the mass of earth
• its shape and dimensions have no restrictions (i.e., if it's a cylinder, d doesn't have to be approximately equal to h, as normal tater tots are)
• it is solid (i.e., non-porous)

How many ants (your choice of species) would it take to eat the whole thing in a single day?

I have tater tot with the following properties:

• it is the mass of earth
• it has expected dimensions (i.e., it's a cylinder, and d is approximately equal to h)
• it has expected porosity

Given the number and type of ants from the previous result, how much of it would the ants be able to eat, factoring in travel time and crowding?

Thanks, and good luck!

This question made me smile. (Homer Simpson voice) Mmm...tator tots.

According to at least one source, ants eat about 1 milligram of food per day. A tater tot this size would weigh about 610³⁰ milligrams. If have a long skinny tater tot (so that the ants have equal access to its mouth watering goodness), it would take 610³⁰ ants lined up much like horses at a trough.

If we assume the normal dimensions of an equivalently sized tater tot, not all ants will have equal access. Some will have to wait their turn. Assuming the tot is the same size as the Earth, we can fit about 10¹⁹ ants on its surface at any one time. (I'm ignoring porosity, because the ant probably wouldn't have started on the inside.) Let's now construct an elaborate system of bridges to the tater tot surface. Basically it looks like koosh ball, where each of the koosh prongs coming out can be used like a highway system by the ants to access the surface. Assume each ant gets its fill in about an hour and then leaves along the prongs to allow the next ant access. Each ant eats 1 mg of food, tearing away 1 mm of tater tot surface. At this rate, it would take about 700,000 years.

Hom Many M&Ms would I have to eat to gain enough mass to be qualified as a dwarf planet?

Current weight: 203 lbs

The mass of an M&M is about 1.5 grams. The mass of a dwarf planet, lets say Pluto, is about 10²² kilograms. You would need to eat 6*10²⁴ or roughly 10 moles of M&M's to qualify as a dwarf planet.

What is the fastest time a human will ever be capable to run the 100m sprint?

This one is interesting. According to Wikipedia, "modern pilots can typically handle a sustained 9 g." The g is 9.8 m/s^2, meaning humans survive an acceleration of 88 m/s^2. Assuming you build some fast-moving exoskeleton suit out of the nanotechnology stuff we're working on, you still couldn't go much past this acceleration without passing out or possibly killing yourself. With this acceleration, you could finish the 100 m dash in 1.5 seconds while reaching a top speed close to 300 mph.

XKCD did a similar analysis of Nascar racing: http://what-if.xkcd.com/116/

What are the statistical odds your post will reach the front page of reddit?

At this point, probably close to zero unless I start posting naked pictures of celebrities.

Edit: Spelling

How fast does an average person's feet have to move in order for them to walk on water?

Meant to reply to this one earlier. Sorry for the delay.

If you slap water as hard as you can (think Stephen Amell in Season 1 of Arrow), you get a force back on your hand. Let's assume that force can be approximated by the drag force. (Technically, you sink into the water a little bit, but if you do it fast enough you won't submerge.)

Suppose you weigh 180 pounds (~800 N). Assuming water has a density of 1000 kg/m³ and the balls of you feet having an area of 2 square inches with a drag coefficient of 1, you'd need to move about 40 m/s to avoid sinking.

For more, see http://en.wikipedia.org/wiki/Drag_(physics)

Sadly, You seem to be getting nothing but humorous questions from reddit. So here is a serious one that has puzzled me for a long while.

There is a Norse myth about the Ur-cow whose milk, dripping from her udder, congealed into the first man.

So, if the Grand canyon was dammed at both ends, how long would it take the milk from this cow to fill it? I think we can assume a fairly productive cow - say 10 gallons per day.

honorio, thanks for an fun question and a bit of mythology!

The Grand Canyon has a volume of 5 trillion cubic yards. At 10 gallons per day, it would take about 10¹⁸ seconds, or roughly the age of the universe.

How hard would one have to blow at a piece of paper for it to catch on fire?

Paper ignites around 220 degrees celsius, meaning you'd have to raise its temperature by about 200 degrees. It has a specific heat of about 1.3 kJ/kg*K, and a mass of a few grams. From this, we can tell that it would require about 1000 Joules of heat energy for paper to become hot enough to ignite.

Air has a density of about 1.2 kg/m^3, and it's hitting and 8.5x11in sheet of paper. Assuming only 1% of the energy of you blowing goes into heating the paper, you should be able to ignite it by blowing with a speed of 100 m/s for a few seconds.

What kind of background would one need to apply for this chance to study with you? Also, what... is the airspeed velocity of an unladen swallow?!

(1) We're not looking for background per se. I couldn't care less about what classes you've had or what you got on your ACT/SATs. Many of the best students I've had in terms of grades and standardized tests are too afraid to make mistakes in lab. I want students who will try things without being afraid to fail.

If you're creative and can solve problems, I want you on my team.

(2) And what do you mean? An African or European swallow?

Edit: Standardized != Standard Eyes. I am an idiot.

If I throw a triangle out of a car and the car is going 20 KM/H and wind resistance is a thing that exists, how many cupcakes can Pedro buy with one human soul?

^Source

Ok, real question now. How much energy would it take to start a thermonuclear chain reaction in the atmosphere?

Awesome question...

I'm going to assume having temperatures equivalent to those at the core of the Sun would be sufficient. The Sun's core has a temp of about 16 million kelvin. Earth's entire atmosphere weighs about 510¹⁸ kg and a specific heat around 1000 J/kgK. If I wanted to heat the whole atmosphere, it would take about 10²⁸ J. It would take the Earth almost 2 millennia to absorb an equivalent amount of energy from the Sun.

To be fair, that's only an upper bound. You wouldn't need near that amount of energy because the chain reaction would release more energy to cause more reactions.

What's the probability of enough successive quantum tunneling events happening to allow someone to pass through a .5cm thick polyurethane wall?

Ooo...quantum mechanics. Fancy!

Let's assume all of the polyurethane's matter over laps with yours. This means all your atomic nuclei, which are typically at least 1 angstrom away from the atomic nuclei of the polyurethane, are now significantly closer. Let's say they're half as close. Every nucleus in the polyurethane now feels a charge-charge repulsion between itself and the nuclei closest to it. Two protons separated a distance half an angstrom apart feel a repulsion of about 14 eV. Polyurethane has about 10²⁷ protons in it, meaning you have a total energy barrier of about U0=1.4x10²⁸ eV. Let's say you run at 10 m/s. From this we can compute your kinetic energy E. We can then plug into the tunneling formula to find a minuscule probability P ~ 10^-1038. Given the age of the universe, I can't even write that number out because it has too many zeros!

Ok here is one! The guy that died in New Jersey yesterday or Sunday. The tape measure fell from a 50 storeys building from a construction workers belt. The tape measure ricochet hit something and hit the delivery driver in the head and killed him. How fast was the tape measure going? And did the ricochet increase the speed or decrease the speed?

Here is the article (I'm on a phone sorry)

m.nydailynews.com/new-york/delivery-man-killed-freak-job-site-accident-article-1.1997887

Wow...that's awful. Usually my estimates have a certain amount of light heartedness to them, so I feel a little weird answering a question like that in this forum. I don't want to make light what's obviously a tragic situation, but math and estimations aren't just for fun. They can be used to analyze difficult and sometimes even painful situations, so it's that spirit that I'm answering this problem...

Each storey of a building is about 12 feet high, meaning 50 stories would be about 600 feet high. Ignoring air drag, an object dropped from this height would be traveling about 60 m/s (~133 mph). The ricochet might have absorbed some of that energy, but this is still more than fast enough to kill a person if it hits you the wrong way. If you're a construction worker, make sure fasten your equipment; the safety of other clearly depends on it.

(I ignored friction here. That might be fine for a tape measure, but it won't work for things like pennies, which are less massive and will reach terminal velocity before hitting the ground.)

How much urine or faeces would you need to get out of a frictionless saucer (made from the bottom 10% of a sphere with 100m radius) ? Which would be more efficient in terms of work done by you (not including the effort in producing it, unless you really want to...)?

You may pick the bristol stool chart number, you are not allowed to exhale or inhale whilst doing so to swing out with momentum, you are not allowed to just fill it up and swim/float out.

bonus points for absurd strategy. Your life is on the smelly and somewhat disgusting line!

Ah...now this is my type of question!

Bottom 10% of a 200m diameter sphere? That's only 20m deep. It would take about 300,000 cubic feet of urine to climb out. You'd have to drink about 600 million beers to produce that much urine--wait?! I can't swim out. That sucks!

OK, absurd strategy it is. I need a velocity of about 20 m/s to make it out. We have an atmosphere canon at Simpson that can fire a ping pong ball near the speed of sound. The ping pong ball carries a momentum of 0.8 kgm/s. Let's assume we can make a ping pong ball out of feces. I weigh 180 lbs, meaning I'd need a total momentum of 1600 kgm/s to get out of your evil poop bowl. By firing around 2020 poop ping pong balls, I'd be able to escape your smelly torture chamber.

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I eat about 2000 Calories per day and have been around for about 35 years. With these numbers, I've eaten about 26 million calories.

1. How many miles per year are mousewheels moved in Arizona?

2. How fast would a baseball have to be thrown at sea level to burn up completely?

3. How long would it take you to reach the ground if you jumped off the top of the new One World Trade Center in NYC if the earth were motionless, i.e., not spinning and not orbiting?

1. About 5% of people I know have mice with mouse wheels. They seem like they're on the wheel about 5% of the time I'm looking at them, and they look like they're moving about 1 m/s. Arizona has 6.6 million people. From these assumptions, I'd say about 300 million miles.

2. Baseballs are about the same size as burritos, so I'm going with 1000 m/s. For details, see the Burrito problem I did here.

3. Unless you're measuring with extreme precision, I'm not sure there's a significant different between the Earth spinning/orbiting and not spinning/orbiting. One World Trade Center is 541 m to the tip, meaning it would take about 10 seconds to reach the ground.

Can you calculate why kids love Cinnamon Toast Crunch?

Not really sure, but if I had to guess I'm pretty sure the 9 grams of sugar might have something to do with it.

How many ants does it take to flip a car over ?

They say ants can lift 50 times their weight. Ants weigh few milligrams, meaning they can lift around 200 mg. A car weight about 2000 kg. You'd need 10 million ants to flip the car.

Lets say all of humanity is standing right on the equator except two people, one at each pole. If Earth suddenly stopped spinning on its axis and orbiting the sun in an instant, what would happen to everyone?

The rotational velocity of the Earth is about 1000 mph. Its orbital velocity, the speed it goes around the Sun, is much bigger at about 67,000 mph. If the Earth stopped suddenly, it would be like slamming the breaks on your car when it was traveling at 67,000 mph. The Earth might stop, but you'd keep moving forward at about 67,000 mph. Ignoring air resistance, that's enough to shoot you off the planet (i.e. it's bigger than Earth's escape velocity.) However, there'd be significant air resistance, so that's not a great assumption. The more likely event would be that you'd be traveling so fast that the friction from air resistance would burn you to a crisp very quickly.

So here's a question a friend got on an oral exam: In the Long Beach bay there are tires that are left to float in the water. And they float horizontally at high tide and vertically at low tide. Why is that? Please begin from first principles.

I keep coming by this one, and I have no idea why they should be different. I think I'm missing some important component of physics? The only logical reason I can come up with is elongationfactor1n2's answer.

If I jump up from Deimos with a speed of 5 m/s, how long will it take to get back again?

Deimos's gravity is about 1000 times smaller than Earth's. Jumping with a speed of 5 m/s on Earth takes about 1 second to land. Jumping with the same speed on Deimos would take about 1000 seconds to land.

How much energy is consumed yearly by all televisions in the world yearly? What about by computers?

TVs consume power at a variety of rates depending on the type, but I'll assume about 100 W. The same is true for computers. There are seven billion people in the world. Some watch TV for 40 hours a week, others have never seen a TV. I'll assume the average person watches TV around 2 hours per week, since the average is probably between 30 hours and 3 minutes. With 7 billion people, that gives about 10¹⁷ Watts, or equivalently 10¹⁴ watt*hours.

ignoring identical twins and given the current birthrate and assuming that DNA combinations only come up once and never mutate, in what year will humanity start to see unoriginal people?

I would argue we already see some unoriginal people (e.g. see the number of times I've been asked about woodchucks chucking wood in this AMA.) However, I assume you mean genetically unoriginal.

I'm not a biologist, so I reserve the right to butcher this problem. Still, I know DNA has 4 base types and that there are 3 billion base pairs in the human genome. On average, humans are about 99.9% genetically similar to other humans, meaning there are about 3 million base pairs that differ between you an me. There are 4^3,000,000 different combinations for the base pairs. Assuming 100 million births per year, it would take 4^3,000,000 /10⁸ years to definitely run out of genetic combinations for humans. This number is too long to write out and is much larger than the current age of the universe.

How did 42 become the meaning of life?

Pretty sure that because Douglas Adams is a total BAMF.

Assuming you work 10hours a day, sleep 8 hours and you love cakes, how much cakes will you be able to eat during your free time ? (Decide how much time is needed to bake and eat a cake. You can eat while next cake is in the oven)

Depends what kind of cake you're making. Are you using an industrial oven or an Easy Bake? If the former, you can make multiple cakes at a time. It takes about an hour to make a cake, but if you're doing several at once you can make enough to last the other 5 hours. Assuming you eat one slice of cake every two minutes, you can eat 150 slices in five hours. At 10 slices per cake, that would be 15 cakes. This, of course, assumes you have a digestive system that can handle that volume, or at least that you're not opposed to the idea of a vomitorium.