# calculation

Might as well jump. Jump. Go ahead, jump. - Van Halen
Suppose everyone in the world got together and jumped. Would the Earth move? Yes. Would it be noticeable? Time for a calculation. Note: I am almost certain that I have done this before, but I can't find where.
Starting assumptions.
7 billion people.
Average weight: 50 kg (you know, kids and stuff)
Average vertical jump (center of mass): 0.3 meters - and I think that is generous.
Mass of the Earth: 6 x 1024 kg
Gravitational field near the surface of the Earth is constant with a magnitude of 9.8 N/kg
Ignore the interaction with the…

Try to say that 5 times really fast. Go ahead, try it. Well, at least it is not as difficult as Fox in Socks - man that book is a killer.
This WAW is basically a means to embed Wolfram Alpha queries into a webpage. Pretty cool idea, but I am not sure how well it does the job. In fact, I have tried to embed calculations in my posts before. So, how about I just give a quick review of some different ways to do this. For all these methods, I will put in a calculator to determine the density of something given its mass and volume.
Javascript version
Density calculator
Enter the mass: kg…

Here is part of a picture some of my friends posted from a recent high school reunion.
It may be hard to tell, but this is part of a picture of 7 females all wearing black. I just wanted to show you that they were indeed wearing black without giving away anymore details. If you are one of these people and you want your whole picture included, I will be happy to make that change and include your face.
Anyway, my first comment was: "Wow, everyone is wearing black. Was this a planned event or was black part of the dress code?" The response was that it was just pure chance that all the women…

Somewhere on the internet, I came across this Cracked.com article on movie myths about guns. The article wasn't too bad, but I really liked this video they included from Arnold's movie Commando.
The myth for this particular clip was that guns never run out of ammo in the movies. Right away, I thought: I wonder how many bullets he shot? BRING IT ON.
First, I am going to find the fire rate of Arnold's weapon. Oh, I know I could look it up on Wikipedia or something - but I am not going to do that. I am going to determine the fire rate from the clip.
After capturing an audio segment where…

Honestly, I was going to add this to my previous post about the jumping car but I didn't because I wanted to finish. So, here it is and more. Actually, I will just make a projectile motion spreadsheet. That way, anytime you want to do a projectile motion problem, you can come here. Maybe this is a bad idea, but I am going to do it anyway.
To start with, I will just say that for projectile motion the horizontal and vertical motions are independent (except for the time it takes). If you want a refresher on projectile motion, here you go. Oh, a couple of assumptions:
Object starts at x = 0…

I am still thinking about the Red Bull Stratos Jump. Sorry, but there is just tons of great physics here. Next question - how big of a balloon would you need to get up to 120,000 feet?
I am not going into the buoyancy details of Archimedes Principle - I think that was covered fairly thoroughly with the MythBusters floating lead balloon. However, in short, here is a force diagram for a floating balloon.
For a floating balloon, the buoyancy force must equal the weight of the whole thing. It turns out that the buoyant force is equal to the weight of the gas (or fluid) the object displaces…

While I am still fresh on the Space Jump topic, let me take it to the extreme. Star Trek extreme.
SPOILER ALERT
But really, is this a spoiler alert if it is from the trailer of a movie that has been out forever? Of course, I talking about the latest Star Trek movie where three guys jump out of a shuttle and into the atmosphere.
So, in light of the Red Bull Stratos jump, how would this jump compare? First, my assumptions:
This Star Trek jump is on the planet Vulcan. I am going to assume this is just like Earth in terms of gravity and density of air.
The jumpers in Star Trek have on stuff…

I was going to just leave the oil spill in the gulf topic alone. Not because it isn't important, obviously it is. Rather, I wasn't going to do anything because I didn't really have anything to add to the topic. After a couple of readers requested it, I think I do have something to add. How exactly do you estimate the amount of oil flowing into the gulf?
What do I have to start with? A video. Here is a video of the undersea oil leak.
Now, I am not the first to estimate the oil flow rate (NPR on Purdue Prof's estimation and here a commenter make a quick calculation). Like I said, I am…

If you have been on the internet, you surely have seen this website showing the sizes of different starships. Way cool. Here is a small sample - but it doesn't do the site justice. You really need to go browse around.
Of course, I can't let something like this just go. One of the things I always think is interesting is to consider objects of different size. Perhaps the general idea is that you can just scale stuff up or down as you like. But, it doesn't work this way. Let me start with my own spaceship. It is a sphere with a thruster on the back. It just holds one person.
Now, what…

In this part of the world, we have oak trees. Technically they are called live oaks - but I don't get it. Of course they are alive. I was at a soccer game and this is the tree I always look at.
Look how far those limbs extend horizontally. That branch is about 12 meters long. Why is this amazing? Have you ever tried to hold an 8 foot 2 x 4 board horizontally by holding one end? Pretty tough. How about I calculate the forces needed to hold that branch in place? I will do a simple model and then maybe later I can make it more complicated. Suppose I replace that limb with one straight…

Time for another Fermi problem. There was a recent story in Science News that talked about the effects of the Chilean quakes on the Earth's rotation. The basic idea is that some ginmourmous amounts of rock moved closer to the Earth's center. Since the angular momentum of the Earth is conserved, the angular rotation rate would increase. The estimated change of the day was by about 1.26 microseconds.
Could all the cars in the USA be used to change the rotation of the Earth?
Well, I shouldn't have phrased the question that way. Of course 1 car technically is all you need to change the…

I already looked at ESPN's Sport Science episode where they calculate that Marshawn Lynch produces 54,000 watts when pulling some tires. Yes, that is way too high. However, what would happen if some was actually that powerful? What could that person do? How fast could they run 100 meters? That is what I am going to calculate.
First, I am going to assume that Marshawn has a mass of about 100 kg. Also, let me say that he can produce 54,000 watts no matter what his speed.
Take a short time interval. During this time, Marshawn will increase his speed from say v1 to v2 this would be a…

Let me be clear. I am not really an attacker. If someone wrote a report about ski jumping or something and misused the word "momentum", no big deal. However, if you have a show that claims to be about SCIENCE and you are obviously putting a lot of money into this show AND a whole bunch of people will see and think this is science - then you need to be a little careful. I think shows like ESPN's Sport Science are a good idea - you know, introduce some cool science ideas by using cool sports. This show just needs some help.
Yes, I know I make mistakes. I try to correct them when I become…

Oh, I know you missed it. Really, it wasn't your fault. Pi day fell on a Sunday, so how are you supposed to have pi-day activities in class? Don't let it stop you. You are better than that. Do the activity anyway. What to do? Here are some suggestions. (Suggestions aimed mostly at the high school level)
Plot Diameter vs. Circumference
This is a great one. Let your students find as many round things as they can (cylinders work the best - or flat stuff). Measure the circumference (you can use a string or a tape measure) and the diameter. Since the relationship between these two is…

I already went over a Monte Carlo method for estimating Pi - you know, for Pi-Day (March 14). Well, here is a small addition. This is the same thing done in Scratch.
If you create an account on Scratch, you can download the code of any project. I like Scratch.

Pi day is March 14th - get it? (3.14) I am a big fan of Pi. Here is my first post to celebrate the awesomeness of Pi (I know this is early, but I was too excited to wait).
How can you determine Pi?
Oh sure, tons of high schools do the classic experiment. Measure the circumference and diameter of as many round things as possible. Plot diameter vs. circumference. The slope will be Pi. Really, this is a great lab to do for all sorts of ages. The key thing is that students can see what Pi really means. I am not going to talk about this lab, I am going to do some thing cooler.
What if I…

I know many readers like the fermi questions (like how much would it cost to review all youtube submissions). Well, you are in luck - Diary of Numbers is having an estimation contest. Here is the question:
Mario has appeared in over 200 video games as Nintendo's main mascot. He has starred in TV shows, comic books, and feature films, but anyone who's played one of his games knows it's not all fun and games for the lovable plumber. He is constantly falling down bottomless pits, getting eaten by giant mutant mushrooms, and otherwise killing himself all while trying to save a princess who is…

Note: The following is a repost from some time ago. Today is the officially day to celebrate Dr. Seuss, so here is my Seuss-related post. Enjoy.
In the second Cat in the Hat book (I think it is the second one), the Cat reveals that he has more smaller cats under his hat. They are labeled A - Z with Z being so small you can't even see. Question: What is the sequence of sizes for successive cats? How big would Cat Z be?
Here is the first picture that Cat reveals Cat A. It is not trivial to measure their relative sizes because they are in different positions. I drew two circles, one…

There was a Buzz Out Loud episode in the not-to-distant past where the discussion of youtube came up. I can't remember the exact details, but the main point was that it would be impossible for google (the owners of youtube) to review all of the videos that were submitted.
And here is my calculation. How much would it cost google a year to do this? First, I need to pick some variables (and I will first do this symbolically - then you can put in your own values if it makes you happy).
Submission Rate (s): This is how many minutes of video are submitted each minute (so the units would be…

I ride my bike and mostly the wind makes me unhappy. On a very few days the wind is with me on the way to work and then changes so that it is with me again. But most days the wind is fairly constant. So, if the wind is constant then shouldn't everything even out? (Even Stephen).
Assumptions:
Let me start with the assumption that I (a mere mortal) can output at a constant power (but not 57,000 Watts like some people). I will also assume an air resistance force that is proportional to the square of the relative air speed. Here is a diagram.
A couple of quick things to point out. First,…