Real Answers to Ridiculous Questions

Randall Munroe, author of the ever-popular geeky stickman webcomic XKCD, is also a physics & math nerd. So he gets a lot of weird hypothetical questions from his readers. Now he’s starting to answer them, and it’s pretty entertaining.

Here’s a snippet from his first question, What would happen if you tried to hit a baseball pitched at 90% the speed of light?

“After about 70 nanoseconds the ball arrives at home plate. The batter hasn’t even seen the pitcher let go of the ball, since the light carrying that information arrives at about the same time the ball does. Collisions with the air have eaten the ball away almost completely, and it is now a bullet-shaped cloud of expanding plasma (mainly carbon, oxygen, hydrogen, and nitrogen) ramming into the air and triggering more fusion as it goes. The shell of x-rays hits the batter first, and a handful of nanoseconds later the debris cloud hits.”

3.4 Orbits

Critical Questions:

  • What do the orbits of the planets really look like?
  • What causes the tides?
  • How do artificial satellites orbit the Earth?

Back in Section 2.9, I explained a bit about how orbits work. I said that things in space orbit other things because gravity acts as a centripetal force, resulting in circular motion that goes on forever because there is no friction to slow things down. Now I get to do the fun part: go back and explain why much of what I said then was incorrect.

First of all, no orbits are perfectly circular. Circular orbits require a very specific combination of speeds, forces, and distances, but nature doesn’t like specific requirements, preferring instead the exciting chaos of random numbers. If you take a planet and get it moving near a star, then there are a few possible outcomes depending on speed and distance. The planet may end up with a circular orbit, but that is so unlikely it’s essentially impossible.

The second option is an elliptical orbit. An ellipse is just a circle that has been flattened (a circle is actually just a special kind of ellipse, just like a square is a special kind of rectangle). The ellipse is the shape of all of the orbits we know about, including Earth’s path around the sun and the moon’s path around the Earth. And in an elliptical orbit, the thing that is being orbited doesn’t sit at the exact center of the ellipse, but is located a bit off to one side.

elliptical orbit
This is a highly exaggerated elliptical orbit – Earth’s orbit, for example, is almost perfectly circular.

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Seven Minutes of Terror

In November of last year, NASA launched a rocket carrying a brand new Mars rover. Dubbed Curiosity, it is five times larger than the two previous rovers (Spirit and Opportunity) and is scheduled to land on August 6 of this year.

As with everything NASA does, the Mars missions might seem a bit underwhelming at this point. After all, they’ve done it before, right? How hard can it be?

Well, aside from the fact that Mars is currently 200 billion kilometers away from the Earth (and that changes each day, as the two planets orbit the sun at different rates) through an endless ocean of empty space, there’s also the problem of successfully landing a robot onto the planet’s surface.

In this video, the team that designed Curiosity’s landing system discusses just what makes this so difficult to achieve:

(via Waxy.org)

3.3 Mass, Weight, and Weightlessness

Critical Questions:

  • What is the difference between weight and mass?
  • Why do you weigh less on the moon?
  • Why does your stomach lurch when the elevator you’re in starts moving?

You might have noticed that in the last section, I used the words “mass” and “weight” interchangeably. If a certain type of physicist were reading that section, I might be in jail by now. At this point, I should placate the purists out there and be a bit more precise about all of these terms.

George Bluth in jail, from Arrested Development
At least there’ll be ice cream sandwiches.

Imagine stepping onto a simple bathroom scale and seeing the little needle turn. You might think that the way a scale works is obvious, but let’s Think Like a Physicist here and describe this situation technically. First of all, your body is pulled downwards by the gravitational attraction between yourself and the Earth. A coiled spring inside the scale compresses, providing you with more and more upwards force the more it is compressed. The whole thing adjusts itself, with a bit of wobbling, until it stops at a point when the upwards force from the spring is exactly equal to the force of gravity pulling you down. (At that point, the net force on you is zero, so you don’t accelerate.)

We know from the previous section that objects of greater mass experience a greater force of gravity, so heavier objects will stabilize with a more tightly compressed spring and thus a higher scale reading.

That may seem like a needlessly complicated way to describe what’s happening, but it reveals an interesting truth about weight. The scale isn’t directly measuring anything about you. It measures the amount a spring compresses, which measures the amount of gravitational force acting on your body.

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3.2 Gravity

Critical Questions:

  • Why do things fall?

The most remarkable thing that Newton’s Law of Universal Gravitation tells us is that everything attracts everything else with a force that we call gravity.

Stephen Hawking in Zero Gravity
Stephen Hawking: Exempt from your petty “laws”.

This is not an obvious point. If you hold up two objects right now, like a pen and a glass of water, I doubt you’ll feel them pulling towards each other. You can try moving the pen back and forth a bit and you still won’t feel anything. If you let go of it, it’s not going to zip over towards the glass and stick to the side of it like a magnet. And yet the miraculous Law of Universal Gravitation tells us that the pen and the glass actually are pulling towards each other – not with the same type of force we see in magnets, but with a force that acts in much the same way. So why can’t you feel it?

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What is Time?

You might have noticed that we’re slowing down the posts here at Pop Physics HQ. That’s because summer is in full, sweaty swing, the students are busy forgetting everything they’ve learned sitting at their school desks, and I want to make sure this site’s got some momentum when we pick up the pace again in September.

But the public demands more. With that in mind, here’s a good article about the basic ways physicists think about Time, written by author Paul Davies. I’ll be talking about some of these ideas in greater detail in later chapters.

“Thinking of past and future brings us to another problem that has foxed scientists and philosophers: why time should have a direction at all. In every day life it’s pretty apparent that it does. If you look at a movie that’s being played backwards, you know it immediately because most things have a distinct time direction attached to them: an arrow of time. For example, eggs can easily turn into omlettes but not the other way around, and milk and coffee mix in your cup but never separate out again.”

Read the full article here!

3.1 Introduction to Gravity and Orbits

Things fall.

This is such a basic part of life that our very bodies are built to function in a world where things fall. When astronauts go up into space, they have to exercise hard to combat the effects of a lack of gravity, and when they come back to Earth, their heads are swollen and their legs are thin for a few days afterwards.1

Astronaut floating in space
Still, it’s probably worth the discomfort.

We’ve been dealing with the fact that things fall since the moment the first homo sapien came up with a word (or particular tone of grunt, maybe) to describe falling. Longer than that – we’ve been dealing with it since the time when our distant evolutionary ancestors began to be able to develop a dim distinction between up and down.

We knew that things fell long before we knew that the stuff around us was made up of little bits called atoms, before we knew what stars were, even before we knew how to rub two sticks together to make fire.

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  1. I am not making this up.

Mythbusters: Sail on a Boat

Back in the section on Newton’s First Law, I mentioned one of the classic examples of internal forces: a fan on a sailboat. It has since been pointed out to me a few times, usually in a somewhat smug and conclusive tone of voice, that Mythbusters busted that myth a long time ago.

mythbusters episodes
Smugly awesome.

So why did their boat go forward, as in the video below? I’m a big fan of the show, but I do think Grant’s explanation (at around 4:16) is a bit misleading.

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