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How to Convince Your Flat-Earth Friends the Earth Is Round

Illustration: Rhett AllainYou can see that we have a right triangle with the hypotenuse equal to the distance from the observer's eyes to the center of the Earth (R + h), with the other two sides being just R and the distance to the horizon (s). Using the Pythagorean theorem, we can solve for s:Illustration: Rhett AllainNow we just need to plug in our values for R and h to get a distance of 4,657 meters, or about 2.89 miles. Of course, if you increase your distance from the surface (h), then you can also see farther. But…

Why the Polar Vortex Is Bad for Balloon Artists

It's been crazy cold this week, even down where I live in Louisiana, thanks to an outbreak of a polar vortex. This frigid air is bad for all kinds of things, including football helmets, apparently. But it's actually a great time to demonstrate one of the basic ideas in science: the ideal gas law.You probably have some balloons somewhere around the house, maybe left over from New Year's. Try this out: Blow up a balloon and tie it off real tight. Got it? Now put on the warmest jacket you have and take the balloon outside.…

School of Rock: The Physics of Waves on Guitar Strings

The rubber band example does indeed have two nodes—they are at the ends of the rubber band where your fingers hold it. We only have half a wavelength in the standing wave, but there is indeed a relationship between the length of the rubber band and the size of the wavelength.Guitar StringsIt's time to put all these ideas together and look at a guitar string. Once you hit that string, it's going to create a standing wave with an antinode in the middle and two nodes on the ends. This is called the first harmonic wave.It's…

How to Measure the Impact From a Collision

Not only do I get the "shape" of the acceleration curve for the colliding cart, but I also get a maximum acceleration of –6.67 meters per second squared. With that acceleration and the mass of the cart (0.566 kilogram), we get a maximum impact force of 3.73 newtons.This isn't quite the same value I obtained from the force sensor—and that's OK. There are two main reasons why the maximum force is different with this method. First, I've only collected a position point every 1/30th of a second, because my video frame rate was…

How to Measure the Calories in a Candy Bar—With Physics!

This Halloween, when you grab a candy bar, pay attention to the wrapper. In the United States, a "nutrition facts" label has been required for all packaged foods since 1994, giving the serving size and the amount of sugar, protein, fat, and sodium the food contains. But the most interesting bit is the metric for energy, which is listed as "calories." What does energy really mean when it comes to candy?Flavors of EnergyIn physics, the concept of energy helps us keep track of different types of interactions. We say energy…

Could a Cockroach Survive a Fall From Space?

There's some cool stuff going on here. Notice that for the objects with air resistance, they all reach incredibly high velocities as they fall in the upper atmosphere where they encounter very little air resistance. However, once they get into the thicker air they slow down. The cockroach slows in a weird way because my air density model (for very high altitudes) has low resolution.But all of those objects eventually reach some terminal velocity. For the bowling ball, this final velocity is 83 meters per second (185 mph),…

When You Drop a Rock Overboard, What Happens to the Water Level?

Physics questions are the most fun when people don't immediately agree on the answer. What feels intuitive or obvious—sometimes isn’t. We can argue over the solution for hours of entertainment, and we might even learn something in the end.Here's one of these seemingly obvious questions that's been around a long time: Suppose a large rock is on a boat that is floating in a very small pond. If the rock is dumped overboard, will the water level of the pond rise, fall, or remain unchanged?Go ahead and debate it with your…

OK Surfers, How Much Would It Cost to Power Your Own Wave?

That expression doesn't look nice, but at least now the energy calculation is in terms of things that we actually know or can estimate. All we need to do is convert our estimates from imperial units to metric and we are all set. Using a wave traveling at 20 miles per hour, with these estimations I get a wave energy of 16 million joules.Is this a lot of energy? Here are some quick numbers for comparison. Suppose you pick up a textbook from the floor and put it on a table. This takes roughly 10 joules. Your smartphone’s…

All the Ways to Slow a Car (Even Some Bad Ways)

Since the vehicle is moving up the incline and gravity only pulls straight down, there is a component of this force that pulls in the opposite direction as the velocity to make the vehicle slow down. As it moves up the incline, there is an increase in gravitational potential energy. The higher it goes, the greater the potential energy.Of course, the same thing can happen in reverse. If you let an object move down a ramp, there would be a decrease in gravitational potential energy and a resulting increase in kinetic…

Can You Strike Out a Major League Baseball Player by Pitching Super Slow?

If you want to be a Major League Baseball pitcher, you need to be able to throw a ball really fast—like 85 to 100 miles per hour. The faster the pitch, the less time a batter has to react and swing the bat, which means you have a greater chance of getting the ball past him for a strike. (For folks who aren’t baseball fans: A strike is when the batter swings and misses, or fails to swing at a ball that’s in the strike zone. Three strikes, of course, and you’re out.) This requirement has considerably dampened my dream of…