Study Guide

Energy and Momentum In the Real World

  • Pop Culture

    Superman and Conservation of Energy

    In the pantheon of superheroes, Superman is unquestionably king. The Flash has his speed, Spiderman has his web slinging, Wolverine has his claws, Batman has his, um, grappling hooks...but Superman. Superman has it all. He can lift mountains, survive nuclear explosions, fly through space, shoot lasers out of his eyes—power, it seems, that's limitless.

    Turns out old Supes might need to spend a little more time sunbathing and a little less time fighting crime to truly be "faster than a speeding bullet, more powerful than a locomotive, and able to leap tall buildings in a single bound.'' This looks like a job for science.

    Superman gets his mighty powers from Earth's sun, and on a generously sunny day in Metropolis, the sun is going to be radiating about 1400 W/m2. We'll assume Superman is able to convert 100% of that energy to useful work (another superpower—the best solar cells on the market currently are hard-pressed to beat 30%).

    Superman's around 2 m tall and, depending on the exact comic book you're reading, looks to be about 1 m wide at his barrel of a chest, so we'll give him the benefit of the doubt and say he's got a good 2 square meters of surface area to soak up some rays with. That puts him at 2800 J of energy from the sun per second when he whips out the tanning lotion.

    Faster Than a Speeding Bullet

    Every kind of gun is going to fire bullets at different speeds, but a good typical value for small rifles is right around the speed of sound in air, or 340 m/s. Superman's a burly guy, and probably tips the scales at 100 kg. So in order to run at speeds exceeding a bullet, he's going to need  of energy—about 35 minutes of exposure to the sun. We'll assume another superpower is the ability to ignore friction and air resistance, a power we employ often in physics exercises.

    More Powerful Than a Locomotive

    A modern diesel-electric locomotive, such as the JT56ACe used in China, weighs 150,000 kg and can pull another 5,000,000 kg at speeds of 120 kilometers per hour (75 mph, or 33 m/s). That's a kinetic energy of , or almost twelve whole days of constant sunbathing. (Superman can fly fast enough to stay in the sun for 24 hours, obviously.)

    Able to Leap Tall Buildings in a Single Bound

    The tallest building in the world is the Burj Khalifa in Dubai, shooting up over 800 m from the sand below. We'll assume some really tall buildings in Metropolis are a more reasonable 400 m, somewhere between the Empire State Building's roof and its spire's tip.

    The gravitational potential energy Superman has at the top of the building is U = mgh = (100kg)(9.81m/s2)(400 m) = 392,400 J—a quick two and a half minute power-tan. Five minutes, and he can make it over the Burj Khalifa faster than you can say "Tom Cruise in a catsuit."

    So for each battle against Lex Luthor, where Superman is running around and punching buildings to rubble to his heart's content, he's going to need a lengthy Caribbean vacation to recover his strength. After all, even superpowers are no use against the might of the law of conservation of energy.

  • Engineering

    Making Car Collisions Safe(r) with Crumple Zones

    The biggest issue in automotive safety engineering is how to remove energy after a collision. A car traveling at highway speeds has a lot of kinetic energy—in fact, even a car traveling at low speeds has a lot of kinetic energy—and in the event of a collision, all that energy needs to go somewhere. And preferably "somewhere'' isn't "the driver.''

    It's impossible to just suck up excess energy, so instead automotive engineers design cars that break strategically. Older cars without this innovation tend to break catastrophically in a crash, sending a large percentage of the energy of the crash straight to the people in the car. But newer cars use "crumple zones,'' sections of the car (not around the passenger compartment, don't worry) that fold and buckle in the event of a collision.

    A car with a well-designed crumple zone may look absolutely destroyed after a bad crash—but the middle section, where the driver and passenger sit, will look untouched. All of the energy that goes into bending and crushing the metal of the crumple zone is energy that isn't ever going to be transferred to bending and crushing the people inside.

    No matter how good the crumple, however, some energy will still make it to the driver. That's where crumple zones' other advantage comes into play: by deforming as the car hits an object (say, a wall), the crumple zone increases the amount of time the car is in contact with the wall.

    See, the same amount of momentum transfer is happening—unless you're driving the Marauder, which would just keep going—but the longer time given by crumple zones reduces the force felt by the driver immensely, according to the formula for impulse (Δp = FΔt). Less force is always a good thing when we're talking about large metal objects and soft human bodies.

  • Enviroment

    Energy Density and Batteries versus Fossil Fuels

    There's a simple reason mankind uses gasoline and diesel for moving so many of its creations around: there are very few materials that can match the energy stored in fossil fuels. Case in point: energy density, a measure of how much energy is in one kilogram of material. The energy density of these liquid fuels is astronomical, which is very important in something like a car, where you have to carry the weight of your fuel with you—and even more important in a plane, where you have to carry the weight of your fuel with you and also 30,000 feet up into the air.

    Diesel fuel has almost 45.5 MJ of energy per kilogram inside it—that's 45,500,000 J, which is enough energy to accelerate a large dog to Mach 5 (or enough to move your Camry about 35 miles). Crude oil's about the same, and gasoline is slightly higher at 47 MJ/kg. Even running a car on steam generated by burning coal would create 27 MJ per kilogram of coal.

    Electric carmakers would obviously love to compete with this, but that's hard to do when a lithium battery has an energy density of 2 MJ/kg. A gasoline car isn't quite 20 times more efficient at converting its fuel into energy (you can't get 100% of the energy in a liquid fuel; some of it escapes as heat, noise, etc.), but it's close.

    But fear not. There's hope for greenhouse gas-free cars yet. The energy density of gasoline and oil is fixed and is never going to increase. Batteries, on the other hand, are constantly getting better storage densities. While they may never be the equal of gasoline, they're definitely set to be a viable alternative in the near future.

    Better energy storage devices, such as energy-dense batteries, are also a boon for renewable energy generation. One of the biggest challenges facing solar and wind farms is the intermittent nature of the technology—sometimes the wind blows, sometimes the sun shines, and sometimes they don't.

    The times when the sun is out or the wind is particularly blustery don't necessarily line up with the times people turn on their TVs, and so renewables suffer from a problem fossil fuels don't have—it's possible to have too much energy available, yet also definitely possible not to have enough. We can always throw more coal on the fire, but we can't ask the sun to shine just a little bit brighter for an hour. Being able to store energy from renewable sources cheaply and densely makes intermittent power a lot less intermittent.