To further illustrate the advanced features of the Google calculator, we will consider several example calculations, exploiting the Google features to tailor the form of the answer we obtain.

Space travel is fun, and though the Internet won't allow us to do it from the comfort of our homes, we can get a sense of what it would be like to visit another planet without the harmful side effects of toxic atmospheres and unbearable temperatures (see Fig. 2). We can use Newton's law of gravity to determine what we would weigh on other planets. Suppose our mass is 80 kg (i.e., our bathroom scale on Earth reads 165 pounds of force). To find out what the scale would read if we took it to the Moon, google "convert(G*mass of the moon*80 kg/(radius of the moon)2) to pounds force." The answer is "29.2619238 pounds force." (You will have to adjust the number of significant figures yourself.) Replace the Moon with the Sun to find that we would need to take a better scale as our weight there would be "4,934.55214 pounds force." Try it for Mars or any other planet in the solar system by using "mass of planet name" and "radius of planet name" in Newton's law of gravity.

Figure 2.

Let's suppose you built a crazy car that converted mass into energy directly. So you put in a kilogram of matter, perhaps old cereal boxes, and the engine of this car converts it directly into energy through Einstein's famous energy/matter relation, E = mc². Maybe we have to put in an equal dose of anti-matter to get 100% conversion, but we'll assume that somehow it happens. Let's suppose that it is capable of converting one kilogram per year under constant operation. How many horsepower does this engine have? Google "convert 1 kilogram*c2 / year to horsepower" and it returns "3,819,290.09 horsepower." It makes a Ferrari look like a go-cart.

The force that the Sun exerts on the Earth can be calculated by googling "(G*mass of the earth*mass of the sun/(1 astronomical unit)2)" to find that the force binding the Earth to the Sun is "3.54296305 × 10²² newtons." Using the equation for centripetal acceleration, a = v²/r, the Earth's orbital speed can be determined. To do so google "sqrt(G*mass of the sun/(1 astronomical unit))" to learn that the Earth is hurtling through space at the rate "29,785.5982 m/s."

Coulomb's law for electrostatic forces is analogous to Newton's law of gravitation with the masses replaced by charges and the gravitational constant replaced by the Coulomb constant, which is written 1/(4_o). The constant _o is the permittivity of free space, or in Google, the "electric constant." How does the electric force between the electron and proton in the hydrogen atom compare to the gravitational force between them? To find the ratio of the electric to gravitational force in the hydrogen atom, google "((elementary charge)2 / (4 *pi*electric constant))/(G*mass of electron*mass of proton)" to find that the electric force is "2.26910384 × 10³⁹" times stronger.

Using the Bohr model of the hydrogen atom, we can compute the rotational kinetic energy of the electron were it orbiting the nucleus as in a planetary system by googling "convert 0.5 * ((elementary charge)2 / (4*pi*electric constant *(0.529189379 angstrom))) to eV." The answer is "13.6053788 electron volts," which is darn close to the measured value for the ionization energy of hydrogen. We could have just obtained the answer in joules, but hardly anybody thinks about atomic energy levels in joules.