Everything here can be done easily without a calculator, especially if you remember to use 10 m/s^2 for g .
No problem!
Order of Magnitude Estimates
These test your understanding of the size of things, measurements, or just numbers.
Which of the following best approximates the gravitational force experienced by a high school student
due to the student sitting in an adjacent seat?
(A) 10^1 N
(B) 10–8 N
(C) 10–18 N
(D) 10–28 N
(E) 10–38 N
Wow, at first you have no idea. But let’s start by looking at the answer choices. Notice how widely the
choices are separated. The second choice is a hundred millionth of a newton; the third choice is a
billionth of a billionth of a newton. Clearly no kind of precise calculation is necessary here.
The answer can be calculated with Newton’s law of gravitation . You complain:
“They didn’t give me any information to plug in. It’s hopeless!” Certainly not. The important thing to
remember is that you have very little need for precision here. This is a rough estimate! Just plug in a
power of 10 for each variable . Watch:
G : The table of information says that the constant G is 6.67 × 10−11 N·m^2 /kg^2 . So we just use 10−11
in standard units.
- m 1 , m 2 : It doesn’t say whether this is Olympic gymnast Shawn Johnson (41 kg) or football offensive
lineman John Urschel (137 kg). What do I do? Just use 10^1 or 10^2 kg. If you’re really concerned, you
can make one 10^1 kg and one 10^2 kg. It won’t matter.
r : The distance between desks in any classroom will be more than a few tens of centimeters, but less
than a few tens of meters. Call it 10^0 meters and be done with it.
Okay, we’re ready for our quick calculation:
(You remember that to multiply powers of 10, just add the exponents; to divide, subtract the exponents.)
You still object, “But when I use my calculator and plug in more precise values, I get 3.67 × 10−7 N.
Or, if I use both masses as Shawn Johnson’s, I get 1.1 × 10−7 N.” Look at the choices again; the second
answer choice is still the best answer. We got that without a calculator—and a lot quicker, too.