AP Physics C 2017

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:

1. 
   

        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.

   
   


2. 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.

3. 
   

        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.