Transcript physics_1_stuff - Humble Independent School District

Physics Basics
First Week of School Stuff
Sig. Figs, Dimensional Analysis,
Graphing Rules, Techniques,
and Interpretation
Sig Figs

The purpose of sig figs is to eliminate
assumptions from your data. When
measuring an object, we can only be as
accurate as our instrument enables us.
For example, when using a ruler we can
only read to the nearest mm, then
estimate one more digit. When doing
calculations sig figs are determined by our
most inaccurate number.
Rules for Sig Figs
All non-zero numbers are significant
 Any zero between 2 significant digits
are significant (sandwich rule)
 Any zero after the decimal at the end of
a number are significant
 Zeros that are used only as place
holders are NOT significant
 If you need to make a zero significant
when it is normally not, place a line
over that zero.

Examples for Sig Figs
all digits are non-zero and therefore significant
1, 245  4 sig figs
347.58  5 sig figs
23  2 sig figs
zeros between two sig figs are significant (sandwich rule)
102  3 sig figs
13.505 5 sig figs
23060.7  6 sig figs
zeros after the decimal at the end of a number are significant
1, 245.0  5 sig figs
2.30  3 sig figs
347.580  6 sig figs
zeros that are used only as place holders are NOT significant
120 2 sig figs 0. 0153  3 sig figs 0.00304  3 sig figs
0.00250400  6 sig figs
to make a zero significant when it is normally not, place a line
over that zero.
100  2 s.f. 100  3 s.f 1000  3 s.f.
Multiplication & Division with Sig Figs
– First, count the number of sig figs in each
number to be multiplied or divided and
make note of the smallest number of sig
figs.
– Then carry out the multiplication or division
as indicated in the problem
– Finally, round the answer to the number of
sig figs that is the same as the number
multiplied or divided with the smallest
number of sig figs to begin with.
Example: Mult. or Div.
3459 4 sig figs
x 25  2 sig figs
86,475  Answer without rounding
86,000  Answer rounded to the
proper number of sig figs
According to Sig Fig rules the answer must
have the same number of sig figs as the
number with the least sig figs…in this case
 2 sig figs, so now you need to round the
answer to 2 sig figs
3654 ÷ 151 = 24.1986755
4 s.f. 2 s.f. Ans. w/o rounding
3654/151 = 24.2
Answer must be rounded
to 3 sig figs because 151
has the least s.f. with 3.
Addition & Subtraction with Sig Figs
– First, decide what the precision of each number is
(What place value is each number expressed to?)

Ex: 2351 is precise to the ones place
and 14.7 is precise to the tenths
– Then carry out the addition or subtraction as
indicated in the problem
– Finally, round the answer to the place value of the
least precise number you began with.

In our example above: the answer to an addition or
subtraction with these numbers would be rounded to the
“ones” place because “ones” is a less precise measurement
than “tenths”
Example: Add & Subtract
258.2
to the “tenths”
+ 6.539 to the “thousandths”
345.3876  “ten-thousandths”
- 6.45__  “hundredths”
338.9376  answer without
rounding
264.739  answer without rounding
According to sig fig rules,
According to sig fig rules,
answer should be rounded to
answer should be rounded to
the “tenths” place because that
the “hundredths” place because
is less precise than
that is less precise than “ten“thousandths”
thousandths”
So…answer is 264.7 for
So…answer is 338.94 for
proper sig figs.
proper sig figs.
Dimensional Analysis
 Dimensional
Analysis is a simple
way of converting from one unit to
another.
 It
is also a way of solving problems
using units as a guide to the
mathematical steps necessary.
Dimensional Analysis

Example:
To go from 100km per hour to cm per sec
we would begin by writing out 100km over
1 hour. Then we would multiply it by the
number of meters in 1 km and then by the
number of cm in 1 meter. Now we need to
convert to seconds. We would divide the
whole answer by 60 to get to minutes and
then again to get it to seconds.
 100km  1000m  100cm  1hr  1min 





  2777.8 cm sec
 1hr  1km  1m  60 min  60sec 
Graphing Rules and
Techniques



Identify the dependent and independent variables. The
independent variable is the one that is intentionally
changed while the dependent variable changes as a result
to the alteration of the independent variable.
Choose the scale you will use for the graph. Make the
graph as large as possible and use a convenient spacing.
For example, dividing ten into four spaces is not as simple
as dividing it into five.
Remember that not all graphs will go through the origin
(0,0).
More Graphing Rules

Each axis should be labeled with the name of the
variable and the units you are using. Make the axis
darker as to be easily identifiable. Plot the
dependent variable on the horizontal (x) axis and
the independent variable on the vertical (y) axis.
Plot every point.

Title your graph. The title should state the purpose
of the graph and include all the dependent and
independent variables.

In some instances, such as acceleration and
velocity, you may get data points that are, or
appear to be in a straight line. When that
happens, draw a straight line going through
as many points as possible and having the
same number of points above and below the
line.
Interpreting Graphs

Most graphs that you will encounter in
physics either A) have the dependent
variable vary directly to the
independent variable B) Vary inversely
to the other variable or C) vary directly
to the square of the other variable.