Physics 100 Lab – Measurements, Conversions, Equations
The purpose of this lab is to become familiar with some of the lab measuring devices we will use in
this class and to practice how to measure things in different units, how to convert between units, and
how to read scientific equations.
Measurements
Four fundamental quantities for measurements in science are: length, mass, time, and temperature. In
this exercise we measure the first two and use our result to calculate some other physical quantities.
1. Use a meter stick to determine the length and width, in meters and inches, of the lab table:
L = __________ m
W = __________ m
L = __________ in
W = __________ in
The area of a rectangle is found by multiplying the length by the width. Calculate the area of the
lab table:
A=LxW
A = ___________ m2
A = ___________ in2
2. Use the Vernier caliper to find the length and diameter, in centimeters, of a brass cylinder:
L = __________ cm
D = ___________ cm
The volume of a cylinder is found using the formula V= L x A where A is the cross sectional
circular surface area of the cylinder. This area is calculated using: π(D/2)2, where π = 3.14.
Calculate the volume of the cylinder:
V = L x A = __________ cm3
3. Use the triple beam balance to determine the mass, in grams, of the brass cylinder:
M = __________ g
4. The density of a substance is a constant for that material, independent of its shape. Density is
defined as the ratio of the mass to the volume of a sample ρ = M/V. Using your findings in step 2
and 3, calculate the density of the brass cylinder:
ρ = __________ g/ cm3
5. The accepted density of brass is 8.9 g/ cm3. Determine your experimental error in percent by using
the following formula:
Error = (ρcalculated – ρaccepted) x 100
ρaccepted
Error = __________ %
Conversions
Scientists use the International System of Measurement (S.I. units) when making measurements. This
is a modern adaptation of the metric system (using meters, kilograms, and liters), and it is used by
nearly all of the people in the world. Because S.I. units are based on multiples of 10, it is very straight
forward to convert between the SI units and prefixes. In this activity, you will practice changing units
to larger or smaller prefixes and powers.
The basic S.I. units for length, volume, and mass are meter (m), liter (L), and gram (g). These units
often have prefixes added to them to form units that are larger or smaller. Some of the prefixes are
listed in the table below:
Prefix
Symbol
Value
Numeric Value
Power of Ten Notation
giga
G
one billion
1 000 000 000
1 x 10
mega
kilo
M
k
one million
one thousand
1 000 000
1 000
1 x 10
3
1 x 10
hecto
h
one hundred
100
1 x 10
2
deka
da
ten
10
1 x 10
1
deci
d
one tenth
0.1
1 x 10
-1
centi
c
one hundredth
0.01
1 x 10
-2
milli
m
one thousandth
0.001
1 x 10
-3
micro
nano
µ
n
one millionth
one billionth
0.000 001
0.000 000 001
1 x 10
-9
1 x 10
9
6
-6
Note:
• There is no prefix that means one. For example, a liter is simply L.
• Capital letters make a difference. Make sure that you use the proper case.
• The letter m is used often. Lower case m means meter or the prefix milli- (so that a millimeter
is mm). The prefix micro- uses the Greek letter µ.
• Prefixes do not exist for every value. For example, there is no prefix that means 10,000 or
100,000.
1. Write the prefix that is the equivalent to each value below. The first one has been done for you:
a. 0.1 gram =
1 decigram (dg)
10-1 gram
b. 100 meters = ____________________
c. 0.000001 liter = __________________
d. one billion liters = ________________
e. 10 grams = ______________________
f. 0.001 meter = ____________________
________________________
________________________
________________________
________________________
________________________
2. To convert S.I. prefixes, you can use multiplication and division, for example:
1 kg = 1000 g, so 2 kg = 2 x 1000 g = 2000 g
1 m = 1/1000 km or 0.001 km, so 2 m = 2 x (1/1000 km) or 2 x 0.001 km = 0.002 km
Using the method above complete the following:
1 microgram (µg) = ______________________ g
20 kilometers (km) = _____________________m
5 centimeters (cm) = _____________________ mm
Physics 100 Lab – Measurements, Conversions, and Equations
pg. 2/4
3. Another way to convert S.I. prefixes and powers is to move the decimal point a particular number
of places. This is easiest done by writing out the units from largest to smallest. This is done below
for you using the mass unit gram (g), with spaces left for values that have no prefix.
Gg
Mg
kg
hg
dag
g
dg
cg
mg
µg
ng
When you convert, look at the direction and number of spaces moved on the grid above. This will
tell you the direction and number of spaces that the decimal point should move. For example, to
convert from Megagrams (Mg) to decigrams (d)g the decimal would move to the right seven
spaces. This procedure will work for any S.I. prefix, not only for grams.
Convert the S.I. prefixes below. The first one has been done for you:
a). 0.00028 mg =
0.28 __________µg
b) 226 cg = ___________________ g
c) 9.4 kg = ___________________ dag
d) 5400 mL = _________________ L
e). 2.73 hL = __________________ dL
f). 436 mm = __________________ m
g) 32.8 Mm = _________________ cm
4. Using your value from problem 1 in the Measurements section, convert the lab table area to these
prefixes:
Atable = __________________ m2 (copy from problem 1)
Atable = __________________ cm2 (convert from above line) Hint: notice cm2, not just cm.
Atable = __________________ in2 (convert by using 1 inch = 2.54 cm)
What is the percent error of your converted value in inches compared to what you measured and
calculated in problem 1? (Use your problem 4 value as Acalculated and your converted value from
problem 1 as Aaccepted.)
% Error = ______________ %
5. Using everything you have learned from the previous exercises, find the density of the wood block:
ρblock = __________ g/ cm3
Usually, density is measured in kg/m3, determine the blocks density in this unit:
ρblock = __________ kg/ m3
Physics 100 Lab – Measurements, Conversions, and Equations
pg. 3/4
Equations
In science, we use equations to describe relationships between different quantities and to calculate
specific values for those quantities. Equations are expressed in symbolic form, for example:
V=
d
t
In this equation, the variables V, d, and t represents velocity, distance, and time. The equation simply
states that to calculate velocity (V), you divide the distance (d) by the time (t).
To calculate the velocity, I would have to know the values and the units of the variables in the
equation. For example, if the distance is 100 km and the time is 10 s (seconds), then the velocity is
found by the following expression:
V = 100 km = 10 km/s
10 s
In the following expressions, put an x under the variables, circle the values, and underline the units.
Note: not every expression have to contain one of each, they may all be different combination of one or
several of the things you are supposed to identify.
a=V/t
My Age = 33 years
A=LxW
A = 100 km
2
d=Vxt
d = 10 ft
1 quarter ≈ 11 weeks
Equations are also useful for examining the how different variables are dependent on each other. For
example, in the expression V = d/t what would the magnitude of the value of V be if the original value
of:
1. d doubled? ____________________________
2. t doubled? ____________________________
Physics 100 Lab – Measurements, Conversions, and Equations
pg. 4/4