__Experiment 1__

__– METRIC__

SYSTEM MEASUREMENTS AND CONVERSIONSSYSTEM MEASUREMENTS AND CONVERSIONS

**BACKGROUND:**

In order to enhance commerce and science throughout the world, it is

vital that there be a standardized system of measurements and units. Actually,

there are two widely used systems.

In the U.S., we use the English system of

units; common units for length, mass, and volume are feet, slugs, and

gallons. Mass is a quantity of matter,

and is a measure of inertia. The pound, a unit in the English system that we

use for weight, is actually a force due to gravity.

In most of the rest of the world,

the metric system, known now as the International System (S.I.), is used. The

standard S. I. metric units for length and mass are the meter (m) and kilogram

(kg); the “unofficial” standard unit of volume is the liter (L).** **Non-standard

units are commonly used in the S.I. system (and English system), and

conversions to standard units, or vice versa, often are done. Common conversion

prefixes are: mega- = 1,000,000, kilo- = 1000,

centi- = 1/100, and milli-

= 1/1000. A further list of conversion factors is seen in the Appendix.

One milliliter is 1/1000 of a liter

and it equals one cubic centimeter (1 mL = 1 cm^{3}). By definition,

one gram of water occupies one cubic centimeter of volume (at 4^{o}C

(39^{o}F)).

Some units are represented as

ratios, e.g., for density, which is defined as mass per unit of volume. A

non-standard, but commonly used S.I. unit for density is grams per cubic

centimeter, g/cm^{3}. A common

English unit for density is pounds per cubic foot, lb/ft^{3}. (For

example, the density of water is 62.4 lb/ft^{3}).

**OBJECTIVES:**

– To learn and use the proper S. I. metric units.

– To learn how to make simple

measurements and to understand accuracy

.

– To learn

how to convert a measurement or quantity from one unit to another

**PROCEDURE:**

The following equipment will be

needed: meter sticks (2), bathroom scale, wood block, balance, graduated

cylinder (100 mL), graduated cylinder (25 mL), beaker (250 mL), iron nails (3).

**A. Measurements**

**of Length**

Where applicable, show all

calculations.

1.

__Bench (or table) dimensions__:

a.

Predict the length of your table top, in units of

meters. Then use the meter stick (or a tape measure) to verify your prediction.

Measure to the nearest centimeter, and convert to meter units (to two decimal

places (e.g., 384 cm converts to 3.84 m)).

Prediction __ __ m Table

Length __ __ cm;

__________ m

b. Measure the width of the Table top: Width __ __ cm;

__________ m

c. Calculate

the area of the Table top, using the formula:

area = length x width (A =

LW)

A = _________ m^{2}.

2. __Heights of student scientists__:

a. __Height Measurements.__ Have your height measured by someone, to the __nearest __

__centimeter__, using two meter

sticks and sliding one on the other. Record your height (in centimeters).

Your

height in centimeters __ __cm

Convert

your height to inches (1 in = 2.54 cm) __ __in

**B. Measurements of Mass, Volume, and Density**

1. __Mass:__

a. Weigh yourself on a bathroom

scale. __ __lb

b. Convert the pounds to kilograms (1 kg = 2.2

lb) __ __kg

{Each student should do

this calculation individually; show the setup}

2. __Density of solids:__

This procedure is useful for

measurement of the density of materials and objects that have a regular shape, e.g., a rectangular

solid, or a sphere, or a cylinder.

a.

Measure the dimensions (length, width, height) of a block of wood*.*

b. Calculate the volume (V) in

cubic centimeters (cm^{3}), using the formula:

volume = length x width x height [V = L W H] ^{}

^{}

c.^{ }Using a

balance, determine the mass __to the nearest 0.1 g__

d.

Density is the mass per unit of volume. Using the formula for density, *p*

= m/V, calculate the densities

of the blocks.

m__ass (g)__ __length (cm)__ __width (cm)__ __height (cm)__ __Volume (cm ^{3})__

__density (g__

^{}/cm^{3})Wood

____ ______ _______ _____

_______ _______

e.

The accepted values for density of the various

materials, in units of g/ cm^{3}, are:

wood, 0.4-0.5; aluminum, 2.7; lead, 11.4; brass, 8.6; and iron,

7.9. How does your experimental value

(EV) for the metal compare with the accepted value (AV)? That is, is it exact,

or close (slightly off), or not close (way off)?

___________________

3. __Density Of Water__:

a. Using the balance, weigh a 100 mL graduated

cylinder __to the nearest 0.1 g__.

________ g

b. Then carefully pour water

from a 250 mL beaker into the graduated cylinder,

so that the volume is close or equal to

100.0 mL.

__Record__this volume,__ to the nearest 0.1 mL__ ________

mL

c. __Weigh__the cylinder *plus* water.

________g

d. __Calculate__

the mass of the water (c. minus a.) ________g

e.

__Calculate__ the volume of water, in units of cm^{3} ________

cm^{3}

(Remember: 1 mL = 1 cm^{3}).

f.

__Calculate__the density of water, using the equation: *p* =

m/V. _________ g/cm^{3}

(Record this value to

two decimal places)

g. The accepted value (AV) for

the density of water is 1.00 g/cm^{3}.

__Calculate__ the accuracy, as represented by the experimental error,

for your experimental measurement (EV) of

this density, using the equation:

Experimental Error

= 100(EV –AV)/AV =

_______ %

4. __Density Of Iron:__

This procedure is useful for

measurement of the density of solid materials and objects that have an irregular shape.

a. Determine

the mass of three nails, __to the nearest 0.1 g__. __Record__the mass in

the table below.

b. Add

water into a 25 mL graduated cylinder to about the 18-20 mL mark. __Record__the

volume of water,__ to the nearest 0.1 mL.__

c. Place

the three iron nails in the water. __Record the new volume__. The rise in

water level is equal to the volume of the nails. __Calculate__this volume.

d. Now

__calculate__ the density of iron, using the equation: *p* = m/V.

Mass

of iron nails __________

g

Volume of

water *plus* iron nails ________

mL

Volume of

water ________

mL

Volume of

iron nails

_________mL = __ __cm^{3}

(remember – – 1 mL = 1 cm^{3})

Density of

iron (*p* = m/V)

___________ g/cm^{3}

The

accepted density of iron is 7.9 g/cm^{3}. __Calculate__ the experimental error for

your measurement of this density, using the equation:

Experimental Error =

100(EV –AV)/AV = _______ %

**C. Additional Questions:**

1. Why is it important to establish standard

units of measurement?

2. What are the standard units of length and

mass in the S.I. metric system?

A] length B] mass

3. What is the difference between mass and

weight?

4. What are two methods measuring the volume of

solids?

A] B]