# Experiment 2: measurement: length, mass, volume, density, & time

Objectives: To make basic distance, mass, density, and time measurements,

To make calculations of volume and density, using proper units, and

To use spreadsheet software to practice graphing the relationship

between the circumference of a circle and its diameter.

Materials: Student Provides: 3 Box-like objects (block, thick book, shoebox, etc.)

2 Pencils or pens

Chair or step stool

5 Circular objects of different size (cups, plates, etc.)

Computer and spreadsheet program

A lab partner (optional)

From LabPaq: Stopwatch Meter tape

Metric ruler String

Metal bolt 10-g Spring scale

500-g Scale (optional) Graduated cylinder

Discussion and Review: Physics is a quantitative experimental science and is based

on measurement. In the physics laboratory it is important to know how to measure

fundamental quantities like length, mass, and time with precision and accuracy.

In this experiment you will learn the techniques for using several pieces of laboratory

equipment and become familiar with the units of measurements most frequently used in

laboratory work. Scientific measurements are normally carried out using metric units:

LENGTH: The meter (m) is the basic SI (Systeme International) unit of length. A meter is

just a little longer than the American yard.

1 in = 2.54 cm 1000 m = 1 km

1 km = 0.621 mi 1 m = 100 cm

1 m = 1.09 yd 1 m = 1000 mm

1 m = 3.281 ft 1 cm = 10 mm

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VOLUME: The basic unit of volume used in the chemistry lab is the liter (L), which is

slightly larger than an American quart. Related to the liter is the milliliter (mL), which is

one-thousandth of a liter (0.001 L). A milliliter is equal to the volume of a cube that

measures 1 cm on each side. Since the volume of a cube is equal to the length times

the width times the height, the volume of a cube that measures 1 cm on each side is

equal to 1 cm3

.

1 L = 1000 ml = 1000 cm3

1 mL = 1 cm3

1 L = 1.06 qt

MASS: The kilogram (kg) is the SI unit of mass and equals about 2.2 American pounds.

In the laboratory we usually work with the gram (g), which represents one-thousandth of

a kilogram and with the milligram (mg), which equals one-thousandth of a gram.

1 kg = 1000 g 1 lb = 454 g

1 g = 1000 mg 1 kg = 2.20 lb

It is important to note that mass and weight are not the same thing! Mass is a quantity of

matter while weight refers to the gravitational force of attraction exerted upon an object.

In the laboratory we will only be concerned with mass measurement and the verb

“weigh” is only used to instruct the student to determine the mass of an object.

DENSITY: The density of a substance is its mass per unit volume. The densities of

liquids are usually reported in grams per milliliter (g/mL) and the densities of solids are

usually reported in grams per cubic centimeter (g/cc or g/cm3

). The density of water is 1

g/ml; thus the mass of one liter of water is one kilogram. Substances with densities less

than 1 g/ml will float on water.

d = m

V

Example Densities: Water = 1 g/ml Aluminum = 2.70 g/cc

Iron = 7.85 g/cc Lead = 11.35 g/cc Gold = 19.30 g/cc

Density can be determined by the water displacement method or by using Archimedes’

Principle. In the water displacement method we place an object into a graduated

cylinder with a known volume of water. The object in the graduated cylinder will displace

an equal volume of water to its own volume. That means we simply subtract the original

water level from the new water level and the difference represents the volume of the

object.

Archimedes’ Principle states that a floating object displaces a weight of fluid equal to its

own weight, and the weight of a submerged object is diminished by the weight of the

displaced fluid. That means if we weigh an object in air and water we can use the

following relationship to determine its density:

M obj = ρ obj or d = M air/(M air – M water)

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The density of an object is thus obtained by dividing its mass in air by the difference of

its mass in air and its mass in water.

The quality of your physics lab work depends mainly on how accurately you use

measuring tools. In this experiment you will use your hand, a meter tape, and a metric

ruler to make length measurements. You will use a graduated cylinder to measure

volume via water displacement and a spring scale to determine mass. For basic time

measurements you will use a stopwatch.

All measurements have some degree of uncertainty. For example, your watch is

seldom perfectly on time but runs a little fast or slow. A ruler is not perfectly accurate. It

may be stamped imperfectly or humidity and temperature may affect it by expanding or

contracting the wood or metal and distorting the scale. Since uncertainty is unavoidable,

a physicist must understand how uncertainty affects the outcome of an experiment.

No measurement is complete without the units of measurement. Measurements and

calculations must always include the units!

PROCEDURES:

1. Estimation of Various Measurements:

A. Length:

1. Estimate the length of a meter by putting a pen or pencil at one end of a table

and then placing a second pen or pencil about one meter away from the first.

2. Using your meter tape measure the actual length of your meter estimate.

3. Record the length of your meter estimate.

4. Calculate the percent error of your estimated meter from the actual meter.

B. Time:

1. Estimate a 30 second time period while someone else times you using a

stopwatch. (If you don’t have a partner, you can do this experiment by closing

your eyes; start the stopwatch and stop it when you think 30 seconds have

elapsed.)

2. Record the actual time of your estimate.

3. Calculate the percent error of the estimate to the actual time.

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C. Mass:

1. Pick up a small paperback book or similar small object and estimate its mass.

2. Determine the actual mass of the object using your 500-g spring balance.

3. Record the estimated mass and the actual mass and calculate the percent

error.

Question: Why is it important for you to have a “feel” for length, time, and mass?

2. Measurements Using Instruments of Various Degrees of Precision: For

recording data set up data tables for each of the three items you will measure below.

Description of Object Measured: Measurement of your hand span: ________ cm

Length Width Height Volume

Hand (hand units)

Hand (cm)

Ruler

Meter tape

A. Your hand:

1. Spread out your hand and measure the distance from the tip of your thumb to

the tip of your little finger in centimeters.

2. Record this measurement on your data sheet.

3. Now use your hand to measure the length, width, and height of three

rectangular items such as small books, shoeboxes, or similar. The objects

should weigh less than 500 g, so you can also determine the mass if you

wish.

4. Record these measurements in hand units on your data sheet.

B. Metric ruler and meter tape:

1. Use the metric ruler to measure the length, width, and height of the same

objects from Step A and record the measurements in centimeters. Be sure to

place the markings on the ruler directly against the object to minimize the

possibility for error. Since the ends of the rulers are often worn a bit, start your

measurements at the one centimeter mark, then count the units rather than

relying on the numbers marked on the ruler.

2. Record your measurements to the nearest half millimeter. All your

measurements should have two places to the right of the decimal point and

thus end with either a 5 or a 0, i.e., 12.35 centimeters or 9.60 cm.

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3. Measure the length, width, and height of the box with the meter tape.

4. Record all measurements on your data sheet. Units should be in centimeters

and recorded to the nearest half millimeter as before.

C. Calculations:

1. Convert the hand units to centimeters and record.

2. Find the volume of the object using the three different sets of measurements.

Remember, the volume of a rectangular box is: v=length x width x height. You

must show the units, cubic centimeters, when recording calculated volume.

Questions:

A. Can you think of an occasion when it would be adequate to use your “hand”

measurement?

B. What would happen to your volume calculations if the length, width and height

measurements were off a little?

3. Graphing data and the determination of π:

A. Select five circular objects of different sizes, such as an AAA battery, a crew cap

from a soft drink bottle, the cardboard center of a paper towel roll, cups of various

sizes, plates of various sizes, etc.

B. Using the metric ruler or meter tape measure the diameter, d, in centimeters to

two decimal points and record.

C. Using the meter tape measure the circumference, C, in centimeters of each

object to two decimal points and record.

D. Graph C vs. d using a computer spreadsheet program.

E. Use the linear fit command from the menu to plot a best-fit line. Remember, the

equation for the slope of the line is, y = mx + b, where the slope is m.

F. What is the slope of the line? What does it represent?

G. Calculate the percent error of your value from the true value.

4. Density Measurements: Determine the density of q metal bolt (or any irregular

metal object) by the water-displacement method:

A. Half-fill the graduated cylinder and record the volume of the water without the

object. Hands-On Labs SM-1 Lab Manual

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B. Place the metal bolt into the graduated cylinder and record the new volume. The

difference between the two volumes represents the volume of the bolt or object.

C. Tie a string around the metal bolt and attach the string to the bottom of the 10-g

spring scale so that the bolt hangs down about 5 cm. Record the bolt’s mass in

air.

5. Determine the density using Archimedes’ Principle:

A. Partially fill a cup with water.

B. While holding the top of the 10-g spring scale, suspend the metal bolt hanging

from a string into the partially filled cup of water. Make sure that the bolt doesn’t

touch the sides or bottom of the cup.

C. Read the 10-g spring scale. This is the bolt’s mass in water. Record it.

D. Subtract the bolt’s mass in water from the bolt’s mass in air (recorded in 4.C

above). This is the apparent mass lost in water.

E. To calculate density, divide the bolt’s mass in air by the bolt’s apparent mass

lost.

Question: Which of the two volume determinations will be more accurate? Why?

6. Time measurements:

A. Measure and mark a vertical distance of two meters from the floor up.

B. Stand on a chair and hold a small box or similar object at the marked height in

one hand and the stopwatch in the other hand.

C. Start your stopwatch at the same instant you release the object and stop the

watch when you hear the box hit the floor. Record the time to the nearest tenth

second. Repeat three times. Units will be seconds. If you have an assistant, have

the assistant time you while you drop the box – use verbal commands like “start”

or “now” to synchronize the dropping and timing.

D. Find the average drop time of the object and record it in seconds.

Drop time (seconds)

Trial 1

Trial 2

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E. Repeat this experiment with your eyes closed.

Drop time (seconds)

Trial 1

Trial 2

Trial 3 Average =

Question: Do you think the average drop time is more accurate than any of the

individual drop times? Sometimes many trials are run and recorded. Then the

highest and lowest data points are disregarded when taking the average. Could this

technique help in this experiment? How?

NOTE: Do not discard your unused string.

It will be used again in a later experiment.