Download PHYS 1400 Lab_ Estimates and Measurements - UCA

Physical Science for General Education
Summer II 2008
Nancy J. Austin
Azida Walker
Carl Frederickson
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 01: Estimates and Measurements
Introduction
Making measurements is fundamental to science: geologists measure the age of rocks,
astronomers measure the distances to the stars, biologists measure the rates of cell metabolism,
physicists measure the masses of subatomic particles. Because measuring is so important, we need
to have a good understanding of how measurements are made. This week we will practice making
some simple measurements and drawing useful conclusions from our data.
Typically, we tend to think that precision and accuracy mean the same thing, and we probably use
the words interchangeably. However, they do represent separate and distinct concepts, so we need
to have a clear definition for each.
A carpenter building a house needs to be precise to 1/8, or maybe 1/16 of an inch. So a tape
measure or T-square marked in inches, subdivided down to an eighth or sixteenth of an inch is an
adequate enough tool for him to use. But a machinist milling parts for a jet engine will need a
more precise measuring tool--something that can measure much smaller increments, down to a
thousandth or even a ten-thousandth of an inch. The carpenter's ruler simply isn't going to be
useful to him. However, just because the carpenter's ruler is less precise than the machinist's
micrometer does not automatically mean that the machinist is more accurate!
While precision is an inherent property of a measuring instrument, accuracy is related to the use
of that tool. A machinist with a very precise micrometer can still make an inaccurate
measurement--what if he has aligned the tool improperly, or read the dial incorrectly, or done
something otherwise careless? The carpenter, using a less precise tool may be more accurate, if he
is using his instrument properly and making his measurement carefully.
Objectives
Become familiar with the process of making numerical estimates
Understand the difference between precision and accuracy in measurement
Learn to make reliable and repeatable measurements
Practice recording data and information in a structured format
Learn to identify trends in recorded data
Instrumentation
meter stick
triple beam balance
graduated cylinder
water
Activity 1: Numerical Estimates
Select four common items from among your workgroup
(pencils, combs, keys, coins, etc.).
Independently (without your lab partners), estimate the length
(longest dimension) of each item in both inches and
centimeters, and record.
Compare your estimates in centimeters with those of your
partners. For each item, note the smallest estimate made by
anyone, and the largest. Record this range of estimates.
Using a ruler or meter stick, measure each item (again, in
inches and centimeters) and record.
If you have not already, organize a neat and logical table of
your estimates and measurements.
Questions:
1. Find the estimate that you made that is closest to the actual measured length. Calculate the
percent error using:
2. Did you over- or under-estimate? By how much (an error of about 5-10% would be pretty
good). Look at your data and note if there is a pattern in your estimates: do you tend to
consistently over- or under-estimate, or is there randomness (some over-, some underestimates)?
3. In general, were your estimates in one set of units consistently more accurate than your
estimates in the other? If so, which set was more accurate? Why do you think that the units
might make a difference in your estimates?
4. Using the meter stick, which set of units (inches or centimeters) is more precise? Why?
5. If two people measure the same object using the same tools, will their measurements have
the same precision? The same accuracy? Explain briefly.
6. Compare the actual measurements (in centimeters) with your table of high and low
estimates. Are the actual measurements within the range of estimates? Is your range of
estimates bigger or smaller than ±10%?
Activity 2: Mass, Volume, and Density
Measure and record the mass of the empty graduated cylinder.
Fill the cylinder with 20ml of water.
Measure and record the mass of the cylinder + water. Subtract
the mass of the cylinder to obtain the mass of the water. Make
a neat table for your data.
Repeat, increasing the volume of water in 20 ml increments
until the cylinder is full.
Questions:
7. Prepare a graph of mass as a function of volume. This means that mass belongs on the x-axis
and volume belongs on the y-axis. Scale your axes appropriately and apply the scale
consistently. When the data are plotted, use a ruler to draw the best-fit line for the data.
8. Find the slope of the line that you have drawn. What are the units on your slope?
9. Calculate the density of the water for each trial, using:
10. Compare the values on the density table to the slope of the line. Related?
11. Why are the individual values for the density not all identical? Does the density of the water
change when you change the amount of water in the cylinder? Explain.
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 02: Free Fall
Introduction
According to legend, Galileo performed an experiment in which he dropped
objects from the top of the Leaning Tower of Pisa to study their motion. This is
almost certainly not a true story, but his experiments with inclined planes did
reveal the relationships between velocity and acceleration and distance and
acceleration. It was Isaac Newton who, half a century later, actually developed
the laws of motion that govern freely falling bodies. Newton determined that the
force of gravity caused objects to fall, and that all objects experienced the same
acceleration due to gravity, 9.8 m/s 2 , or 980 cm/s2 .
Objectives
Observe motion with a constant acceleration
Measure and record motion data accurately
Use the kinematic equations for constant acceleration to to perform data
reduction
Prepare a detailed graph, and use it to determine the acceleration of an
object in free fall
Show how a large data set improves the accuracy of experimental results
Equipment
Behr Free-Fall Apparatus
Spark timer
Spark tape
Ruler
Procedure
Position the marker at the top of the column so the magnet holds it in place.
While one person presses the spark timer switch, another person should release the marker
by switching off the power to the electromagnet.
As the marker falls, it will leave burn marks on the paper tape as the sparks jump from the
wire to the metal collar of the marker. Examine the tape to make sure that there are no
obvious gaps in the data or scratches that obscure the spark marks.
Carefully measure the distance Δx between each spark in centimeters. Please try not to mark
or scratch the wax coating on the tape (other lab groups will have to measure this tape, too).
In your notebook, make a table for your data (see example shown below). The time interval
between sparks is always 1/60 of a second (t 0 = 0, t1 = 1/60sec, t2 = 2/60sec, etc.), and you
should have a value for Δx corresponding to each time interval, as shown on the sample tape
below. Notice that, even though the same amount of time has elapsed between each spark
(Δt 1 = Δt 2 = Δt 3 , etc.), the distance traveled by the marker keeps getting bigger (Δx1 < Δx2
< Δx3 , etc.).
Make sure that you have not skipped any data points. If it is obvious that there is a point
missing, from the spark tape, then you should label accordingly (for example, 15/60sec may
be followed by 17/60 sec, if the 16th dot is clearly missing).
Questions
1. Calculate the speed of the marker at each time interval. The units will be cm/s:
Include this calculated value in your data table, which should look something like this:
Spark
Time (s)
Δt (s)
Δx (cm)
v (cm/s)
1
1/60
1/60
1.0
(60)(1.0) = 60
2
2/60
1/60
1.4
(60)(1.4) = 84
3
3/60
1/60
1.6
(60)(1.6) = 96
The values in this table are similar to, but will not be identical to your values; every spark
tape is unique! Your table will also be considerably larger; you will have about 25 or so data
on your spark tape.
2. Prepare a careful graph of speed as a function of time. This means that speed belongs on the
y−axis and time is plotted on the x−axis. Scale your axes carefully, and apply your scale
consistently. Use an entire page; make your graph very large to maximize the accuracy of the
scale. Label your axes (include units).
3. Use a ruler to draw the best fit line for the data. Do not force the line to pass through the
origin or any other point; let the data decide where the line belongs! When the line is drawn,
find the slope:
where (ti, vi) and (tf , vf ) are two points that are exactly on the line you have drawn. They do
not have to be data points, but they do have to be on the line!
4. Compare the value of the slope of your graph with the known value for the acceleration due
to gravity. Calculate the percent error in your slope:
5. Is every data point precisely on your best−fit line? Are there points a bit below and a bit
above the line? Does this mean that whoever was measuring with the ruler was doing a
careless job and making mistakes?
6. It is very simple to show that when you drop a tennis ball, it hits the ground sooner than a
feather dropped at the same time from the same height. Does this mean that the acceleration
due to gravity depends on how heavy an object is? Is there something else happening at the
same time? What?
7. Try this: hold a sheet of paper vertically, and let it fall to the floor. Take the same sheet, and
hold it horizontally. Compare what happens when you release this same object the second
time.
8. In your own words, explain the concept of acceleration. Think about this: when the light
turns green, you hit the gas. Are you accelerating? What is happening to the speed of your
car? The next light just went red, so you hit the brakes. Are you accelerating? What is
happening to the speed of your car?
PHYSICAL SCIENCE SUMMER 2008
GOLF BALL DROP LAB 03
STUDENTS’ NAMES
Set Up
Obtain a meter stick and golf ball.
Experimental Procedure
1. Hold the golf ball center 20 centimeters above the table
in front of a vertical meter stick.
2. Drop the golf ball.
3. Measure the maximum height of the first bounce.
4. Record the drop height and bounce in centimeters in the
table below.
5. Repeat the procedure for 40 cm and 60 cm.
6. Drop the golf ball on the floor from 80 cm, repeating the
rest of the above procedure.
7. Continue dropping the golf ball on the floor for 100 cm,
120 cm, 140 cm, and 160 cm.
8. Find the mass of the golf ball in grams:
__________________
Table
Drop Height/cm Bounce Height/cm *** Drop Height/cm Bounce Height/cm
20
____________
*** 100
____________
40
____________
*** 120
____________
60
____________
*** 140
____________
80
____________
*** 160
____________
PHYSICAL SCIENCE SUMMER 2008
GOLF BALL DROP LAB 03
STUDENTS’ NAMES
Graphing the Data
1. Graph the drop height in cm on the x-axis and the bounce height in cm on the yaxis.
PHYSICAL SCIENCE SUMMER 2008
GOLF BALL DROP LAB 03
STUDENTS’ NAMES
Calculations
1. Fit a best line to the points.
2. Determine the slope.
a. Pick two points, one near each end of the best fit line.
b. Determine the coordinates of the two points, (x1 , y1) and (x2, y2)
c. Use the formula for determining the slope from two points to obtain the
slope:
m = (y2- y1) / (x2- x1)
slope m = __________________
3. Determine the y-intercept.
a. Use the formula for determining the slope from two points to obtain the
slope:
(y - y1) = m(x - x1)
y-intercept = _____________
4. Determine the potential energy at the start of the 160 cm drop.
a. The potential energy of the golf ball can be calculated from PE = mgh
where m is the mass of the golf ball in grams, g is the acceleration of
gravity (980 cm/s2), and h is the height of the golf ball above the ground in
centimeters. The mass of the golf ball was determined above. Calculate
the potential energy of the golf ball when it is 160 cm above the ground:
PE = mass*(980 cm/s2)(160 cm)
PE160 = _____________
5. Determine the potential energy at the top of the first bounce after the 160 cm
drop.
a. Calculate the potential energy of the golf ball at the top of its first bounce
after a drop of 160 centimeters using the data collected in the laboratory
above.
PEfirst bounce after 160 drop = _____________
PHYSICAL SCIENCE SUMMER 2008
GOLF BALL DROP LAB 03
STUDENTS’ NAMES
Questions
1. What will the bounce height in centimeters be for a drop height of 200 cm?
2. What will the bounce height in centimeters be for a drop height of 4 meters?
3. What will the bounce height in centimeters be for a drop height of 0 cm?
4. Did the golf gain or lose energy between the drop from 160 cm and the top of the
first bounce?
5. Energy being conserved, into or from what form was the energy difference
converted between the drop from 160 cm and the top of the first bounce? In other
words, what happened to the energy difference? If the ball gained energy, where
did it come from? If the ball lost energy, into what other forms of energy was the
energy converted?
Physical Science Summer 2008
Burning Food Lab 04
Personal Form
Today you will measure the caloric content of some common junk food. You will
use the temperature rise in a known mass of water to determine the amount of heat
released by burning the food.
Procedure:
1) Mass a portion of junk food to the nearest 0.01 gm.
2) Position the portion of junk food on the stand under an aluminum can hanger.
3) Mass at least 50 gm of water to the nearest 0.01 gm, in the aluminum can hanger.
4) Record the initial temperature of the water.
5) Light the portion of junk food on fire. Stir the water in the can while the portion of
junk food is burning.
6) Measure the temperature of the water after the portion of junk food has completely
burned. Don’t let the thermometer touch the bottom of the can while you measure the
temperature.
Analysis:
1) Calculate the number of calories that were required to increase the temperature of the
water in the can. To do this you will need to use the specific heat of water 1.0 kcal/kg oC.
2) Determine the food calories per gram in the portion of junk food and compare this to
the value listed on the bag.
3) List possible sources of error in your measurement of the energy released by the
portion of junk food as it burned. How could the measurement be improved?
PHYSICAL SCIENCE SUMMER 2008
Electric Circuits LAB 05
STUDENTS’ NAMES
In this week’s lab you will be working with series and parallel circuits. In a
series circuit, there is only one path for the current to follow while in a
parallel circuit there is more than one path for the current to follow.
The figure above is an example of a series circuit. The first part of this
experiment we will explore more details about a series circuit. Let’s get
acquainted with the equipment.
Apparatus list:
DC Power supply (observe the +’ve and –‘ve signs on the power supply)
DC Ammeter (observe that there are two different scales – you will be using
the smaller scale. Can you identify which connection you will be using?
Digital Multimeter (observe the Ω and the V symbols- you will be using the
settings on these to take measurements of the voltage and the resistance)
Bulbs
Connecting wires ( observe the different types. There are pin connectors
and ones with jaws. The ones with jaws are called alligator clips!)
Spend some time with your lab group identifying the different components
that you will be using to build your circuits.
Activity 1
Series Circuit
1. First let us get some information from the power supply. Connect the
power supply to the electrical outlet and turn it on. Using the digital
multimeter with the selector knob on the Volts side (green side) at
the number 20, place the probes from the multimeter across the +’ve
and –“ve pins on the power supply. Make sure your power supply is at
the 3V setting. Record the voltage across the power supply in the
table below.
2. Starting with the –‘ve pole on the DC Power Supply, connect a pin
connector from this point to the –‘ve on the DC ammeter.
3. Using an alligator clip connect the 1A connector on the ammeter to
one end of the light bulb.
4. Using another alligator clip connect the other side of the light bulb to
the +’ve on the power supply.
5. Congratulations you have just completed your first series circuit.
Please let Dr. Walker check your connections before turning on the
power supply!!!
6. Now that your connections are correct you are ready to start making
measurements.
7. Using the digital multimeter, turn the selector knob to the side that
measures volts (the green side). Put it on the 20V setting.
8. Place the two probes from the multimeter across the bulb. Measure
the voltage reading. Record in the table 1 below.
9. Record the current measure in the ammeter.
10. Repeat the measurement for the power supply setting on 4.5 V
11. Draw a diagram of your circuit.
TABLE 1 : ONE BULB SERIES CIRCUIT
Power supply
setting (V)
Actual
reading of
voltage from
power supply
(V)
Voltage (V)
drop across
bulb
Current (I)
measured in
ammeter
Resistance. R
= V/I
(Ω)
Activity 1 Questions:
1. Did the brightness of the bulb vary when the power supply was
increased from 3V to 4.5
volts?________________________________________
2. Why do you think this was
so?__________________________________________________
____________________________________________________
____________________________________________________
_______________________
3. What do you notice about the difference in the current when the
voltage was
increased?____________________________________________
____________________________________________________
_______________________________
4. What do you notice about the voltage supplied by the DC power supply
and the voltage across the
bulb?________________________________________________
____________________________________________________
____________________________________________________
________________________
Activity 2- Two bulbs in series.
1. Turn off the power supply.
2. Remove the connectors. Let us restart.
3. Repeat Nos. 2 and 3 from Activity A.
4. Using another alligator clip, connect the other end of the light bulb to
one end of a second light bulb.
5. Connect the end of the second light bulb to the +’ve connector on the
DC Power supply.
6. Turn the voltage selector knob on the DC Power supply back to 3 V.
7. Have your connections checked before continuing.
8. Now that your connections are correct, turn on the DC Power supply.
9. Using the multimeter like you did before in the voltage setting, record
the voltage drop across each bulb. Label these bulbs, bulb 1 and bulb
2.
10. Record the current in the ammeter and fill in the table 2 below.
11. Draw a circuit diagram for this arrangement.
TABLE 2: Two bulbs in series
Voltage
on DC
Power
Supply
(V)
Actual
Voltage
measured(V
)
Voltage
(V1)
across
Bulb 1
Voltage
(V2)
across
Bulb 2
Current
(I) in
the
Circuit
(A)
R1 = V1/I R2 = V2/I
(Ω)
(Ω)
Activity 2 Questions:
1.2 How did the brightness of two bulbs in series compare with one bulb with
the same
voltage?___________________________________________________
_________________________________________________________
_________________________________________________________
_________________________
2.2What happened to the brightness of the bulbs when the voltage was
increased?_________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________
3.2 How does the current in the circuit differ between a circuit with two
bulbs in series and a circuit with one bulb? Why do you think this is
so?______________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________
4.2 Is the voltage drop across each bulb the same as the supplied
voltage?___________________________________________________
_________________________________________________________
_________________________________
5.2 Add the voltage drop across bulb 1 and bulb 2 in the two-bulb series
circuit, with a 3V DC Power supply. What do you notice about the sum of
these voltages, are they close to the voltage supplied bye the power
supply?_____Sum=___________________________________________
_________________________________________________________
________________________________
6.2 Repeat the calculation in 5.2 for the voltage drop across the light bulbs
when a 4.5 V supply is used, do you notice a trend? What is
it?_______________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Activity 3: Light bulbs in parallel
1. Turn off the power supply.
2. Disconnect all the wires.
3. Let us connect a parallel circuit.
4. Repeat steps 2 and 3 from Activity 1.
5. Using an alligator clip, connect the same side of the light bulb 1 that is
connected to the ammeter to a light bulb 2.
6. Using another alligator clip connector the other side of light bulb 2 to
the second side of light bulb 1.
7. Finally, make a connection using an alligator clip from this second side
of light bulb 1 to the +’ve on the DC Power supply.
8. Check your connections.
9. Congratulations you have completed your first Parallel circuit.
10. Now let us get some data!!!
11. Record the current measured by the ammeter.
12. Using the Digital Multimeter with the setting on the green voltage
side at number 20, place the probes across bulb 1 and record the
voltage.
13. Repeat this for bulb 2.
14. Record your measurements in the Table 3, below.
Voltage
setting on
power supply
(V)
Actual
voltage
recorded (V)
Voltage drop
across bulb 1
(V)
Voltage drop
across bulb 2
(V)
Current
reading on
ammeter (A)
Activity 3 Questions:
1.3 What do you notice about the voltage across each bulb when connected in
parallel, are the almost similar to the supply
voltage?___________________________________________________
_________________________________________________________
_________________________________________________________
_________________________
2.3What do you notice about the current in the circuit when the bulbs are
connected in parallel compared to the bulbs connected in
series?____________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Summary of Lab:
Write a paragraph on what you have learned based on your measurements
and calculations.
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 06: The Speed of Sound in Air
Introduction
It is possible to investigate
sound waves by creating
standing waves in a column
of air. If the air column is
driven by a sound wave of the
right frequency, a standing
wave will be produced in the
column which results in an
audible tone. The process is
closely related to what
happens in a wind
instrument like a flute,
clarinet, trombone, or organ.
We will use a glass tube
partially filled with water. The
water level represents a
closed end of the air column,
and can be varied in order to
adjust the length of the
column. If we hold a
vibrating tuning fork over the
column and vary the water
level, we will hear a louder
sound whenever the column
length is right for standing
waves at the frequency of the
tuning fork.
The water line is always a
node, having zero amplitude.
When the sound is the
loudest, the amplitude of the
wave is greatest at the mouth
of the tube. The actual
position of the node will
depend on the wavelength,
but the relative spacing of the
resonances will always be the
same fraction of a
wavelength, either ¼λ or ½λ.
Equipment
Objectives
Create a standing wave in an air column
Observe the change in the wave pattern when the
column length is changed
Use these observations to calculate the speed of sound
Calculate the amount of error in an experimental
value
Predict the frequency of an unmarked tuning fork
Thermometer
Two tuning forks of known
frequency
Rubber strike plate
Masking tape
Glass column connected to a
water reservoir
Overflow pan
Procedure
1. Work in groups of four; you will need that many
people cooperating simultaneously to use the
apparatus correctly and record accurate
measurements.
2. Make sure that the column and stand are on the floor,
in the overflow pan.
3. Adjust the reservoir on the stand until it is at the top
of the glass column. Fill the reservoir until the water
level in the column is within about 10cm of the top.
This should give you enough water to work with and
avoid overflows.
4. Strike a known tuning fork on the rubber strike plate
to make it vibrate. Do not strike the fork against the
glass tube or the lab table or your lab partner's
forehead. Hold the fork over the open end of the glass
tube.
5. Starting with the water in the tube at its highest level,
gradually lower the water level by lowering the
reservoir. Use masking tape to mark the water levels
where the sound is loudest as you increase the length
of air in the column. You should have a long enough
tube to hear three resonances with each fork.
6. The highest water level (shortest air column) is
approximately (¼λ) below the top of the tube, but the
distance between successive levels is quite accurately
(½λ). Use the meter stick to measure the distance
between successive resonances and record them.
Measure from tape to tape.
7. Repeat the measurements for the second known
tuning fork.
8. If you have not already, make sure you have arranged your data into a neat table with all of
the quantities labeled (include units!).
Frequency y (m) λ = 4y (m) y (m) λ = 2y (m) y (m) λ = 2y (m)
1
1
1
2
2
2
3
3
3
(Hz)
λav m
384
512
9. Make sure you remove every molecule of masking tape from the glass column before you
leave.
Calculations
1. The speed of sound waves in gases depends on the type of gas and on the temperature. For
ordinary air it is:
where T is the temperature in o C. Record the air temperature, and use it to calculate the
actual value for the speed of sound.
2. Calculate the average wavelength for each of the two tuning forks.
3. The speed of the sound wave with wavelength λ and frequency f is:
Calculate the average speed of sound for each of the two known tuning forks, using the
average value for each wavelength.
4. Calculate the percent error for each of these average values:
Questions
5. How do the average speeds compare the the theoretical value calculated? Are your values
high or low? Are the errors in each value similar?
6. Why is it typically more accurate to calculate the speed using the higher frequency fork?
7. You measured each resonance with respect to the previous one (tape−to−tape). If you
measured each resonance with respect to the top of the tube, would this increase or decrease
your accuracy? Why? (Note that you would have to calculate the wavelength a little
differently, but it could be done.)
8. If the temperature in the room suddenly increased, what would happen to the speed of the
wave? How would this affect the wavelength?
9. Would you expect the speed of sound to be greater through air or water? Explain.
10. Suggest two ways to improve your measurements or your technique to achieve more
accurate results. (Remember, accuracy is about technique--your measuring tools are
definitely precise enough!)
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 08: Reflection and Refraction
Activity 1: Plane Reflection
Set up the optics bench so that you
have a single ray of light striking
the plane mirror (detailed
instructions provided in lab).
Rotate the ray table so that the
incoming beam makes a 10° angle
to the mirror, and record the angle
of reflection.
Repeat for several more angles,
recording both the angle of
incidence and angle of reflection.
Questions
1. Sketch the the incoming and
reflected light beams, showing the
relationship between the angle of
incidence and the angle of
reflection. Use a ruler and
protractor to make an accurate
diagram.
2. Is there any angle of incidence for
which the angle of reflection is not
equal?
Activity 2: Curved Mirrors
Set up the optics bench so that you have
multiple parallel beams of light. The beams
should be aligned along the normal on the
ray table.
ray table.
Place the plane mirror on the ray table so
that the beam is reflected straight back at the
source. This shows that you are properly
aligned.
Replace the plane mirror with the convex
mirror, and note the direction of the
reflected beams.
Replace the convex mirror with the concave
mirror, and note the direction of the
reflected beams.
Questions
3. Use the ruler and protractor to make an
accurate sketch of the incoming and
reflected beams for each of the mirrors.
4. Does the rule that angle of incidence = angle
of reflection apply to curved mirrors?
Explain.
5. Which mirror could also be called a
converging mirror? Which mirrorcould be
called diverging?
Activity 3: UFO Mirror
Examine the curved dish containing the
pennies.
Questions
6. Where does the image of the
pennies appear? Is it inverted? Is
this a real or virtual image?
Activity 4: Snell's Law
Set up the optics bench so that you
have a single ray striking the
cylindrical lens on the ray table.
Initially, the ray should be aligned
along the normal and incident on
the flat side of the lens.
Rotate the platform for an angle of
incidence of10°. Record the angle
of refraction as the beam emerges.
Repeat for angles of incidence 20°,
30°, and 40°.
Questions
7. Sketch the path of the light beam
from the source until it exits the
cylindrical lens.
8. If the beam strikes the tank
perpendicular to the tank (0° on
the marker), is the beam refracted?
Why not?
9. How does changing the angle of
incidence affect the amount of
refraction? Include this on your
sketch.
10. Use Snell's Law to determine the
index of refraction of the glass lens:
In our example, air is the incident
medium (1) and the glass lens is
the refracting medium (2). This
means that n 1 = 1, and n 2 is what
you are finding.
Activity 5: Total Internal Reflection
Set up the optics bench so that you have a
single ray striking the cylindrical lens on
the ray table. Initially, the ray should be
aligned along the normal and incident on
the curved side of the lens.
Slowly rotate the ray table until there is no
emergent beam: all of the light is reflected
back. Record the angle.
Questions
11. What is the critical angle for total internal
reflection?
12. It can be shown using Snell's Law that the
critical angle can be determined if the
indices of refraction are known:
In our example, the glass lens is the
incident medium (1), and air is the
refracting medium (2). So n 2 is the index
of refraction for air (n 2 = 1). Use the above
equation to find the index of refraction for
the glass lens (n 1).
13. How does the value of of the index
compare to the value you calculated in
Activity 4? Which value do you think is
more accurate? Why?
14. If the index of refraction for water is n 1 =
1.3, will the critical angle for total internal
reflection be greater than or smaller than
the critical angle you recorded for glass?
Physical Science
Lab 08
Summer II 2008
M&M®
Half-Life Laboratory
We will look at the determination of half-life for a bunch of M&M’s®. You will be using fresh M&M®
candies (they are straight out of the bag, no one else has touched them). Recall from class that the radioactive
decay of an atomic nucleus is a random occurrence. There is no way of looking at a specific atom and
determining when it will decay. We are going to model this process by “rolling” M&M® candies onto a paper
plate. If the individual candies represent individual nuclei, we can determine which have decayed by looking
for the “m” when they are on the plate. Our unit of time for this lab will be the “roll.” As a class, we will build
up the decay curve for a large number of M&M’s® (this will help with the statistics) and from that determine
the half-life of these M&M’s®.
Materials:
• One Styrofoam Cup
• Two Paper Plates
• A Bunch of Plain M&M® candies
Procedure:
1) Dump your M&M’s® on to the paper plate. Remove any candies that do not have an “m” on them (you
can eat these as they are defective). Count the number of candies that are left.
# of M&M® candies
2) Put your candies back in the cup, shake them up and down a couple of
times and dump them back out onto the paper plate. Remove all the
candies that have the “m” showing to the second paper plate, these
M&M’s® have “decayed.” Count the number of candies left (these
have not decayed). Repeat this process until all of the candies have
decayed. Keep track of the number of candies left after each roll.
Looking at the results for the entire class, what is the half-life of a
“radioactive” M&M®?
Radioactive Measurement
Roll #
Candies Left
0
1
2
3
4
5
6
7
8
9
10
11
12
Physical Science
Lab 08
Summer II 2008
3) Next we will simulate the lifetime of a radioactive isotope in the
body. Your body is continually replacing its atoms with new ones.
This is also a random process and there is a half-life associated with
the different elements in your body.
Partition your plate into four equal sized sections. Mark one of these
sections as the “Flush” section. Dump all of your M&M’s® onto the
plate and remove the one’s in the “Flush” section. This represents
atoms that have been replaced by the body. Count the number of
candies left and enter them into the table on the right. Repeat this
process until there are no candies left.
Looking at the results for the entire class, what is the biological half-life
of an M&M®?
4) In the body the, there are two processes that will remove a
radioisotope. One is the normal radioactive decay governed by the
half-life of the isotope. The second is the biological half-life of that
element in the body. When these two processes are combined they
provide a half-life for a radioisotope in the body that is shorter than
either the radioactive half-life (t1/2) or the biological half-life (tb)
teff = (t1/2tb)/(t1/2+tb)
5) Repeat (3) but this time, remove all candies in the “Flush” region and
all candies in the other regions that have the “m” showing. Count the
number of candies left after each roll and record this in the table to the
right. Repeat until all the candies are gone.
Biological Measurement
Roll #
Candies Left
0
1
2
3
4
5
6
7
8
9
10
11
12
Effective Half-Life
Roll #
Candies Left
0
1
2
3
4
5
6
7
8
9
10
11
12
Looking at the results for the entire class, what is the effective half-life of an M&M®?
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 09: Spectroscopy
Introduction
Why do neon lights glow? That, and why do they glow in
different colors? First the glow: a neon tube is sealed and
contains atoms of gas (neon, or maybe something else−more
on that in a minute). When a voltage is applied, the tube
begins to glow: flip the switch, the light comes on. The gas is
energized by the voltage: all the neon atoms are the same,
which means that the electrons of all the atoms exist in orbits
with the same energy levels. Whatever precise amount of
energy it takes to move an electron from one orbit to another,
it's the same for all the neon atoms. So what you are seeing as
the glow is electrons jumping from one energy level to
another. As they fall back down to their original orbits, they
emit an exact amount of energy in the form of a photon.
When the millions of atoms in the tube all do this at the same
time, all those emitted photons create the glow.
Now about the color. We know that the orbits correspond to
precise energy quanta. But the quantum of energy is different
for electrons belonging to different types of atoms. It does
not take the same amount of energy to move an electron from
one orbit to another in a hydrogen atom as it does to move
between orbits in a neon atom. Different energy, different
color. Neon glows strongly red, but mercury glows strongly
blue. So it's not always actual neon in the neon light; it may
be argon (with mercury particles), helium (yellow-gold) or
even CO 2 ; (bright white).
Objectives
View emission−line spectra of various elements
Identify elements based on the pattern of emission lines
Associate wavelengths of visible light with color
Correlate the color of emitted light to the temperature of an
object
Equipment
Handheld spectroscope
Gas−filled lamps
Procedure
Point the slit of the spectroscope directly at the gas−filled
lamp
View the emission lines that appear, and record their color
and wavelength
Note the color−code identification band on the lamp
Repeat for the remaining lamps
Questions
1. Make a table of the lamps you have viewed, and use it to identify the vapor in each lamp.
You will need more rows for more lamps, and more columns for more observed emission
lines than shown below.
Color Band
Emission Line Wavelength (top) and Color (bottom)
Vapor ID
2. Use the table shown below to complete your identification of the lamps:
Strongest Emission Lines
Wavelengths in nm
Element
hydrogen
434
486
656
helium
447
471
492
502
588
668
707
neon
540
585
587
588
594
597
598
599
603
607
mercury
435
491
546
579
607
argon
416
420
428
435
476
488
497
617
642
697
krypton
409
427
429
432
436
446
473
477
557
587
sodium
570
589
615
610
3. The emission spectrum for cadmium (Cd) is shown below in color. Using your table that
correlates the color of the emission line with wavelength, label each emission line with an
approximate wavelength.
4. The temperature (measured in Kelvins) of an object can be determined by noting the
wavelength of its strongest emission (brightest color):
with λmax measured in nm. Find the temperature of
A. a red star with λmax = 650nm.
B. a blue star with λmax = 425nm.
C. a block of ice, with λmax = 104 nm.
640
651
The University of Central Arkansas
Department of Physics and Astronomy
PHYS 1400: Physical Science
Summer II 2008
Lab 10: Measuring the Size of a Molecule
Introduction
Atoms and molecules are small. No, really. So small that you cannot see them with the unaided
eye, which makes their size all the more difficult to measure. However, using some simple
materials and methods, we can get a pretty reasonable approximation of the size of a molecule.
First, though, we will use a similar technique to determine the thickness of a sheet of aluminum
foil, which is too thin to measure directly using the meter stick.
Objectives
Learn to combine direct and indirect methods of measurement
Become familiar with formula notation for complex molecules
Further explore the relationship between mass, volume, and density
Perform calculations using numbers in scientific notation
Examine experimental results for credibility and identify the limits of experimental accuracy
Equipment
Square of aluminum foil
Triple−beam balance
Ruler
Oleic acid, motor oil
Lycopodium powder
Pan of water
Transfer pipette
Activity 01: Thickness of Foil
Using the ruler, measure and record the length and width of the square of aluminum foil.
Weigh the foil on the balance, and record its mass in grams.
Questions
1. Using 2.7g/cm 3 as the density of aluminum, calculate the volume of the sheet of foil:
2. The volume of the aluminum is shown below. Use your recorded length and width, along
with the volume you just determined, to calculate the height, or thickness of the sheet.
3. Why could we not simply use the ruler to measure how thick the foil is?
4. Is the thickness (height) of the sheet of foil the same as the size of an aluminum atom? In
other words, is the sheet of aluminum foil exactly one atom thick?
Activity 02: The Size of an Oleic Acid Molecule
Oleic acid is a monounsaturated omega−9 fatty acid.
Huh? Olive oil! Olive oil and grapeseed oil are largely
made up of this stuff. This is the fat that does not clog
your arteries and kill you, it raises your good
cholesterol. Chemically, it has the formula C 18 H 34O2 ,
which tells you that it takes a lot of atoms to make one
oleic acid molecule. Written this way:
CH 3 (CH 2 )7CH=CH(CH 2 )7COOH, it tells you just how
all those atoms are stuck together. In fact, it tells you
that the molecule is formed by joining multiple
molecules together. The molecular structure is shown
on the left, and "reads" from left to right, just like the
molecular formula.
When a drop of acid is placed on the surface of water, it
will spread out. It will continue to spread: the area of
the drop gets bigger. But at the same time, the
thickness of the drop decreases (because there's no
change in the total volume of the oleic acid). When the
droplet has spread as far as it can, the oleic acid will
exist in a monolayer on the surface of the water: the
thickness of the spread−out drop will be one molecule.
If we know the volume of the acid to begin with, we can
measure the area of the spread−out drop, and use the
same technique as we used for the foil to determine the
thickness. In this case, the thickness will match the size
of the molecule of acid.
Draw some oleic acid into the pipette.Holding the pipette vertically over the flask of acid,
allow a drop to form at the tip.
Quickly but carefully use the ruler to measure the diameter of the drop (d s). Let the drop to
fall back into the flask, and repeat with two more drops. Record each of the three drop
diameters in millimeters (mm).
Fill the pan almost full of water.
Sprinkle a light, even layer of lycopodium powder over the surface of the water. The
lycopodium is inert, but you probably don't want to eat it.
Hold the pipette vertically over the center of the pan, close to the surface, and allow a single
drop of oleic acid to fall onto the surface of the water.
Measure and record the diameter of the spread−out drop of acid in millimeters (d c).Because
the circular shape is probably not perfectly regular, measure three diameters in different
directions.
Questions
5. Find the average diameter of the three drops that you measured, and use this to calculate the
average radius of an acid drop:
6. Calculate the volume of the spherical drop. The units will be mm 3 :
7. This is not the actual volume of acid; because the solution is only 0.5% oleic acid, 99.5% of
that volume is actually something else (methanol)! The volume of acid is, then:
8. The spread−out acid is no longer shaped like a sphere; it is now a pancake shape, or a very
thin cylinder. However, the entire cylinder will be acid (the methanol evaporates almost
instantly). From your three measurements, calculate the average diameter of the cylinder,
and use it to find the radius:
9. The volume of a cylinder is defined as:
But the volume of the spread−out cylinder is exactly the same as the volume of the original
acid (Va = Vc), so we can calculate the height of cylinder directly:
Calculate carefully, and remember to keep track of your values for the sphere and cylinder!
10. Is your answer reasonable? Is it more likely that your answer is too large or too small? Why?
11. A single molecule of motor oil has about twice the diameter of a molecule of oleic acid. If you
added a drop of motor oil instead of oleic acid to the pan, would your "pancake" be larger or
smaller? Assume that you have initial drops of the same size (for this comparison, also
assume that your oleic acid is pure, not diluted with methanol).
12. An old riddle asks, how many angels can dance on the head of a pin? If we assume that an
angel is the same size as an oleic acid molecule, and the circular head of a pin is 2mm across,
how many angels will fit?