Download Unit 6 - A Property of Matter (Mass)

INQUIRY PHYSICS
inquiryphysics.org
A Modified Learning Cycle Curriculum
by Granger Meador, ©2010
Unit 6:
A Property of Matter (Mass)
Teacher’s Guide
Student Papers
Sample Notes
6 A Property of Matter (Mass)
Teacher's Guide
Inquiry Physics
Key Concepts
W eight is the result of gravity acting on an object.
Mass is the quantity of m atter in an object and is responsible for its inertia.
Acceleration is inversely proportional to the m ass being accelerated when a constant force is applied.
Student Papers
Lab A: The Inertial Balance
Metal Plates Version
Cylinder Version
Reading: Mass - Not A W eighty Matter
W orksheet: “The Vom it Com et”
Lab B: Mass and Acceleration
Air Track Version
Air Track Lab Report Version
Dynam ics Cart on Floor Version
Dynam ics Cart and Table Pulley Version
Introduction
To this point in the course, the concept of m ass has not been m entioned, and if brought up by a student, it
has not been pursued. Hence the title of the unit is “A Property of Matter” and not “Mass”, as you do NOT
want to give them the idea of m ass until the discussion phase of 6 Lab A.
Using weight up to this point is justified by students' grasp of that concept from life experience: weight is
how heavy an object is. Their conceptual understanding of m ass is often quite lim ited and flawed. This
investigation forces the students to address the m ass concept, which in turn dem ands a better definition of
weight. The investigation also has students discover the relationship between m ass and acceleration
when the applied force is constant.
Take care to also NOT invent F=m a in this investigation, and for now ignore the issue if students bring it
up. That law will be invented in the next investigation, using both Unit 5 Lab B and Unit 6 Lab B.
LAB A: THE INERTIAL BALANCE
Exploration
Equipm ent for each group (of 3 to 4 students):
Inertial balance of either style: one style has an attachable
cylinder, another has m etal pieces that clam p onto
the balance (you can also just add sm all C-clam ps to
any style balance, or you can m ake your own
balance with a shielded saw blade (see NASA
activity in the “acrobat/Other Resources”
subdirectory on the Inquiry Physics CD; use the
appropriate version of the lab, m odifying as needed
C-clam p
thin board to protect desk/counter surface
stopwatch
ruler
500 g m ass and m asking tape (or a big clam p) for single-cylinder balances
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I’ve seen and used two styles of inertial balance. One uses a m etal cylinder that inserts in a hole in the
pan, while the other clam ps m etal pieces onto the pan. I’ve included a version of the lab instructions for
either style, and you can even m ake your own version as shown in NASA’s Inertial Balance lab on the
Inquiry Physics CD in the “acrobat/Other Resources” subdirectory.
Just m odify the W ord or W ordPerfect version of m y lab to m atch your equipm ent, including playing around
with how far to have the students pull aside the pan and how long to tim e it to find out what works best for
you.
Tim ing the unloaded balance when the springs are stiff can be a challenge for the students, and they m ay
com plain about that. Insist that they devise a procedure to get as accurate a count as possible. The
actual num bers they obtain really are not very im portant; the crucial bit of data is that the counts go down
as m ore "weight" is added to the balance. (One m ethod of obtaining an accurate count for the unloaded
balance is to attach an index card to one side and have it oscillate in front of a m otion detector with
com puter interface; a d vs. t graph of the m otion can be studied to count the oscillations. Or sim ply have it
lightly tap against a piece of paper held up beside it to facilitate counting, although this can dam p out the
m otion.)
The Idea
Inventing the concept of m ass and the differences between weight and m ass require class discussion.
Part of that discussion focuses upon extracting key ideas from investigations 3 through 5. This lab is a
wonderful opportunity to confront students with a phenom enon that cannot be explained by weight, but
only by m ass. W eight cannot directly affect horizontal m otion (a concept the students should have
grasped in their study of projectile m otion), so it cannot explain why loading the balance up causes it to
oscillate m ore slowly. Only m ass can explain this, and you should allow the idea of m ass to be invented
by the students; do NOT accept flawed reasoning on their part to bring weight into the answer, and do
NOT sim ply give them the idea of m ass. They will be able to construct the idea given tim e and a thorough
class discussion of the questions on the lab. Also, do not attem pt to introduce the concepts of frequency
or period in this lab - focus on the m ass concept.
Sample Answ ers for Lab A: The Inertial Balance
1.
W hat is the direction of the acceleration vector of a falling object?
It is downward (toward the center of the earth).
2.
W hat is needed to cause an object to accelerate?
An unbalanced force.
(The students know about vectors, so you can stress the importance of an unbalanced
force here.)
3.
W hat force causes the acceleration of a falling body?
Gravity causes the acceleration of a falling body.
(Technically, the acceleration arises from the interaction of the object and the gravitational
field, but such distinctions are not important here.)
Now the investigation introduces the concept of w eight, taking it beyond the idea of how heavy an
object feels. The students need to realize that w eight is a vector that points dow nw ard, a key idea
if they are to properly interpret the inertial balance data. W eight pushes dow n, w hile the spring
force on the balance is sidew ays, and the dow nw ard w eight vector is cancelled by an upward
force from the platform on the balance.
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4.
The term that is used for force due to gravity on any object is w eight. So the force due to gravity
on you is your
5.
weight.
Sum m arize the results of the lab. (How did the added objects affect the num ber of oscillations?)
Adding objects decreased the number of oscillations.
6.
W hat is the first explanation you can think of for this data?
answers will vary
(M any students w ill say that the increased w eight slow ed the balance; that will suffice until
they are confronted w ith questions 7 and 8 and hopefully realize that explanation is
invalid.)
7.
W hat effect does gravity have on the m otion of the balance? Think about the direction of gravity
and the direction the balance m oved before answering. Explain your answer com pletely.
Gravity cannot affect the motion of the balance, because vertical forces
cannot affect horizontal motion (or because the force of gravity is being
cancelled by the upward push of the table/countertop/balance platform).
8.
Given your answer to question 7, what effect does w eight have on the m otion of the inertial
balance? Explain your answer com pletely.
Weight does not affect the motion of the balance, because weight is due to
gravity and gravity has no effect on the motion (or because weight is a
vertical force that cannot affect horizontal motion, or because the weight is
being cancelled by other forces).
9.
Your answers to questions 7 and 8 m ay have invalidated your initial response to question 6. If
your answer to question 6 is no longer valid, give the correct explanation below:
A greater mass will oscillate more slowly (greater mass accelerates less).
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Expansion of the Idea
After com pleting lab A, it is tim e to define weight and m ass in the students' notes and practice with the
various related units, equations, and conversions. You should also connect the idea of m ass with inertia.
See the sam ple notes for m y approach, although I’ve outlined the m ajor m ethods below.
M ass, W eight, Volume, Density Concepts
You can define each of the above with the students, perhaps indicating com m on units of each. Then
practice the distinctions by taking a Nerf ball and having the students consider various situations in a
signal exercise: Describe the situation, give the students a m om ent to consider, and then direct them to all
sim ultaneously show on their raised fingers how m any of the four quantities changed. Discuss the
answers with them , focusing on the students who gave im proper signals.
Situation:
Crush the
Nerf ball in
your hands
Say that you
are taking
the ball to
the m oon
Back on earth, toss the ball in the
air
Say you've ripped
off part of the ball
and thrown that
part away
Num ber of
Changes
2
1
0
3
Mass Effect
no change
no change
no change
sm aller
W eight Effect
no change
sm aller
no change (ignore slight variation
in gravity at different heights)
sm aller
Volum e Effect
sm aller
no change
no change (ignore m inute air
resistance distortions)
sm aller
Density Effect
higher
no change
no change (ignore m inute air
resistance distortions)
no change
M ass and W eight Calculations
You can introduce the equation F g=m g (be careful NOT to expand this equation into F=m a yet!) by
hanging a one kilogram m ass on a large newton scale. The students will notice that it weighs slightly less
than 10 N, and a bit of prom pting will lead them to:
9.8 N = 1 kilogram
which is im possible, for weight cannot equal m ass. So a correction can be inserted:
9.8 N = (1 kilogram ) (?)
and they will quickly suggest that the m issing factor is a 9.8, as in 9.8 m /s 2:
9.8 N (1 kg) (9.8 m /s 2)
and you can point out that translates to F g=m g, using F g for weight, m for m ass, and g for the acceleration
due to gravity. (I avoid using W for weight since later we’ll use that sym bol for work. And using F g here
m akes the leap to F=m a in the next unit that m uch easier.)
Then discuss the units of weight and m ass, and use your own weight to m ake the following calculations,
while the students duplicate your procedures in their notes, using their own individual weights. (Since they
are each doing their own work, they will not feel threatened by having their weight publicized.)
I weigh
pounds.
170 pounds
I weigh
newtons.
170 lb * (4.4482 N/lbs) = 756.19 N = 756 N
My m ass is
kilogram s.
m = F g/g = (756.19 N)/(9.8 m /s 2) = 77.162 kg = 77.2 kg
My m ass is
slugs.
m = F g/g = (170 lbs)/(32.2 ft/s2 ) = 5.2873 slugs = 5.29 sl
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I extend into how weight varies with location and m ass varies with speed (due to special relativity), using a
PowerPoint you will find in the PowerPoint directory on the Inquiry Physics CD-ROM. I also like to show
clips from an old 1994 video, W e’re Go for Launch to Zero-G , about the effects of “weightlessness” on the
hum an body and I show clips of folks and cats aboard the old Vom it Com et zero-g sim ulator aircraft. Do
an online search and you can find lots of clips. I’ve included a worksheet on that plane.
Here is how I introduce the idea that weight varies with location:
Location
Chicago
Panam a Canal
North Pole
Space Station
Moon surface
g
9.803 m /s2
9.782 m /s2
9.832 m /s2
8.71 m /s2
1.62 m /s2
My W eight There
F g = m g = (77.2 kg)(9.803 m /s 2) = 756.79 N
F g = m g = (77.2 kg)(9.782 m /s 2) = 755.17 N
F g = m g = (77.2 kg)(9.832 m /s 2) = 759.03 N
F g = m g = (77.2 kg)(8.71 m /s2 ) = 672.41 N /
F g = m g = (77.2 kg)(1.62 m /s2 ) = 125.06 N /
/ 4.4482
/ 4.4482
/ 4.4482
4.44822
4.44822
N/lb
N/lb
N/lb
N/lb
N/lb
=
=
=
=
=
170. lbs
170. lbs
171 lbs
151 lbs
28.1 lb
Sample Answ ers for the Reading: M ass - Not A W eighty M atter
1.
W hat is an unbalanced force? W hat does an unbalanced force do to an object? (Be exact.)
An unbalanced force is one which is not balanced by another force. It
causes an object to accelerate.
(Do not accept "move" in place of accelerate.)
2.
Victor Vector weighs 650 newtons, while Velm a Velocity weighs 750 N. W ho has greater inertia?
Describe your entire train of logic which led you to that conclusion.
Velma has more inertia, because she weighs more and thus has more
mass and thus has more inertia.
3.
Suppose you were in a w eightless environm ent. If you looked in a m irror, would you appear any
thinner? Justify your answer.
answers will vary
(The simple answ er is that you w on’t be thinner since your mass is unchanged. But if
you’ve shown them some online clips about the effects of zero-g on the body, they may
know that you w ould appear thinner around the middle, as the body's organs tend to shift
upw ard into the abdomen in a w eightless environment and the spine lengthens by an inch
or tw o, w hile you appear fatter in the face, since fluids shift into the face and make it
puffy.)
4.
Under what condition did Einstein say the m ass of an object would increase?
Mass increases as speed increases (near light speed).
5.
Describe a situation in which knowing the m ass of an object would be preferable to knowing its
weight. Be specific and creative! Explain your answer, and be careful not to confuse m ass
with volum e.
answers will vary
(Do not accept answers which confuse mass w ith w eight, or mass w ith volume. Correct
answ ers w ill often deal w ith motion in space or w ith horizontal motions in general.)
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Sample Answ ers for W orksheet: The “Vomit Comet”
1.
The plane traces a parabola, so for half
of the “weightless” or “zero-gravity”
period the plane is actually rising
through the air, and falling during the
other half. Draw the vertical
displacement, velocity, and
acceleration graphs for the occupants
during the “weightless” sensation
period, recalling that they are not
really weightless, and are both rising
and falling.
2.
Suppose during one arc the occupants are “weightless” for a total of 20.0 seconds. So they spend 10.0 s
ascending and 10.0 s descending. Using the true acceleration of gravity of 9.80 m/s 2, calculate how far the
plane would fall in meters and then in feet (1 m = 3.281 ft) from vertical rest during the descending half of
its arc:
Fall in meters (m):
Fall in feet (ft):
show your work
= 490. m
= 1610 ft
3.
Let’s suppose that an occupant’s pre-flight weight was 175 pounds. Compute his mass in slugs, using F g =
mg where g is 32.2 ft/s2 . Stay in US Customary units throughout your calculation – do NOT convert to
SI/metric units.
4.
Now convert the occupant’s mass into kilograms, using the US-to-metric mass conversion factor in your
notes:
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Special Relativity
Students are fascinated by the bizarre effects of extrem e speeds due to special relativity (increasing
m ass, tim e slowing down, objects becom ing thinner in the direction of m otion). I like to introduce special
relativity with the PowerPoint on the CD and excerpts from a funny old 1957 film by Dr. Irwin Moon, The
Mystery of Time, which you m ight be able to to get from www.archive.org, but be aware that Dr. Moon had
a religious m otive and was covering m ore than special relativity; we only watch 16:42-23:00 of that video.
I refer students who want to delve m ore into special relativity and why it occurs to their textbook for details.
If som eone really gets into the topic, I loan them Martin Gardner’s great book on the topic, Relativity
Simply Explained (form erly titled Relativity for the Million).
Here is how one quantifies the concept from the reading that m ass varies with speed:
where c=3x10 8 m /s (186,000 m i/sec).
Speed
0
Concorde (m ach 2; 1354 m ph; 605 m /s)
Voyager Probe (37240 m ph; 16648 m /s)
one-half light speed
three-quarters light speed
99% of light speed
light speed
% of m ass increase
0
0.0000000002%
0.000000154%
16%
51%
600%
infinite; m atter cannot achieve light speed ("warp one")
LAB B: ACCELERATION vs. M ASS
Here the students explore how m ass, rather than force, affects acceleration. Make sure the results are
acceptable, for in the next investigation you will use the results of this lab and 5 Lab B to invent F=m a.
Equipm ent for each group (of 3 to 4 students):
Air track version:
1.5 m or longer air track with end pulley
2 red 300 g gliders and 1 gold 150 g glider with velcro on their bum pers (or carefully brought
together on an active air track and secured with paperclips)
stopwatch
string/fishing line
hanging weight holder
Dynam ics cart on floor version:
dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient m ass can save
lab tim e)
5 N and/or 20 N spring scale
m eterstick
long spring (perhaps cut a worn-out wave dem onstrator spring to 50 cm ; avoid Slinkies, which are
too large, and rubber bands, which don't have a constant force/stretch ratio)
tape (or thum btack or sm all nail) to secure spring to m eterstick
enough 1 kg m asses to bring loaded cart up to 6 kg
Dynam ics cart and table pulley version:
dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient m ass can save
lab tim e)
table pulley
string/fishing line
hanging weight holder
m eterstick
enough 1 kg m asses to bring loaded cart up to 6 kg
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It is best to begin the lab with the largest m asses and work downward, especially if using the dynam ics
carts on the floor, where holding the spring force constant is difficult with a low-m ass cart. The air tracks
will usually give good results, but the dynam ics carts are m ore problem atic, especially when used on the
floor. You m ay need to group data, drop highs and lows, and have them graph the class average, or even
send them back to recollect data if it is too poor the first tim e. For the air track and dynam ics cart with
table pulley versions, keep the pulling force sm all so that the later low-m ass runs don't becom e too fast for
the students to tim e.
Am ong other variants is using a dynam ics cart on a special grooved track. Som e schools use photogates,
sonic rangers, and the like to analyze the m otion. You can m odify the W ord or W ordPerfect versions of
the student handouts on the CD-ROM to m atch your equipm ent.
Lab Report Option
At this point, you m ay want to have the students write up their own lab report, with plenty of guidance and
support from you as to the proper form . I’ve included a lab report handout I use with m y AP Physics B
students when they do the air track version of the lab. I have their groups confer to answer the initial
questions on the sheet and then call groups aside to ask each student about the lab to ensure they have a
workable procedure and understand what is going on
If you go with the lab report option, here are the correct answers to the questions I ask of them before
allowing them to collect the data:
1.
W hat are the independent and dependent variables?
M ass is the independent variable; acceleration is the dependent. (Time is also
technically a dependent variable here.)
2.
W hat quantities will you hold constant, at what values, and how will you
accomplish that?
Force w ill be held at [w eight of w eight holder in new tons]
Distance will be held at [0.9 m or w hatever is practical]
Initial speed w ill be held at zero
3.
W hat data must you collect, and what standards of reproducibility will you
enforce? (How many trials will you take? How close must the data be before
continuing to another trial?)
Collect time for each run, requiring that there be three runs within 0.1 s for each
glider set.
4.
W hat is the best order to the data collection which will minimize human error?
Use the largest trains first, since they have the most mass and w ill be slow er and
easier to time, saving the short trains for last.
After the Sam ple Answers on the following pages, I’ve included the grading rubric I use for the lab report.
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W hat if my students do not have access to a computer or calculator for graphing?
Many of the graphs in this curriculum are linear, so students can sim ply plot the points by hand and
eyeball a best-fit line. Careful plotting and drawing of the best-fit line will yield equations with useful slope
values. However, in this lab they face an inverse relationship, and hand-drawn hyperboles are seldom
accurate.
If your students need to construct graphs by hand (or if the graphing software cannot handle inverse fits),
that need not prevent them from decisively determ ining the num erical relationship between acceleration
and m ass. They’ll just need to draw two different graphs - one to determ ine the type of relationship and
the second to find the num erical values in it. You will probably need to lead them through the process with
sam ple data or a class average.
1.
Plot the data and note the shape of the best-fit curve and its general meaning.
First have the students graph acceleration vs. m ass (acceleration on the y-axis and m ass on the
x-axis). Have them eyeball a best-fit curve to the data points, which should yield a reasonable
hyperbole with the axes as asym ptotes. You will then need to ask them to identify the
m athem atical m eaning of that shape, or lead them to realize that it im plies that acceleration is
inversely proportional to m ass.
2.
Re-compute for the discovered relationship and re-plot accordingly.
The next step is to test for that inverse relationship. The students will now com pute the inverse of
the m ass for each part of the experim ent. Then have them graph acceleration on the y-axis and
1/mass on the x-axis. If their data is good, the points should plot out in a roughly straight diagonal
line.
3.
An inversely proportional relationship will yield a straight line on the second graph.
Ask the students what the line m eans. It m eans that acceleration is directly proportional to the
inverse of m ass, which is the sam e thing as saying acceleration and m ass are inversely
proportional. Have them eyeball a best-fit line for the second graph. (Here is useful to rem ind
them that a best-fit line need not hit even a single plotted data point nor go through the origin. A
best-fit line runs through the “m iddle” of the data point distribution.)
4.
Using the slope of the best-fit line to obtain the relationship.
Once the students have drawn the best-fit straight line, have them com pute its slope. The
resulting equation will be a = k (1 / m) + b where a is the acceleration, k is the slope, 1/m is the
inverse of the m ass, and b is the graph’s y-intercept. Voila! They now have the sam e equation a
fancy com puter or calculator would have calculated when form ing a best-fit hyperbole to the
original acceleration vs. m ass graph.
5.
Use the results.
Now the students should be able to give fairly decent answers to the questions in the lab about
the equation of the graph and m ake decent predictions about the acceleration for various m ass
values. They m ust use the second graph (the linear one of a vs. 1/m ) to obtain decent
predictions, for the hand-drawn best-fit hyperbole on the first graph will likely be inaccurate.
Do NOT assum e students will easily follow all of this! A com m on error is thinking that the second graph
indicates acceleration and m ass are directly proportional, ignoring the inversion of m ass and its physical
m eaning. Som e students will sim ply go through the drill of m aking the graphs without thinking about what
they are doing, unless you question them verbally or in written form .
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Sample Answ ers for Lab B: Acceleration vs. M ass
1.
W hat happened to the acceleration of the gliders as you increased their m ass?
The acceleration decreased as the mass increased.
2.
Describe the shape of the curve on your graph. W hat kind of function does it represent?
The shape was hyperbolic, representing an inverse function.
3.
That shape/function allows you to predict how m ass affects acceleration. If the m ass was cut to
one-fourth of its previous value, what would the new acceleration be?
The acceleration would quadruple.
4.
W rite the full equation for your graph. Rem em ber to substitute the proper variable nam es for y
and x and to indicate the correct values for any constants. Rem em ber to round off values for
significant figures.
a=x/m
(x w ill vary, and should be close to the amount of force used, but don't point that out to the
students yet; if x isn't close to the force used, check for errors in the data)
5.
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration
for two values of m ass, one four tim es larger than the other. W rite down those values and then
com pare them m athem atically in a ratio. (Divide the larger acceleration value by the sm aller one.)
W rite your ratio down too, using 3 significant figures.
Accel. of
kg =
m /s2
Accel. of
kg =
m /s 2
Ratio =
to 1
answers will vary; the ratio should be close to 4 to 1
6.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to
question 3 to help you answer this question. Notice how we changed the m ass.)
The ratio should be 4 to 1.
7.
W rite in words the m athem atical relationship you have found between m ass and acceleration.
Mass and acceleration are inversely proportional.
(Do NOT accept "indirectly" in place of "inversely".)
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Grading Rubric for Lab Report Option for Lab B: Acceleration vs. M ass
I copy this page and cut it in half so that I have one strip for each student’s paper. Then I fill out the rubric as I grade the
lab and staple it on front of the report for return to the student.
6 Lab B: Acceleration vs. M ass
Lab Report Grading Rubric (45 points)
6 Lab B: Acceleration vs. M ass
Lab Report Grading Rubric (45 points)
___ General legibility; if typed, doubled-spaced (2 pts.)
___ General legibility; if typed, doubled-spaced (2 pts.)
Purpose (5 points)
Purpose (5 points)
___ Correct statem ent of relationship under study (4 pts.)
___ Correct statem ent of relationship under study (4 pts.)
___ Spelling, gram m ar, usage (1 pt.)
___ Spelling, gram m ar, usage (1 pt.)
Procedure (15 points)
Procedure (15 points)
___ Major equipm ent identified (1 pt.)
___ Major equipm ent identified (1 pt.)
___ Leveling of track m entioned (1 pt.)
___ Leveling of track m entioned (1 pt.)
___ Independent variable of m ass identified (1 pt.)
___ Independent variable of m ass identified (1 pt.)
___ Dependent variable of acceleration identified (1 pt.)
___ Dependent variable of acceleration identified (1 pt.)
___ Force held constant; value shown (2 pts.)
___ Force held constant; value shown (2 pts.)
___ Distance held constant; value shown (2 pts.)
___ Distance held constant; value shown (2 pts.)
___ Initial speed specified as zero (1 pt.)
___ Initial speed specified as zero (1 pt.)
___ Three trials within 0.1 s m entioned (1 pt.)
___ Three trials within 0.1 s m entioned (1 pt.)
___ Specified m ass decreased to im prove tim ing (1 pt.)
___ Specified m ass decreased to im prove tim ing (1 pt.)
___ Spelling, gram m ar, usage (1 pt.)
___ Spelling, gram m ar, usage (1 pt.)
Data (8 pts.)
Data (8 pts.)
___ Data table intelligible and com plete (2 pts.)
___ Data table intelligible and com plete (2 pts.)
___ Units shown on data or in header rows (1 pt.)
___ Units shown on data or in header rows (1 pt.)
___ Graph with correct best-fit curve (5 pts.)
___ Graph with correct best-fit curve (5 pts.)
Conclusion (15 pts.)
Conclusion (15 pts.)
___ Verbal statem ent of relationship m á 1/a (5 pts.)
___ Verbal statem ent of relationship m á 1/a (5 pts.)
___ Equation w/ proper variables, sig figs, values (6 pts.)
___ Equation w/ proper variables, sig figs, values (6 pts.)
___ System atic errors ID e.g. friction (3 pts.)
___ System atic errors ID e.g. friction (3 pts.)
___ Spelling, gram m ar, usage (1 pt.)
___ Spelling, gram m ar, usage (1 pt.)
TOTAL: __________
TOTAL: __________
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
FO R
U N IT 6: A P RO PERTY O F M ATTER ( M ASS )
P AG E 12 O F 12
INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 6:
A Property of Matter (Mass)
Student Papers
©2010 by Granger Meador
inquiryphysics.org
6 A Property of Matter
Nam e
Lab A: The Inertial Balance
Metal Plates Version
Introduction
When you step on a bathroom scale, you measure your weight. Many purchases we make, such as
meat and vegetables, are made in terms of weight. Bridges specify the maximum weight they can
support. Trucks are rated according to hauling weight limits. When a truck smashes into a building
or through a wall or fence, what property of the truck causes the damage? (Speed is not a property
of an object, merely a measure of its movement.) In this investigation, we will identify a property
of matter which is sometimes confused with weight.
The Inertial Balance
Clamp the inertial balance to the table with the C clamp as shown in the figure below. Place a
protective piece of wood between the balance and the table to prevent scratching. Set the
balance in oscillation by pulling it horizontally 5.0 centimeters to one side.
Count the number of complete oscillations (a swing
from the starting position, through the resting
position, and back to the starting position) occurring
in fifteen seconds. (You may need to let the balance
lightly strike a piece of paper in order to count the
number of swings.) Repeat the exercise once more,
and record your data in the table.
Next, load the balance with one piece of metal, securing it with the
eyebolt keeper. (Pass the nut of the keeper through the hole in the
platform and place the metal piece above the pan but below the collar
on the eyebolt. Tighten the wing nut down onto the collar while the nut
is pressed against the side of the hole so that the metal piece is held
securely.)
Repeat the measurements you made in the previous section. Take two readings. Record your data
in the table. Then load the balance with two pieces of metal and then three, repeating the
measurements as before.
Number of Oscillations in 15.0 Seconds
Trial
Unloaded
Balance
Balance w/ One
Metal Piece
Balance w/ Two
Metal Pieces
Balance w/ Three
Metal Pieces
1
2
Average
Unit 6: A Property of Matter, Lab A: The Inertial Balance
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter
Nam e
Lab A: The Inertial Balance
Cylinder Version
Introduction
When you step on a bathroom scale, you measure your weight. Many purchases we make, such as meat and
vegetables, are made in terms of weight. Bridges specify the maximum weight they can support. Trucks
are rated according to hauling weight limits. When a truck smashes into a building or through a wall or
fence, what property of the truck causes the damage? (Speed is not a property of an object, merely a
measure of its movement.) In this investigation, we will identify a property of matter which is sometimes
confused with weight.
The Inertial Balance
Clamp the inertial balance to the table with the C clamp as shown in the figure below. Place a protective
piece of wood between the balance and the table to prevent scratching. Set the balance in oscillation
by pulling it horizontally 10 centimeters to one side.
Count the number of complete oscillations (a swing
from the starting position, through the resting position,
and back to the starting position) occurring in fifteen
seconds. (You may need to let the balance lightly
strike a piece of paper in order to count the number of
swings.) Repeat the exercise once more, and record
your data in the table.
Next, load the balance with the metal cylinder provided. Repeat the measurements you made in the previous
section. Take two readings. Record your data in the table. Load the balance with a 500 gram weight, taping
the weight so that it will not shift as the balance oscillates. Repeat the measurements you made in the
previous section. Take two readings, and record your data in the table.
Number of Oscillations in 15.0 Seconds
Trial
Unloaded Balance
Balance w/ Cylinder
Balance w/ 500 g
1
2
Average
Unit 6: A Property of Matter, Lab A: The Inertial Balance
©2010 by G. Meador – www.inquiryphysics.org
The Idea
(FOR EITHER VERSION OF INERTIAL BALANCE )
answer all questions in complete sentences; remember “Affect” is usually a verb while “Effect” is usually a noun
1.
W hat is the direction of the acceleration vector of a falling object?
2.
W hat is needed to cause an object to accelerate?
3.
W hat force causes the acceleration of a falling body?
4.
The term that is used for force due to gravity on any object is weight. So the force due to gravity on you is your
_________________ .
5.
Summarize the results of the lab. (How did the added objects affect the number of oscillations?)
6.
W hat is the first explanation you can think of for this data?
7.
W hat effect does gravity have on the motion of the inertial balance? Think about the direction of gravity and the
direction the balance moved before answering. Explain your answer completely.
8.
Given your answer to question 7, what effect does weight then have on the motion of the inertial balance? Explain your
answer completely.
9.
Your answers to questions 7 and 8 may have invalidated your initial response to question 6. If your answer to question
6 is no longer valid, give the correct explanation below:
Unit 6: A Property of Matter, Lab A: The Inertial Balance
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter - Mass
Nam e
Reading: MASS — NOT A W EIGHTY MATTER
You have been investigating the idea of mass.
You know that the greater the mass an object has,
the greater its tendency to resist motion. Imagine
that you push two objects of greatly differing mass
– perhaps a large boulder and a small pebble.
Because the boulder has a very large mass, it will
resist a change in its motion more, and your push
will have little effect on it. On the other hand, the
pebble can be easily moved by your push. The
tendency an object has to resist a change in its
motion is called inertia. Inertia has no units, but is
directly proportional to (as well as due to) the mass
of an object.
approximately 4000 miles.) What a marvelous way
to lose weight - clearly superior to all the diets
you've heard of! But what does it mean to lose
weight in space? Does it imply that you've lost
your arms or your legs? Don't lose your head - of
course not! Weight is the force due to the earth's
gravity which acts on you. It changes as you
increase or decrease your distance from the center
of the earth's gravitational field, which is the
geographical center of the earth. But you don't add
or lose any matter - your weight changes, but your
mass remains the same. When would you become
weightless?
Now suppose that the boulder and the pebble
are coming toward you at 60 miles/hour. Which
one would be easier to stop? Since the boulder has
greater mass and, therefore, greater inertia, it will
be much harder to stop than the pebble. You will
have to exert a much greater force to stop the
massive boulder.
How do we know that your weight in the
previous paragraph would be only one quarter of
what it was on the earth's surface? This calculation
comes from the Law of Universal Gravitation
formulated by Sir Isaac Newton. We will study this
law later in the course. One of the primary
predictions of this law is that the weight of an
object decreases as it travels farther from the center
of the earth. This is why objects at the equator
weigh slightly less than they would at the poles; the
earth’s spin makes it bulge around the equator.
When a cup sits on a table, there is a pair of
forces in balance. Consider the forces acting on the
cup. The force due to gravity pulls downward on
the cup, but the table counterbalances this force
with an equal and upward force. When a car is
travelling down a road at a constant speed, a
different pair of forces is acting. The forces of air
resistance and mechanical friction are being
balanced by forces produced by the car's tires. We
may conclude from these and similar examples that
only unbalanced forces accelerate objects.
The mass of an object depends on the quantity
of matter in the object, or in other words, on the
number and kind of molecules which make up the
object. The difference between weight and mass is
most apparent when we examine an object in space.
If we travel a distance above the earth's surface
equal to the radius of the earth, the object will
weigh only one quarter of what it weighed at the
earth's surface. For example, if you weighed 160
pounds on earth, you would only weigh 40 pounds
at an altitude of 4000 miles or 6440 kilometers
above the earth.
(The earth's radius is
Unit 6: A Property of Matter, Reading: Mass – Not a Weighty Matter
For hundreds of years after Newton, scientists
believed that while weight varied with location in a
gravitational field, mass remained constant
regardless of location. Are there situations under
which mass does change?
Albert Einstein
suggested that mass was related to energy by the
famous equation E=mc2, where c is the velocity of
light. Although we have not studied this topic in
enough depth to know why, this equation predicts
that as an object’s speed increases, its mass
increases. This effect only becomes apparent at
incredibly high speeds, much faster than we can
make large objects move. We can, however, make
tiny particles move at speeds near that of light
(186,000 miles per second or 300 million meters
per second) and his predicted increases in mass do
occur. So mass remains constant and unchanging,
except when it travels at speeds which are a
significant fraction of light speed.
©2010 by G. Meador – www.inquiryphysics.org
QUESTIONS
answer with several complete sentences
1.
W hat is an unbalanced force? W hat does an unbalanced force do to an object? (Be exact.)
2.
Victor Vector weighs 650 newtons, while Velma Velocity weighs 750 N. W ho has greater inertia? Describe your entire train
of logic which led you to that conclusion.
3.
Suppose you were in a weightless environment. If you looked in a mirror, would you appear any thinner? Justify your answer.
4.
Under what condition did Einstein say the mass of an object would increase?
5.
Describe a situation in which knowing the mass of an object would be preferable to knowing its weight. Be specific and
creative! Explain your answer, and be careful not to confuse mass with volume.
Unit 6: A Property of Matter, Reading: Mass – Not a Weighty Matter
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter - Mass
Nam e
W orksheet: The “Vom it Com et”
The NASA “Vomit Comet” Zero-Gravity Trainer was used for astronaut
training and low-gravity experiments and to film parts of the movie
“Apollo 13.” A private corporation later began offering rides on this
type of plane for a hefty fee.
The trainers are modified jet airplanes. Most of the passenger seats have
been removed, and the walls padded to protect the occupants. The
planes typically fly for 2 to 3 hours and make 40 parabolic arcs through
the air as shown in the figure at right.
During each arc, a plane first ascends upward at 45E and presses the
occupants down with 2 to 2.5 g’s (19.6 to 24.5 m/s2). Then it traces out
a parabola and the occupants feel nearly weightless for 15 to 25 seconds.
Then it pulls out with another period of 2 to 2.5 g’s before doing another
arc.
The occupants are not really weightless - they are simply in freefall. That is, they are actually accelerating toward Earth at 9.8
m/s2 while they both rise and then fall in a plane that is executing a perfect parabola. The gut-wrenching sensations produced on
the flights have earned the planes the nickname of the “vomit comets.
1. The plane traces a parabola, so for
half of the “weightless” or “zerogravity” period the plane is actually
rising through the air, and falling
during the other half. Draw the
vertical displacement, velocity, and
acceleration graphs for the occupants
during the “weightless” sensation
period, recalling that they are not
really weightless, and are both rising
and falling.
2. Suppose during one arc the occupants are “weightless” for a total of 20.0 seconds. So they spend 10.0 s ascending and 10.0 s
descending. Using the true acceleration of gravity of 9.80 m/s2 , calculate how far the plane would fall in meters and then in
feet (1 m = 3.281 ft) from vertical rest during the descending half of its arc:
Fall in meters (m):
Fall in feet (ft):
show your work
3. Let’s suppose that an occupant’s pre-flight weight was 175 pounds. Compute his mass in slugs, using F g = mg where g is 32.2
ft/s2 . Stay in US Customary units throughout your calculation – do NOT convert to SI/metric units.
4. Now convert the occupant’s mass into kilograms, using the US-to-metric mass conversion factor in your notes:
Unit 6: A Property of Matter, Worksheet: The “Vomit Comet”
©2010 by G. Meador, www.inquiryphysics.org
6 A Property of Matter - Mass
Nam e
Lab B: Acceleration vs. Mass
Air Track Version
How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship
between mass and acceleration when a constant unbalanced force is applied.
You will again be using an air track and gliders for this experiment. At your lab station are three gliders. The two red gliders each
have a mass of 300. g or 0.300 kg. The gold glider has a mass of 150. g or 0.150 kg. The gliders have velcro on their bumpers
so that they can be hooked together in certain combinations.
In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the
independent variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and
initial speed constant; indicate those values below:
Force
Distance
Initial Speed
1. Start with all three gliders hooked together for a total mass of 0.750 kg. (Check that you have not hooked the velcro such that
a glider drags along the track.) Take three measurements of the time required to constantly accelerate the gliders over a set
distance (record that distance below). Record your data in the table. Remember that your times should vary by no more than
0.10 s.
2. Next use just the two red gliders for a mass of 0.600 kg. Repeat step one for this combination.
3. Repeat the procedure for glider(s) massing 0.450 kg, 0.300 kg and 0.150 kg.
Mass of
Glider(s)
(kg)
Time (s)
Average Time (s)
Average
Acceleration
(m/s 2)
0.750
0.600
0.450
0.300
0.150
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
Calculate the average time and your group's average
acceleration for each trial. Use the computer to make a
graph from your group's averages. The independent
variable should be plotted on the x axis. The dependent
variable should be plotted on the y axis. The data will fall
into one of the categories at right, and you should have the
computer perform the appropriate fit.
(Select the
“Automatic Curve Fit” function from the “Analyze” menu.)
Once you have a good fit, turn off the dot-to-dot line on the graph by de-selecting “Connecting Lines” on the “Graph” menu. Have
your teacher approve your graph before printing; save your data.
answer in complete sentences
1. W hat happened to the acceleration of the gliders as you increased their mass?
2. Describe the shape of the curve on your graph. W hat kind of function does it represent?
3. That shape/function allows you to predict how mass affects acceleration. If the mass were cut to one-fourth of its previous
value, what would the new acceleration be?
4. W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the
correct values for any constants. Remember to round off values for significant figures.
class equation:
5. Let’s test your answer to question 3. Use your graph’s equation to find the theoretical acceleration for 0.100 kg and 0.400 kg
of mass. Write down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value by
the smaller one.) W rite your ratio down too, using 3 significant figures.
Accel. of 0.100 kg =
m/s2
Accel. of 0.400 kg =
m/s2
Ratio =
to 1
6. Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer
this question. Notice how we changed the mass.)
7. W rite in words the mathematical relationship you have found between mass and acceleration.
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter - Mass
Lab B: Acceleration vs. Mass
Nam e
Air Track Lab Report Version
How does the mass of an object affect its acceleration? The goal of this experiment will be to find the relationship between mass
and acceleration when a constant unbalanced force is applied.
You will again be using air tracks and gliders for this experiment. At your lab station are three gliders. The two red gliders each
have a mass of 300 g or 0.300 kg. The gold glider has a mass of 0.150 kg. The gliders can be hooked together in various
combinations. Please note that the weight holder has its own mass which must be included in the total mass of the system.
You will be writing your own lab report this time. Your lab group must first design an experiment to determine how mass and
acceleration are related. Study the equipment available at your lab station. Design your experiment so that you will have data
for five different mass values. Be certain that you can answer these questions without notes:
1. W hat are the independent and dependent variables?
2. W hat quantities will you hold constant, at what values, and how will you accomplish that?
3. W hat data must you collect, and what standards of reproducibility will you enforce? (How many trials
will you take? How close must the data be before continuing to another trial?)
4. W hat is the best order to the data collection which will minimize human error?
Before you take any data, design a data table which is clear and consistent. Use the tables from previous experiments as models.
Don't forget that your table needs to have space for calculated quantities as well as raw data. Have one person in the group
construct your planned data table on a sheet of notebook paper. After your group has agreed on a procedure and a data table,
present your experiment to your teacher for approval.
DO
N O T C O N TIN U E U N TIL YO U R EXPER IM EN T IS A PPR O VED .
Now conduct your experiment. You will need to graph your
data and analyze it. The data will fall into one of the categories
at right, and you should have the computer perform the
appropriate fit. (Select the “Automatic Curve Fit” function
from the “Analyze” menu.)
•
•
•
•
Your lab report must be neatly written or typed;
typed reports should be double-spaced
Each student will submit a report, with his or her own unique description of the procedure & conclusions
Do not use first person in the report (no “I” or “we”, etc.)
Past tense is appropriate
Y OU R R EPO RT M U ST I N CLU D E THE F O LLO W IN G :
Purpose - a statement of the relationship you were exploring (note that you probably did not formulate a hypothesis but merely
tested to see what relationship, if any, existed between the variables)
Procedure - thoroughly describe what you did, including the equipment used, the set-up, and address the four numbered questions
listed above (or a list of procedures written in the imperative mood; be sure the four questions are addressed)
Data - your data table (it must be neat; you can use W ord or Excel to create it) and your graph printout
Conclusions
! a verbal statement of the relationship you discovered, including the type of curve fit
! an equation that fits the data (substitute proper variable symbols and appropriate rounded values from your best-fit line or
curve)
! a discussion of the sources of systematic error in the experiment (see reverse for definition of error types)
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
Types of Laboratory Error
Type
Examples
Prevention
Discussion
personal error
(mistakes)
mis-reading a scale
or incorrectly
rearranging an
equation or
calculating a figure
check against lab
partners’ work; redo
parts of lab as
needed when error
discovered
none; should be
corrected before lab
is submitted
systematic error
miscalibration or
uncontrolled
variables
(e.g. friction);
includes unavoidable
timing errors
calibrate equipment
when possible; think
through procedures
to minimize error
identify any
uncontrollable
variables
(do not include
variables causing
random error)
random error
estimating the last
digit on a scale
reading; minor
variations in
temperature or air
pressure
eliminate when
possible; can never
be completely
eliminated
none
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter - Mass
Nam e
Lab B: Acceleration vs. Mass
Dynam ics Cart on Floor Version
How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship
between mass and acceleration when a constant unbalanced force is applied.
In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the independent
variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and initial speed
constant.
You will again be using a dynamics cart, meterstick, and spring for this experiment. Arrange to measure the time required for the
cart to accelerate from rest over a distance of 1.00 m, a distance that will be held constant in this experiment. You will use your
spring and meterstick to apply a constant force of 2.00 N in this experiment. Start with a cart mass of 6.00 kg as before, taking
three measurements of time and recording your data in the table. Then repeat, but lower the mass of the cart to 5.00 kg. Continue
the process to fill out the table; calculate the average time and your group's average acceleration for each trial.
Mass of
Cart
(kg)
Time (s)
Average Time (s)
GROUP
Average
Acceleration
(m/s 2)
CLASS
Average
Acceleration
(m/s 2)
6.00
5.00
4.00
3.00
2.00
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
Your instructor will indicate if you are to use the computer
to make a graph from your group's averages and/or the
class averages. The independent variable should be
plotted on the x axis. The dependent variable should be
plotted on the y axis. The data will fall into one of the
categories at right, and you should have the computer
perform the appropriate fit. Have your teacher approve
your graph before printing; save your data.
answer in complete sentences
1.
W hat happened to the acceleration of the gliders as you increased their mass?
2.
Describe the shape of the curve on your graph. W hat kind of function does it represent?
3.
That shape/function allows you to predict how mass affects acceleration. If the mass was cut to one-fourth of its previous
value, what would the new acceleration be?
4.
W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the
correct values for any constants. Remember to round off values for significant figures.
class equation:
5.
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration for 6.00 kg and 1.50 kg
of mass. W rite down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value
by the smaller one.) W rite your ratio down too, using 3 significant figures.
Accel. of 6.00 kg =
m/s2
Accel. of 1.50 kg =
m/s2
Ratio =
to 1
6.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer
this question. Notice how we changed the mass.)
7.
W rite in words the mathematical relationship you have found between mass and acceleration.
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
6 A Property of Matter - Mass
Nam e
Dynam ics Cart and Table Pulley Version
Lab B: Acceleration vs. Mass
How does the mass of an object affect its acceleration? The goal of this experiment will be to find the mathematical relationship
between mass and acceleration when a constant unbalanced force is applied.
In this lab, we will deliberately vary the mass, and observe what happens to acceleration. Mass is thus called the independent
variable, and acceleration the dependent variable. W e will hold force (the hanging weight holder), distance, and initial speed
constant
You will again be using a dynamics cart and table pulley for this experiment. Arrange to measure the time required for the cart
to accelerate from rest over a large known distance, a distance that will be held constant in this experiment. You will keep the
pulling force of the weight hanger constant in this experiment. Start with a cart mass of 6.00 kg as before, taking three
measurements of time and recording your data in the table. Then repeat, but lower the mass of the cart to 5.00 kg. Continue the
process to fill out the table; calculate the average time and your group's average acceleration for each trial.
Fill in the values below for your experiment:
Force
N
Mass of
Cart
(kg)
Distance
Time (s)
Average Time (s)
m
Initial Speed
GROUP
Average
Acceleration
(m/s 2)
m/s
CLASS
Average
Acceleration
(m/s 2)
6.00
5.00
4.00
3.00
2.00
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
Your instructor will indicate if you are to use the computer
to make a graph from your group's averages and/or the
class averages. The independent variable should be
plotted on the x axis. The dependent variable should be
plotted on the y axis. The data will fall into one of the
categories at right, and you should have the computer
perform the appropriate fit. Have your teacher approve
your graph before printing; save your data..
answer in complete sentences
1.
W hat happened to the acceleration of the gliders as you increased their mass?
2.
Describe the shape of the curve on your graph. W hat kind of function does it represent?
3.
That shape/function allows you to predict how mass affects acceleration. If the mass was cut to one-fourth of its previous
value, what would the new acceleration be?
4.
W rite the full equation for your graph. Remember to substitute the proper variable names for y and x and to indicate the
correct values for any constants. Remember to round off values for significant figures.
class equation:
5.
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration for 6.00 kg and 1.50 kg
of mass. W rite down those values and then compare them mathematically in a ratio. (Divide the larger acceleration value
by the smaller one.) W rite your ratio down too, using 3 significant figures.
Accel. of 6.00 kg =
m/s2
Accel. of 1.50 kg =
m/s2
Ratio =
to 1
6.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you answer
this question. Notice how we changed the mass.)
7.
W rite in words the mathematical relationship you have found between mass and acceleration.
Unit 6: A Property of Matter, Lab B: Acceleration vs. Mass
©2010 by G. Meador – www.inquiryphysics.org
Unit 6: A Property of Matter (Mass)
Meador’s Inquiry Physics
Page 1 of 4
INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
Unit 6:
A Property of Matter (Mass)
Sample Notes
I recommend that you always write out notes,
by hand, on the board for each class. That
allows you to control the pacing and focus,
rather than having students ignore you while
they simply copy down the content of a slide. It
also controls your pacing, so that you don’t race
ahead but instead focus on student
understanding.
©2010 by Granger Meador
inquiryphysics.org
Unit 6 introduces the concept of
mass, relates it to weight, and
then develops that mass is
inversely proportional to
acceleration. Do NOT use “mass”
until you get to the discussion
phase of 6 Lab A.
Ask frequent questions of students to check
their grasp of the material, and call upon
students to provide the next step when working
examples.
My rule for students is that if I write it on the
board, they must write it in their notes, and I
grade their notes each quarter and take off for
any units with incomplete notes or examples.
Trigonometry-Based Physics
(AP Physics B)
This unit is identical for both algebra and trigbased courses.
Unit 6: A Property of Matter (Mass)
Meador’s Inquiry Physics
Page 2 of 4
Sample Notes for Unit 6: A Property of Matter
Unit 6: A Property of Matter
mass (m) =
amount of matter comprising an
object (think protons, electrons, and
neutrons; NOT volume)
The notes don’t begin until after the
discussion of 6 Lab A. So now the students
have begun the process of distinguishing
weight and mass.
measured in kilograms (kg) or slugs (sl)
volume (V) = amount of space occupied by an object
measured in liters, cm3, in3, etc.
weight (Fg) = force due to gravity on an object
measured in newtons (N) or pounds
(lbs)
density (ρ) = mass/volume
measured in kg/m3, sl/ft3, etc.
We complete the Example 6-1 table as a
signaling exercise where I pose the
situation (using a Nerf ball prop), have
them think, and all signal simultaneously
with a show of fingers how many of the
four quantities changed (form an O with
fingers if answer is zero). Then we discuss
and fill out each row.
Example 6-1
Which of these quantities change significantly in each situation?
SITUATION
object is
crushed
object taken to
the moon
object tossed
upward
half of object is
destroyed
MASS
WEIGHT
VOLUME
DENSITY
no Δ
no Δ
decreases
decreases
no Δ
decreases
no Δ
no Δ
no Δ
no Δ
no Δ
no Δ
decreases
decreases
decreases
no Δ
Unit 6: A Property of Matter (Mass)
Meador’s Inquiry Physics
On Earth, 1 kg weighs 9.8 newtons:
2
9.8 N = (1 kg)(?)  insert 9.8 m/s to balance it
Page 3 of 4
I put a large newton dial spring scale on
the board (using a magnet or hook) and
hang a 1 kg mass on it to show them it
weighs 9.8 N.
so
(weight equals mass times the acceleration due to gravity)
and the newton is thus equal to a kgm/s2
Conversions
1 pound (lbs) = 4.4482 N
1 kg = 0.068522 slugs
weight is not mass, so it is NOT appropriate to convert kg to N or lbs; instead we use Fg = mg
Example 6-2 MY WEIGHT AND MASS
I use my own weight in
example 6-2, asking them to
calculate each line with me,
but using their own weight. I
use a different color marker
for all of the numbers that
will be different in their own
notes.
I weigh __170___ pounds.
So I weigh
My mass is
or my mass is
“g” is the “acceleration due to gravity” in m/s2 or can be
called the “gravitational field strength” in N/kg instead
, and it varies with location.
I use the PowerPoint in the
“acrobat/Other Resources”
subdirectory on the CD-ROM
to illustrate gravity
variations due to location and
the effects of special
relativity.
Example 6-3 GRAVITY VARIATIONS
Location
g
My Weight There
Chicago
9.803 m/s2
Fg = mg = (77.2 kg)(9.803 m/s2) = 756.79 N / 4.4482 N/lb = 170. lbs
Panama Canal
9.782 m/s2
Fg = mg = (77.2 kg)(9.782 m/s2) = 755.17 N / 4.4482 N/lb = 170. lbs
North Pole
9.832 m/s2
Fg = mg = (77.2 kg)(9.832 m/s2) = 759.03 N / 4.4482 N/lb = 171 lbs
Space Station
8.71 m/s2
Fg = mg = (77.2 kg)(8.71 m/s2) = 672.41 N / 4.44822 N/lb = 151 lbs
Moon surface
1.62 m/s2
Fg = mg = (77.2 kg)(1.62 m/s2) = 125.06 N / 4.44822 N/lb = 28.1 lb
Unit 6: A Property of Matter (Mass)
Meador’s Inquiry Physics
Page 4 of 4
Special Relativity
Mass itself varies with speed. Einstein’s Special Theory of Relativity predicts a number of odd
changes as an object approaches light speed, and these effects have been experimentally
confirmed:



mass increases (the inertia of the object increases; it does not have any more electrons,
protons, or neutrons but instead they simply become harder to accelerate)
objects shrink in the direction of their relative motion
time slows down
According to this theory
where v = speed relative to the observer and
c = speed of light = 186,000 miles/second = 3.00x108 m/s
Since c is so large relative to v, this effect is only important at immense speeds; even at half the
speed of light the mass only increases by 16%.
If you want details:
Speed
0
Concorde (mach 2; 1354 mph; 605 m/s)
Voyager Probe (37240 mph; 16648 m/s)
one-half light speed
three-quarters light speed
99% of light speed
light speed (“warp one” in Star Trek)
% of mass increase
0
0.0000000002%
0.000000154%
16%
51%
600%
infinite; matter cannot achieve light speed ("warp one")
and a similar formula applies to time dilation (time slowing down; confirmed by flying atomic clocks
aboard commercial planes and also around Chesapeake Bay; the clocks in the air slowed down just as the
theory predicted, falling out of sync with clocks left on the ground)
I like to show my students about 8 minutes from a funny 1957 film by Dr. Irwin Moon, The Mystery of Time,
which you might be able to to get from http://www.archive.org, but be aware that Dr. Moon had a religious
motive and was covering more than special relativity; we only watch 16:42-23:00 of that video.
I refer students wanting more details to their textbook and for those who are really motivated, I’ll loan
them a copy of Martin Gardner’s excellent book, Relativity Simply Explained (formerly titled Relativity for
the Million).
Next I show them fun online clips from NASA’s old Vomit Comet zero-g
simulator plane and some excerpts on the effects of freefall on the human
body from the 1994 video We’re Go for Launch to Zero-G.
Then I assign the reading, the worksheet on the Vomit Comet, and we do
6 Lab B. We capture the big idea from 6 Lab B in the Unit 7 notes.