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Mass – Part IV
Motion and Mass
First of all, think about the following question. We send astronauts into space and some
of them stay out there for long periods of time. It is crucially important for us to monitor
their health and one way to do that is to monitor their weight. So how would you monitor
the weight of an astronaut on the international space station? If the astronaut stood on a
bathroom scale, he or she would just float off of it and the scale would read zero. If we
taped the astronaut’s shoes to the scale, the scale and the astronaut would both float
around and the scale would still read zero. Attaching the scale to the floor won’t help
because everything is just floating around.
 How could we monitor the “weight” of astronauts in space? (Hint: in this case it
isn’t exactly the weight that NASA measures. So think about how you might try
to measure the mass of an astronaut in space. If you can’t come up with an idea,
that’s okay. We’ll come back to it later.)
Let us try to define mass. It is a measure of how much stuff there is “in” an object. In
some sense it is a measure of how many particles make up the object and how tightly
packed they are. The amount of stuff in an object does not change whether it is on the
Earth, the Moon, or elsewhere in the universe, so the mass does not change either.
Vocabulary check:
 The strength of the force of gravity pulling on an object is called ___________.

The amount of stuff (that gravity pulls) in the object is called _____________.

The amount of space that all that stuff takes up is called _______________.
There is a problem with the definition of mass as “the amount of stuff in it.” It is very
difficult to look inside of an object and count all the particles that we find. Imagine trying
to find the mass of a chunk of metal or a fish or a planet that way!
Scientists get around this problem by choosing a specific piece of metal (stored in a vault
in Paris) and defining that object to have a standard mass. We then compare other objects
against this standard. The mass of this special metal cylinder in Paris is defined to be one
kilogram by international agreement.
Now that we have a standard kilogram, we need ways to compare things of different
mass. One way is to measure how a difference in mass changes the behavior of an object.
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Motion:
When we talk about the behavior of an object, we usually observe something that
changes over time. It is hard to talk about the behavior of something that doesn’t move.
So let’s start by looking at motion.

Slide a book or a block of wood along a tabletop. Give it a good push. It probably
slid a little bit but came to a stop. What made it stop? There are two parts to this
question:
o What object slowed down the book or block and made it stop? (In this
case an object is something you can touch.)
o What did that object do to the book or block that made it stop?

Now find a toy cart with good wheels. Roll the cart along the floor. These carts
can roll pretty far so gently roll it toward a wall from a few feet away. The cart
probably stopped, right? What made it stop?
o What object slowed down the cart and made it stop? (An object is
something you can touch.)
o What did that object do to the cart that made it stop?
Another thought experiment: this one comes from Galileo.
Imagine rolling a ball down the ramp on the left as shown above. The ball would roll
down the ramp on the left side, roll across the level part, and then start up the ramp on the
right side. At some point on the right side the ball would stop and roll down again.
 How high would the ball go on the right side? As high as it started on the left
side? Not quite so high? Why or why not? Discuss your ideas as a group and
check your ideas with your teacher.
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
On the last page you probably decided that the ball wouldn’t rise quite as high on
the right side as it had originated on the left side. You probably thought of one or
more factors that would tend to slow the ball down, even if it was rolling on a
level surface. Whatever things you considered that made you think it would not
rise quite as high (there are many factors here) imagine we could magically make
them all go away. (This is why this is a thought experiment.) Now mark the spot
in the diagram below where you think the ball would stop on the right hand ramp.

Now with all of those “slowing down” factors still magically out of the way,
imagine we just made the ramp on the right hand side a little longer (but exactly
the same height as before). Now mark the spot on the diagram below where you
think the ball would stop.

Okay, so now we made the ramp on the right really long, so long that it doesn’t fit
in the picture anymore. Explain in words: how far would the ball go?

And here was Galileo’s masterstroke. If we made the ramp on the right long
enough, it would appear to be flat, as far as we could tell. So what if we replaced
it with a ramp that really was completely flat? Now how far would the ball go?
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Galileo and Isaac Newton changed the way we look at motion. Long before Galileo
came along, Aristotle said that every object really wants to be “at rest” (which means
“not moving”). Galileo and Newton taught us that if an object is at rest, it tends to stay at
rest, but if an object is in motion it tends to stay in motion unless acted upon by an
external force. (FYI: A force is any kind of a push or pull. An external force is a push or
pull from another object.)
Now let’s look at that property of matter that tends to either keep it at rest or (if it is in
motion) tends to keep it in motion.
Mass and motion:
In the picture above you see an aluminum track with a cart sitting on it. Mounted on the
cart is a fan unit with a propeller like the one you might have seen on a toy airplane.
Switching on the fan will cause the cart to be pushed across the track. The air pushing on
the fan provides an external force on the cart. The push on the cart due to the fan is the
same as long as the fan rotates with the same speed. We will try to conserve the batteries,
because your data will not be reliable if the fan speed decreases.
Also seen in the picture are several black brick-shaped steel bars which are very nearly
all of the same mass. We will pretend that this class has agreed that the mass of the steel
bar will be the standard mass.
One of our goals was to compare masses and now we can use motion to do that. Since we
can’t get to the vault in Paris, we will use these steel bars as our standards of mass. Let us
call our standard unit one SB (short for steel bar). Our goal is to measure the mass of
other objects in terms of the mass of the steel bar. For example, we could measure the
mass of a tennis ball in grams or kilograms, but we could also measure it in SB.
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
What do you think would be the mass of a tennis ball? 1 SB? ½ SB? 0.1 SB?
You just need to guess.
Long, long ago, on a page of this module that is now far away, you were asked about the
amount of time required to push a sumo wrestler on skates and get the sumo wrestler
moving with a certain speed. We are going to do a variation of that experiment here, with
the cart and the steel bars substituting for the sumo wrestler.
In addition to the cart, you should have a sonar device that is labeled “motion detector”. It
works just like the radar gun used by the police except that a radar gun uses radio waves
and this uses sound waves at a pitch higher than we can hear (unless you are a bat, a dog,
or a dolphin). You may have used one before to measure the motion of your own body.
This time we are measuring the motion of a cart, so make sure the switch on the motion
detector is set on the picture of a cart.
The Experiment
1) Set up the motion detector and the cart on the track. Note the starting point of the cart.
2) The motion detector must be plugged into a small interface box which is connected to
the computer. From the start menu, on the computer, start up the program called
LoggerPro. Your instructors will show you how to do this if it is not already plugged in.
Once LoggerPro starts up, you have to load in the appropriate file. Again your instructors
will help you with this.
3) Some data we will provide you.
 Mass of the cart = 1.0 SB (Yes, it was made that way on purpose.)
 Mass of fan unit = 0.5 SB (Again, by design.)
Load up the cart with a few steel bars (can you attach three of them? four?). This will be
our model of a sumo wrestler. We will work our way toward the ballerina.
 Once you have your cart, fan, and steel bars loaded up, record the total mass of
the whole shebang. (Remember, you are using SB units.)
4) Now you have to test if the motion detector can detect the cart and give you reasonable
graphs of velocity as a function of time. Click the “Collect” button in the LoggerPro
window and give the cart a gentle push without switching on the fan. Study the graphs to
see if the motion detector can see the cart over a distance of 70-80 cm. If it does, you are
ready to go on. If not, tilt the speaker of the motion detector a little and try again.
So now you are ready to go on.
5) Switch on the fan, click “Collect” on the LoggerPro window and then release the fan.
The computer should plot a graph of distance versus time as well as velocity versus time.
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6) Analysis and calculation for the first run:

What is the shape of your velocity vs. time graph? The part we are interested
should look a lot like a straight line. Identify a portion that looks straight (and not
horizontal).

Now use this graph to see how much the velocity changed during the time that
you measured. You can get numerical readouts of your graph by clicking on
“analyze” and then “examine” (or just the “ x = ” button on the toolbar). You need
to look at how much the velocity of the cart changed during the experiment. The
plus signs and minus signs just depend on which way the fan is pointed and we
don’t care about that. We only care about the change in velocity.

For example, if the cart started out with a velocity of -0.035 m/s and
finished with a velocity of -0.475 m/s, then the change in velocity was the
difference between those two numbers: (-0.035 m/s) – (-0.475 m/s) =
0.440 m/s.

With four steel bars on the cart, you need to make sure the velocity
changed by more than 0.20 m/s. If not, check with your instructor (the
problem is probably that your batteries are too weak but your track could
be tilted or part of your cart could be dragging on the track).

Now record the amount of time that it took for the velocity to change by 0.2 m/s.

Check to see that the time you calculated above is reproducible. Repeat the
experiment. Similar results? We hope so. If not, ask for help (your batteries
could be dying).

Record your value for total mass, (M) and time taken (t) for the run in the table on
the next page. The total mass was: 4 steel bars + 1 cart + 1 fan = 5.5 steel bars
7) Remove one steel bar and repeat the process, but do not choose a new standard
for your change in velocity! Again check to see how long it takes for the velocity
to change by 0.2 m/s. After a couple of trials you should be pretty confident that
your results are reproducible, so you don’t have to check so often. Your goal is to
measure the amount of time required to get the specified change in velocity for
each new mass of the cart. Again, record your total mass and the amount of time
required for the velocity to change.
8) Remove another bar and repeat the process. Keep doing this until you are down
to just the cart and the fan. That will be your “ballerina”. We can’t go any farther.
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Observation Table
Our standard change in velocity for all trials is: _________
Total mass (M), SB Time for each run (t), s
Plotting the data
The first graph you might think of plotting is a graph of mass as a function of time
because we have already plotted things as a function of time. But does that make sense in
this case? What is your “manipulated” or “independent” variable? What is your
“responding” or “dependent” variable? What do you think we should plot (on the vertical
axis) as a function of what (on the horizontal axis)?
You can plot the graphs using Excel. This will allow you to quickly fit a trend line and
display the equation of the trend-line. If you are not sure how to do this, just ask.
Interpreting your results:
1) As the mass of an object increases, does it become easier or harder to make it change
its velocity?
2) Based on your investigation (this part may not be reflected by the data recorded in
your graph), does your answer to question #1 depend on whether the cart is speeding
up or slowing down? Was there much of a difference?
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3) What property of an object determines how hard it is to make that object change its
velocity?
4) How would you describe the relationship between the mass of an object and the
amount of time it takes to get a certain change in velocity?
5) Harder question: How would you describe the relationship between the mass of an
object and the “easiness” of getting it to change its motion?
6) If it is hard to get something to change its motion, we say that object has a lot of
inertia. How would you say that mass and inertia are related?
Applying your results:
1) We did all of these experiment in a laboratory on Earth. Imagine we had an identical
laboratory on the Moon (also sealed with ample breathable air). Would your results
have been any different? What about on the space station?
2) How do you suppose NASA measures the mass of astronauts on the space station?
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3) Real life adventures: It takes Billy Jean 18 seconds to get her two-ton truck up to 50
miles per hour from a dead stop on a level road. How long will it take her to get it up
to 50 miles per hour from a dead stop on a level road when it is loaded up with a ton
of hay? With three tons of gravel?
End of Module Questions:
1. In ancient Mediterranean cultures, coins were made out of pure metal and the value of
a coin was determined by the mass of the metal used to make the coin. Once upon a
time, three merchants from different cultures met to buy and sell goods. Merchant #1
had a pocket full of Nara coins, Merchant #2 had a pocket full of Filsa coins, and
Merchant #3 had a pocketful of Mac coins. The first thing they needed to do was
figure out how many Nara in a Filsa, how many Filsa in a Mac, and so on.
a) Explain in words (and pictures if you like) how the three merchants could have
determined the relative values of their coins using only a few sticks, some cloth,
and some string.
b) It turns out that four Filsas have the same mass as one Mac. Three Macs have the
same mass as two Naras.
i)
How many Filsa would have the same value as 1 Nara? (Show your work)
ii)
Hoping that Merchant #3 didn't pass IDS 101, Merchant #2 decides to try
and fool her. He quickly demonstrates that he can balance one Mac with
one Filsa. How did he do it and where did he have to hang the two coins to
pull of his trick?
2. The following questions all refer to a set of experiments with the balance shown
below. A meter stick is balanced on a pivot point. Four pieces of aluminum metal are
then placed 22 cm from the balance point. Each piece of aluminum has dimensions of 1
cm x 1 cm by 1 cm.
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22 cm
a. If you remove just one of the four pieces of aluminum, where will you have to
place it on the other side to balance the remaining three pieces? Show your
work or explain your reasoning.
b. Next you are going to try balancing all four pieces of aluminum (in the
original position shown in the diagram) with one piece of lead.
Lead is 4 times as dense as aluminum. If you use a 1 cm x 1cm x 1 cm piece
of lead, where will you have to place the lead to balance the four pieces of
aluminum? Show your work or explain your reasoning.
If you use three of pieces of lead,
where will they need to be placed in
order to balance the four pieces of aluminum (in their original position)? Show your
work or explain your reasoning.
Finally, imagine repeating the experiment with a 2 cm x 2 cm x 2 cm piece of lead.
Where should this piece of lead be placed in order to balance the four pieces of
aluminum? Show your work or explain your reasoning.
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3. Consider the lever shown below. If there are no weights on the lever it will be perfectly
balanced on the fulcrum shown in the center.
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a)
Block B has the same width and thickness as block A, but block B is twice
as tall. The lever balances when blocks A and B are the same distance
from the center. How does the density of block B compare to the density
of block A? (Be quantitative and explain your reasoning.)
b)
The two blocks labeled C in the diagram below have masses of 30 g each.
The lever is balanced when one block C is 20 cm from the center and the
other block C rests on block D 5 cm from the center. What is the mass of
block D? (Be quantitative and explain your reasoning and/or show your
work.)
C
C
c)
D
Two identical 12 g blocks are placed on the lever, 20 cm and 25 cm from
the center. Where would one have to place a single 60 g block to balance
the lever? (Be quantitative and explain your reasoning and/or show your
work
60
g
12
g
12
g
?
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4. When moving heavy drums of oil or chemicals on the Tacoma tide flats, workers lift
the drums onto hovercrafts that allow them to move with essentially no friction. Still,
because the masses are so great, the drums must be moved slowly. A worker finds he can
get a 20,000 ton drum moving at a speed of 0.4 m/s in 10.0 seconds. Assume he always
uses the same amount of force, whether speeding up the drum or slowing it down.
a) Starting from rest, how long would it take him to get the 20,000 ton drum
moving at a speed of 0.2 m/s?
b) Starting from rest, how fast could he get the drum moving in 15 seconds?
c) Once he had the 20,000 ton drum moving at a speed of 1.0 m/s which was too
fast for safety. How long did it take him to slow it down to 0.5 m/s?
d) Starting from rest, how long would it take him to get a 10,000 ton drum
moving at a speed of 0.4 m/s?
d) Starting from rest, how long would it take him to get a 10,000 ton drum
moving at a speed of 0.3 m/s?
e) Starting from rest and using that same amount of force, he found he could get a
certain drum moving at a speed of 0.8 m/s in 10.0 seconds. What was the mass of
this drum?
f) Starting from rest and using that same amount of force, he found he could get a
certain drum moving at a speed of 0.6 m/s in 6.0 seconds. What was the mass of
this drum?
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5. For each of the following quantities, state whether the quantity would be greater, less,
or the same if the experiment were repeated on the Moon:
a) The amount of force required to lift a certain steel bar off of a table.
b) The amount of space occupied by a certain steel bar.
c) The speed of a golf ball after being hit with a force of 200 pounds for 0.1
seconds.
d) The pain in your forehead after being hit by a golf ball moving 20 mph.
e) The pain on the top of your head if you could balance all of your college
textbooks there.
f) The pain of answering all of these questions.