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The PASCO scientific Model ME-9426A Amusement
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Over the past few years, an increasing number of high
school physics classes have been taking one day a year
to visit an amusement park for an open air physics lab.
With a few simple instruments - a vertical accelerometer,
a horzontal accelerometer (that doubles as a sextant), and
a piece of string marked out in meters - students make
measurements that allow them to analyze the motion of
the various rides. It's an invigorating form of laboratory
physics, mentally and physically. It's one thing to watch
a lab cart rolling on a table. It's quite another thing to be
in the lab cart yourself.
Description
The Model ME-9426A Amusement Park Physics (15
pack) provides material for 15 vertical accelerometers
and 15 horizontal accelerometers. The kit also includes
a ball of string that can be marked off in meters for
distance measurements, and plastic bags for protecting
accelerometers, paper, etc., from some of the more
aquatic rides. The only materials you'll need that aren't
provided are scissors, masking tape, pliers, clear plastic
tape, and an amusement park. The accelerometers are
designed to be assembled by the students, themselves.
Instruction sheets are included with the kits.
About This Manual
This manual includes some basic information on using
the accelerometers. It also includes three experiments that
do not require an amusement park: two experiments for
playgrounds, and one for elevators.
two reasons. The first is that the rides vary greatly from
park to park. The second is that experimental information
is readily available from other sources. See your local
PTRA (Physics Teacher's Resource Agent) for information.
It’s quite possible that there is already an Amusement
Park Physics Day planned at a park near you, and materials may be available that are applicable to that particular
park.
See the PASCO web site at www.pasco.com for more
information on PASCO interfaces, equipment, and software.
We haven't included amusement park experiments for
1
Amusement Park Physics012-03776E
Materials
Materials Included for Building Horizontal Accelerometers
- Accelerometer Card15 ea.
- Rubber Band15 ea.
- Straw15 ea
- BBs45 ea.
- Plastic Tubing2.4 m
Materials Included for Building Vertical Accelerometers
- Springs15 ea.
- Plastic Tube (30 cm long)15 ea.
- End Cap (for plastic tube) 30 ea.
- Pushpin1 ea.
- Weight (10 g)15 ea.
- Paper Clip (#3)15 ea.
- Red Tape (3 mm wide)1 roll
- Rubber Band15 ea.
Rubber Band
Straw
Red Tape
Spring
Accelerometer Card
Rubber Band
Paper Clip
Weight
Plastic Tube
BBs
Plastic Tubing
End Cap
Pushpin
Also Included
- Plastic "Zip-Loc" Bag15 ea.
- Accelerometer Construction Sheet15 ea.
- String 1 roll
- Pushpin1 ea.
- Bumper Sticker (not shown)25 ea.
Plastic Bag
String
Accelerometer
construction
sheets
2
012-03776EAmusement Park Physics
You will need to supply
- Scissors.
- Masking Tape
- Clear Plastic Tape
- Pliers
Accelerometers: Theory and Operation
Accelerometers measure accelerations by measuring
forces. The vertical accelerometer in this kit consists of
a cylindrical weight hung from a spring. Its operation can
F
be understood in terms of Hooke's law:
where F
is the force applied by the spring to the weight,
s
x is the extension of the spring, and k is a constant that
depends on the spring. The negative sign indicates that
the force is in the direction opposite to the extension. As
the force applied by the spring to the weight increases,
the stretch increases in direct proportion. Thus the position of the end of the spring indicates the amount of force
being applied to the weight by the spring.
Calibration of the device can be in newtons for the spring
F
s
-----
force, or, in the ratio
a=
m
kx–=
s
Clear Plastic
Tape
Scissors
cylinder is given by:
F
netFs
mg–=
Pliers
Masking-
Tape
where mg is the weight of the cylinder.
A diagram of the spring and weight is shown in Figure
1. When the accelerometer is held at rest (1a), the spring
force is equal to the weight but in the opposite direction,
so the net acceleration is zero.
F
0Fsmg== =
net
mg=
F
s
and the scale reads "1g".
No
Acceleration
F
= -mg
s
a = 0
Upward
Acceleration
F
> -mg
s
a > 0
Downward
Acceleration
F
< -mg
s
a < 0
where a is an acceleration, since the mass of the cylinder
remains constant for all uses. With the unstretched spring
position taken as the zero point, the weight of a single
cylinder defines the position corresponding to a restoring
force which has magnitude equal to the weight of the
F
cylinder, or .
-----
m
m
s
----
9.8
=
2
s
Note that if the device is calibrated in units of "g" instead
2
of m/sec
, it should be pointed out that the unit "g" used
here is related to the local acceleration due to gravity only
in that it has the same magnitude. Since the symbol "g"
means local gravitational field strength, a reading of 2.0
g on an accelerometer does not mean that the gravitational
field has increased. It means that the rider feels a force
which is twice the magnitude of the rider's weight.
When the device is held vertically, the net force on the
3
F
s
F
s
F
s
a
mg
(a)
mg
(b)
mg
a
(c)
Figure 1: Diagram of the Vertical Accelerometer
Amusement Park Physics012-03776E
All the spring is doing is supporting the weight of the
cylinder. This is also true if the device is moving up or
down with constant velocity.
If the weight is accelerating upward, the spring must exert
not only the weight but enough additional upward force
to provide the acceleration (1b). With F
greater than mg,
s
the net acceleration is greater than zero and upward. In
this case, the spring will have stretched more than when
at rest and the weight will be below the "1g" position.
If the weight is accelerating downward (1c), the spring
must be applying less force than the weight It will have
stretched less than when at rest and the cylinder will be
above the "1g" position. In this case, the weight helps to
accelerate the mass downward.
The device registers the acceleration as seen in the frame
of reference of the rider. Consider the weight of the
accelerometer to be a "plumb bob". Its direction response
is the same as that of a plumb bob. In this case, the amount
of stretch of the spring gives the weight of the cylinder
in the combined gravitational and acceleration fields of
the ride.
You cannot tell the gravitational field in one direction
from an acceleration in the opposite direction. You cannot
feel the difference between a force due to gravity and a
force due to the ride pushing on you. The scale readings
give what you feel is the local gravitational field. Since
it registers the acceleration in the reference frame of the
rider, the accelerometer readings agree with what the rider
"feels."
A negative or downward acceleration occurs after the tops
of roller coaster hills, when an elevator begins its downward trip, or when one begins to slide downhill. Riders
have a sinking feeling because less force is being applied
upward than they are accustomed to. On some rides the
downward force is partly a push from the safety bar. This
downward push feels as if the rider has suddenly become
lighter and is rising out of the seat. Sure enough, the
accelerometer reads less than one "g."
Upward or positive accelerations are felt in elevators as
they begin to rise, and at the bottom of vertical loops on
roller coasters and swings. As the elevator begins to rise,
the floor must push up with a force greater than the rider's
weight. The rider interprets this as an increase in downward force and feels heavier. The accelerometer spring,
stretching to provide the additional force for the weight,
registers more than one "g". Both the direction and magnitude of the readings agree with the rider’s feeling of an
altered gravitational field.
Upside down, at the top of a vertical circle such as a roller
coaster loop or rotating ride, the rider may feel little if
any force from the seat. The rider feels almost "weightless". At the same point the accelerometer shows little if
any pull being applied by the spring. They are in agreement. At the bottom of the same loop the strong upward
push from the seat feels like a force pushing the rider
down into the ground. This upward force is applied to the
cylinder by the spring which stretches strongly giving a
large reading. In both cases, the rider sees the spring being
pulled "down" toward the rider's seat, which conforms
with what the rider feels.
The Horizontal Accelerometer
With horizontal accelerometers, as opposed to vertical
accelerometers, there is not the same confusion between
the subjective experience and the accelerometer reading.
At rest, the BB's in the horizontal accelerometer settle to
the bottom of the curved plastic tube. There is no horizontal force applied and no horizontal acceleration.
When the BB's are above the bottom, as in Figure 2, the
inside of the curved plastic tube applies a force to them.
The applied force has a vertical component equal to the
weight of the BB's and a horizontal component equal to
the mass of the BB's times their horizontal acceleration.
The applied force acts along the line making the angle q
with the vertical, center line of the accelerometer.
Since the components are perpendicular to one another
and the horizontal force, ma, is opposite the angle θ:
ma
-------
θtan
=
mg
and
ma = mg tan θ.
We can divide both sides by the mass of the BB's to obtain:
a = g tan θ;
where a, the horizontal acceleration, is always directed
forward toward the front of the device.
To measure the horizontal acceleration in the direction
you are moving, just hold the accelerometer level with
the straw pointed in the direction you are moving.
4
012-03776EAmusement Park Physics
Multiply g by the tangent of the angle to the center of the
BB.
Force applied
by tubing
-mg
mg
Figure 2: Diagram of the Horizontal Accelerometer
θ
θ
ma
Direction of
Acceleration
To use the horizontal accelerometer to measure horizontal centripetal accelerations, hold it perpendicular to the
direction in which you are headed and as level as possible.
For example, on the rotor ride at an amusement park,
where you are in a rotating cylinder feeling mashed to
the wall, hold the accelerometer with the short side
pressed to the wall. It will be level with the floor and,
since you are traveling sideways, perpendicular to the
direction of travel.
of King Kong's head, in Figure 3. You can measure these
distances with reasonable accuracy using just the accelerometer, a piece of string that is marked out in meters,
and a little trigonometry. The procedure is as follows:
1. Measure the distance S with a piece of string marked
out in meters.
S is the horizontal distance between your point of
observation and a point directly below the object of
interest.
2. Sight through the straw to the top of King Kong's
head, and measure the angle θ on the accelerometer.
θ
is the angle that the center BB aligns with on the
horizontal accelerometer. It is also the angle between
your horizontal line of sight and your line of sight to the
top of King Kong's head.
3. Measure h
, the vertical distance between the base
0
of your height measurement and your observation point.
As long as the ground is level between you and the
building on which King Kong is standing, h
is just the
0
distance from the ground to your eyes.
4. Then:
H = h
+ h1 = h0 + S tan θ.
0
Before the motion begins, the BBs sit in the bottom of
the tube. When the ride begins to rotate, a centripetal
force is needed to make them go in a circle. The BBs will
ride up the side nearest the wall, as if forced outward. In
fact, the tube will be exerting a horizontal force on them
directed in toward the center of the ride. They will ride
up until the angle is large enough to give the necessary
horizontal acceleration. In circular motion
2
v
-----
=
a
r
where v is the linear speed along the circumference and
r is the radius of the circle. As the ride picks up speed,
the BBs will travel farther up the curve.
Using the Horizontal Accelerometer as a
Sextant
The horizontal accelerometer can be used to measure the
heights of objects that are too high to measure directly,
such as measuring the height from the ground to the top
h
1
H
θ
θ
h
0
S
Figure 3: Measuring Heights with the Horizontal
Accelerometer
5
Amusement Park Physics012-03776E
Construction and other Tips
A. Vertical Accelerometer
When calibrating the vertical accelerometer, it is wise
to employ Hooke's Law and a some foresight. In Figure
4, a thin, solid wire has been attached to a weight. By
hooking the end of the wire onto the lower end of the
spring just before lowering it into the tube, one can
establish the "2g" point easily. Then pull the 2nd weight
out the bottom of the tube and remove it, allowing the
single weight to rise up to the "1g" point. With these two
points determined, it is easy to finish calibrating the
accelerometer.
Fine, solid wire
Figure 4: Method of calibrating
Vertical Accelerometer
B. Horizontal Accelerometer
1. One method for constructing the horizontal accelerometer makes use of the rapid set-up time of hot glue.
Put the clear tubing in one half of the cardboard,
insert the three BB's. Now put hot glue in the places
indicated in Figure 5. Pressing the two halves of the
accelerometer together results in a completed project
(except for the straw which can also be hot glued
on)15 seconds later. NOTE: Do not get hot glue in
the end of the tube as the BB's tend to stick to the glue.
2. For students using simple calculators (no trig functions), a helpful aide is to reproduce the table of
tangents and glue it to the side of the horizontal
accelerometer. Both the acceleration and the heights
of rides depends upon the tangent value.
3. Also for ease of use, the student may wish to put the
length of his/her pace on the side of the horizontal
accelerometer if this is the method being used to
measure horizontal distances.
4. Other uses of the accelerometers:
a. Use the vertical accelerometer to measure the
acceleration achieved when jumping upwards, or to
measure the stopping acceleration when jumping
down from a chair seat. The basic principle of the
device can be clearly learned before going to the
park.
b. Accelerometers can be employed on mass transit
to measure motion, including buses, light rail and
subway systems.
c. The horizontal accelerometer can be used to sight
star altitudes.
Table 1: Table of Tangents
AngleTangentAngleTangent
00.00451.00
50.09501.19
100.18551.43
Hot Glue
Figure 5: Using Hot Glue to Construct the
Horizontal Accelerometer
150.27601.73
200.36652.14
250.47702.75
300.58753.73
350.70805.67
400.848511.40
6
012-03776E Amusement Park Physics
Experiment 1: Playground Physics / Merry-Go-Round
Objective
In this lab you will experiment with centripetal accelerations on a playground merry-go-round.
Discussion
On a merry-go-round, we experience the sensation of being "thrown outward". Physics students know that this
is really inertia trying to keep us moving in a straight line. However, by exerting the right amount of inward or
centripetal force, we can successfully stay in a circular path (and on the merry-go-round). This force is usually
supplied by friction between our shoes and the ride and/or friction between our hands and the bars of the merrygo-round. How does this force change with varying distance from the center of the ride? How does this force
depend on the speed of rotation of the ride?
At least two people are needed to carry out this lab, although three or more would be better. A stopwatch or digital
wristwatch and one or more horizontal accelerometers are needed to conduct the lab. Additionally, a measuring
device capable of measuring to the nearest 0.1 meter is needed.
Procedure
1. Measure off several distances from the center of rotation. Place the lateral accelerometer at one distance,
holding it against a bar if necessary to keep it from moving, and holding it so that it is level. The middle BB
should be at 0°. Record the distance, R, in Table 1. Note: Several riders, each with a lateral accelerometer,
could be positioned simultaneously at different distances.
2. Push the merry-go-round until it is moving at a steady, but relatively slow angular speed.
3. Measure the time it takes to go once completely around at the current speed, or better yet, the time to go five
times around and divide by five to get the average period of rotation, T. While the merry-go-round is turning,
the person on the ride measures the angle that the center BB moves to, θ. Record the period and angle in Table 1.
4. Repeat step 3 with at least three different speeds of rotation, holding the accelerometer steady at the same
radius. Record the appropriate values in the data table.
5. Repeat step 3 after moving the accelerometer to a new radius. Try to rotate the merry-go-round at the same
speed it was turned during the first trial.
Analysis
1. For each trial, calculate the tangential speed, the speed that the accelerometer was travelling around its circular
path, v = 2πR/T . Record your calculated values in Table 2.
2. For each trial, calculate the centripetal acceleration, a
3. For each trial, calculate the "measured acceleration" from the angle of the BB’s, a
4. Compare the calculated and the measured acceleration values for each trial. Were the results identical? Similar?
What type of percentage difference did you get in your results?
5. When the merry-go-round was going at approximately the same speed, how did the measured acceleration
vary with the radius? Was it linear? What was the mathematical relationship?
6. When the accelerometer was held at the same radius, what was the relationship between the measured
acceleration and the speed? Was it linear? What was the mathematical relationship?
7. Finally, what are some of the sources of possible error in this experiment? .
= v2/R or ac = 4π2R/T2 .
c
= g tan θ.
c
7
Amusement Park Physics012-03776E
Table 1:
Trial #
1
2
3
4
5
6
7
8
9
Trial #
Radius
(m)
Tangential
Speed
(m/s)
Table 2:
Centripetal
Acceleration
Period
(s)
(m/s
Angle
(°)
Measured
Acceleration
2
)
(m/s2)
1
2
3
4
5
6
7
8
9
8
012-03776E Amusement Park Physics
Experiment 2: Playground Physics / The Swing
Objective
In this lab you will measure the maximum acceleration on a swing and compare this to a value arrived at through
the principles of conservation of energy and centripetal force.
Discussion
On a swing, we see a number of important physical phenomena, including simple harmonic motion, driven
harmonic motion, inertia, conversion of energy between gravitational potential and kinetic, and centripetal force.
In this experiment, we use the latter two ideas to calculate an acceleration and then compare the results with the
acceleration we actually measure. At least two people are needed to carry out this lab. They will need both a
horizontal and a vertical accelerometer.
Procedure
1. Person A begins swinging with the vertical accelerometer. Person B takes up a position to the side so that he/
she can see and measure the angle of the swinger’s motion.
2. Person A on the swing keeps the vertical accelerometer pointed upwards along the chain or rope, and will
focus on reading the maximum value as he/she passes through the bottom-most point of the swing. This value
will be recorded as a
3. Person B, to the side, will use the lateral accelerometer to measure the maximum angle that the swinger moves
to during the swing. Line the straw side of the accelerometer up with the chain. The angle θ that is indicated
on the accelerometer is going to be 90° minus the angle from the vertical. The angle measured should be
recorded as well as its complement. See Figure 1.
4. When the person on the swing gets to a point where the observer on the ground has a good reading on the
maximum angle, write down both the angle and the maximum acceleration. Repeat in this manner for at least
three different angles, then change places and repeat. Use Table 3 to record your data.
5. Finally, determine the length of the swing. You can use one person’s
height and then scale up, or pace off a horizontal distance and use the
lateral accelerometer to determine the height, or use an appropriate
measuring device. With the swinger seated, you can approximate his/
her center of mass as being close to the seat.
max
.
Analysis
1. Use trigonometry as shown below to calculate the difference in heights
of the swinger between the maximum height and the bottom of the
swing for each trial. Record your calculations in Table 4. NOTE: This
value can actually be measured directly with a measuring tape by
pulling the swing back to the angle determined by person B.
2. Apply conservation of energy between gravitational potential (G.P.E.)
and kinetic (K.E.) to determine the maximum velocity at the bottom
of the swing. Note that the equations give mg∆h = 1/2 mv
mass divides out.
3. The acceleration at the bottom of the swing has two parts: gravity and
centripetal. We can show that the centripetal acceleration is just vL, where L is the length of the swing. Calculate this value and convert
to g’s by dividing your result by 9.8 m/sec
to get the total acceleration.
4. Compare the values you calculated and the corresponding values
2
. Add the 1 g due to gravity
2
, so the
2
9
Figure 1
θ
L
/
L cos θ
h
∆
∆h = L - L cos θ
Figure 2
Amusement Park Physics012-03776E
measured on the swing. Examine the situation and suggest areas where your calculations could have been off
due to approximations.
Data
Table 3:
Trial #Swinger
1
2
3
4
5
6
7
8
9
Max. Angle
Complementary
θ
Angle
θ
Measured
Acceleration (g’s)
Table 4:
Height Diff.
∆h
Maximum Angle
θ
Maximum
Velocit y
v
max
Centripetal
Acceleration
a
c
Maximum
Acceleration
a
max
10
012-03776E Amusement Park Physics
Experiment 3: Elevator Physics
Objective
During this lab you will determine the vertical accelerations in an elevator using an accelerometer. You will also
analyze the motion of an elevator.
Discussion
The net force on the mass in the accelerometer is given by the relationship
: F
where F
the mass is at rest or moving with constant speed in an upward or downward direction, the upward pull of the
spring is equal in magnitude to the downward pull of the weight. In these cases, the net force is zero and the net
acceleration of the mass is zero. If the accelerometer is calibrated to read "1g" when it is at rest, that recognizes
the 1g effect of gravity. To get the net acceleration of zero, you subtract 1g from the reading. If the mass is
accelerating upward, it will be in a position below "1g" or at a reading greater than 1g. Again, the net acceleration
can be determined by subtracting 1g from the accelerometer reading. The reading will still be above zero (positive)
indicating an upward acceleration. If the mass is accelerating downward, it will be above the "1g" position, or a
reading of less than 1g. Subtracting 1g will yield a negative net acceleration in agreement with the downward
acceleration of the mass.
s
- mg = F
s
is the force applied by the spring to the mass, and mg is the weight due to gravity of the mass. When
= ma
net
net
Procedure
Hold the accelerometer vertical by pressing it to the wall of the elevator. Take readings in each of the following
instances (see Table 5).
Table 5:
Trial 1Trial 2Trial 3
Standing still
Beginning ascent
Middle of ascent
Slowing ascent
Stopped
Beginning descent
Middle of descent
Slowing descent
Stopped
Questions
1. Are the magnitudes of the accelerations different at the beginning of the ascent than in the middle of the ascent?
Explain why this is so.
2. Are the magnitudes of the accelerations different at the middle of the ascent than at the middle of the descent?
Explain why this is so.
11
Amusement Park Physics012-03776E
3. How does the starting acceleration compare with the stopping acceleration? Was it the same during the ascent
as it was during the descent?
4. Were the acceleration values constant during any of the periods of acceleration, or did they vary? How did
they vary? Were they all the same pattern?
5. How did you feel in each of the situations where you took readings? Compare your feelings with the
accelerometer readings.
Mathematical
If instructed, take a new set of readings, adding in the time for which each interval to occur, the distance over
which it occurred and the net acceleration.
Table 6:
TimeDistanceNet Acceleration
Standing still
Beginning ascent
Middle of ascent
Slowing ascent
Stopped
Beginning descent
Middle of descent
Slowing descent
Stopped
Questions
1. What was the average speed going up?
2. What was the average speed going down?
3. Use your acceleration values and times to calculate distances for each of the accelerations. How do your
calculated values compare with the ones measured (or estimated)?
4. What was your average speed during the periods where you were moving at a constant speed?
Use your data to construct a distance vs time and a velocity vs time graph.
6. Do these graphs accurately reflect the motion you experienced on the elevator? Explain your feelings at different
places during the experience.
12
012-03776E Amusement Park Physics
Technical Support
Feed-Back
If you have any comments about this product or this
manual please let us know. If you have any suggestions
on alternate experiments or find a problem in the manual
please tell us. PASCO appreciates any customer feedback. Your input helps us evaluate and improve our
product.
To Reach PASCO
For Technical Support call us at 1-800-772-8700 (tollfree within the U.S.) or (916) 786-3800.
email: techsupp@PASCO.com
Tech support fax: (916) 786-3292
Contacting Technical Support
Before you call the PASCO Technical Support staff it
would be helpful to prepare the following information:
• If your problem is computer/software related, note:
Title and Revision Date of software.
Type of Computer (Make, Model, Speed).
Type of external Cables/Peripherals.
• If your problem is with the PASCO apparatus, note:
Title and Model number (usually listed on the label).
Approximate age of apparatus.
A detailed description of the problem/sequence of
events. (In case you can't call PASCO right away, you
won't lose valuable data.)
If possible, have the apparatus within reach when calling. This makes descriptions of individual parts much
easier.
• If your problem relates to the instruction manual, note:
Part number and Revision (listed by month and year on
the front cover).
Have the manual at hand to discuss your questions.
13
Amusement Park Physics012-03776E
Notes:
14
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