Probeware Workshop
SEPS/AAPT
April 2, 2011
University of the Sciences
Bill Berner, Univ. Pennsylvania
Barry Feierman, Westtown School
We will review in this session how to
use the following Vernier probes:
Motion sensor - one dimension
Force probe - dual range
Acceleration probe – one dimension
Microphone
Voltage and Current probes
SETUP sensors
DATA COLLECTION
choices
SET UP your Windows
with tables, meters, graphs
What can you do with a “motion sensor”?
Record position (+ / - 1 mm)
Calculate velocity
Calculate acceleration
Plot graphs instantly
Start with the easy stuff …..
Ask students to first predict the shape
of the position-time graph for an
object which is AT REST
Will they know that the graph
of position-time is a horizontal line
for an object at rest?
Next, ask students to predict the
position-time graph for an object moving
at constant velocity.
Most of the “learning” takes place
here where students get to test out their
initial ideas and assumptions
Here is the graph of a Vernier cart
moving along a horizontal track after
being given an initial push.
The data are sampled at 10 Hz.
cart moving at constant speed
Ask students to figure out the speed
of the cart from the graph itself
Some will estimate the number of
meters covered during each second
Some will estimate the time needed
to cover each meter.
some might think of “slope”
slope of graph indicates the
average speed of the cart
about 0.5 m/s
Logger Pro can display graphs of
position - time
velocity – time
acceleration – time
Logger Pro will also “fit” a variety
of mathematical functions to the
data
average speed about 0.52 m/s
Acceleration is one of the toughest
concepts to understand since it is
a “rate of a rate”
Acceleration occurs whenever the
speed or direction changes
Always begin with the motion of an
object with constant acceleration
Investigate the motion of a cart
moving up and down an inclined plane.
The cart begins at the bottom, is given a
push up the plane, and then let go.
Ask students to first predict the shape
of the position-time graph for both the
uphill and downhill motion of the cart.
Will the graph be a line or a curve?
This is a challenge for students, since
they can see the speed of the cart
changing throughout the experiment.
They know the cart slows down on the
way uphill, stops for a moment, and
then speeds up on the way downhill.
The motion sensor is located at the
TOP of the inclined plane, facing
downwards.
cart at rest
cart at rest
PUSH CART
cart moving up plane
slowing down
cart moving down
plane
speeding up
cart at the top of the plane: speed is zero
Now predict the velocity-time graph
for this same event.
note on +/- sign convention
Any object moving towards the motion
sensor has a “negative velocity”.
Any object moving away from the
motion sensor has a “positive” velocity.
cart moving downhill
speeding up
cart pushed by hand
cart at rest
at top of inclined plane
cart moving uphill
slowing down
What is the acceleration of the cart
when moving uphill?
What is the acceleration of the cart
when it comes to rest at the top?
What is the acceleration of the cart
when moving downhill?
Is the acceleration reasonably constant?
slope = average acceleration
acc = 1.0 m/s/s
Physics classses often measure
the acceleration of gravity
by various methods
In this next demo, we drop a ball from
a height of about 2 meters and record
the ball’s position and calculate the
ball’s instantaneous velocity.
The motion sensor is in the ceiling
facing downwards
First, ask students to PREDICT the
shapes of the position-time graph and
the velocity-time graph for a ball bouncing
on the floor a few times.
Question: is the deceleration of the ball
when rising the same value as the
acceleration of the ball when falling?
ball hits floor
ball hits floor
ball falling
max height
max height above floor
falling
ball falling
hit floor
ball rising
ball falling
ball at rest
ball rising
average acceleration about 9.5 m/s2
You could use a motion sensor to
investigate the potential and kinetic
energy of a falling object.
Here is a tray falling from a height
of about 1.5 meters. The motion sensor
is near the ceiling, facing down.
First ask students to PREDICT the
shapes of the potential energy graph,
the kinetic energy graph, and the
total energy graph for a falling object.
Hint: think conservation of energy
Here is an interesting question.
If a tray is dropped, what would the graph
of the PE vs. KE look like?
As the tray falls, it loses PE and it gains
KE producing a graph with the shape
of a ________________ ?
What about the PE, KE and total
mechanical energy of a bouncing ball?
Let’s look at the gravitational PE first,
found by plotting the height of the ball
above the floor
The ball has zero PE when on the floor
Now let’s examine the KE of the
same bouncing ball.
When the ball is AT REST
its kinetic energy is zero.
Predict the shape of this graph first.
Now predict the total mechanical
energy of the bouncing ball
The SUM of the PE + KE
plotted against time.
One could ask whether the same
PERCENT of energy is “lost”
(to heat and sound) on each bounce.
Looks like an exponential decay!
At times the total energy is near zero.
So if not PE nor KE, what kind of
energy does the ball possess?
What could you do with TWO motion
detectors?
How about test for the conservation of
momentum in an elastic collision of two
toy carts of equal mass.
Each cart’s velocity is determined by a
motion sensor both before and after a
head-on collision.
Here is a snapshot of the velocity of
each cart a moment before they make
a head-on collision
Both velocities are “positive” since
each cart is moving away from its
own motion sensor
Now let’s look at the velocity of each
cart just after the head-on collision.
Each cart has a “negative” velocity
since each cart rebounded and is moving
back towards the motion sensor.
change in velocity of cart 1 = 0.73 m/s
change in velocity of cart 2 = 0.72 m/s
carts had equal mass: 1.0 kilogram
The change in momentum of cart 1
closely matches the
change in momentum of cart 2
FORCE PROBES
Force probes can measure forces
from 0 – 10 N at high resolution
+/- 0.001 N
and from 0 – 50 N at a lower resolution
+/- 0.01 N
Forces can be measured at high
sampling rates.
Predict the FORCE – TIME graph
for lifting a 1000 gram mass (10N)
very slowly ……….
and then lowering it very slowly.
the force is constant if there is
no acceleration
Now predict the force-time graph for
QUICKLY raising a 500 gram mass,
holding it steady for a moment, and then
then lowering it QUICKLY
Hint: the weight must accelerate and
then decelerate, then stop.
raise quickly
lower quickly
hold steady
hold steady
hold steady
Holding it steady is a constant 5 N
Accelerating upwards the force moves
up to 10N maximum, then drops to
about 2N when the weight decelerates
Then steady again at 5 N
Lowering it quickly reduces the force to
2 N, and then catching it increases the
force back up to 10 N maximum
One can demonstrate that the force
recorded by the force meter is
the sum of the static weight (mg)
plus the force needed to accelerate the
weight (ma)
F = mg + ma
where mg = 5N
The maximum acceleration was about
+/- 10 m/s2
With a force sensor you can
demonstrate that starting friction
is higher than kinetic friction
Attach a force sensor to a 4x4 block
of wood and drag it across the table
at constant speed
starting friction force
kinetic friction force
block at rest
A force probe can be used to
determine the WORK required to
stretch an elastic material a known
distance (area under curve).
Here we see the force-displacement
graph acting on an elastic band.
The elastic was then used to accelerate
a toy cart of known mass, predicting its
velocity by the Work-Energy Theorem.
What kind of probes would you need
to test the validity of
Newton’s Second Law?
How about one force probe and one
acceleration probe.
What if you wanted to investigate the
force and the acceleration of a
weighted can bouncing at the end of a
long spring?
You could use a force sensor at the top
of the spring to measure the tension in
the spring, and an acceleration sensor
attached to the can to measure the
acceleration of the can.
Give the can an initial push or pull and
then predict the shape of the
force – time graph
acceleration – time graph
force – acceleration graph
force
acceleration
Note that the force and the acceleration
are “in step”.
When the force is maximum, the
acceleration is maximum.
When the force is minimum, the
acceleration is minimum.
The force is never zero…. why not?
Again, the force meter reads the
tension in the spring which is the sum
of two parts, the static weight (mg)
of the can and spring, and the force
needed to accelerate the can and spring.
T = mg + ma
Now what happens if we plot
force
vs.
acceleration
What shape graph do you predict?
Why?
What does the SLOPE of this
graph represent?
What does the Y-intercept of this
graph represent?
Use Newton’s Second Law to guide
your thinking.
F (net) = M A
slope = mass
about 0.7 kg
Another useful sensor is the
microphone
You can set up the software to look
like a traditional oscilloscope
plotting sound pressure vs. time or
You can set up the software to show
the frequency distribution (spectra)
of the sound to measure the harmonics
or timbre of a musical source.
Here are some examples of a variety
of sound sources.
The first trace is the sound made by
blowing over an empty soda bottle. This
usually produces a clean “sine wave”.
Note the fundamental note (200 Hz)
and its second harmonic (400 Hz)
Here is my voice saying
“ahhhhhh”
Note the simple harmonic series
starting at about 125 Hz with the
Loudest harmonic at 630 Hz
Here is the much more complex sound
(and waves) from an alto saxophone
Saxophones play both “even” and “odd”
harmonics of the fundamental note
(which is why they sound so cool)
Voltage and Current probes can
be used to test Ohm’s Law
Charge a capacitor to 6 v dc
Discharge it into a 10 ohm wire resistor
Measure the voltage across the resistor
Measure the current through the resistor.
Calculate the ratio of voltage/current
Plot the voltage-current graph.
The voltage – current graph is linear
for this wire resistor
This indicates that the resistance
of this wire resistor is constant
(the ratio of voltage/current is 10 ohms)
We call this kind of device an
“ohmic device as it obeys Ohm’s Law
What if we did the same experiment
but discharged the capacitor into a
6 volt incandescent lamp
Would the voltage-current graph still
be linear?
Would the resistance of the bulb
remain constant?
The voltage – current graph is clearly
non-linear for the incandescent lamp
yet linear for the 10 ohm wire resistor.
Does this imply the resistance of the
lamp filament is changing during this
experiment?
Could the temperature of the filament
affect its resistance?
The resistance of the incandescent lamp
began at about 22 ohms when it was hot
(at high current) and decreased steadily
to a low value of 5 ohms when it was
cooler (at low current)
Clearly the temperature of the filament
affects its electrical resistance.
hot wire = more resistance
cool wire = lower resistance
Let’s now investigate the charging of
a large capacitor with a 6 volt battery.
We will put a 10 ohm resistor in series
to limit the initial current surge.
The voltage is measured across the
capacitor, and the current is measured
entering (or leaving) the capacitor.
Charging a capacitor with a battery
Predict the shapes of the graphs of
voltage vs. time
current vs. time
power vs. time
energy vs. time
The capacitor was just about fully
“charged” after 30 seconds.
The total energy stored in the capacitor
was about 2.5 joules.
You can also look at the current-time
graph and ask the question
How much charge entered (or left)
the capacitor?
By integrating the current-time graph
you can determine the number of
coulombs of charge stored on either
plate of the capacitor.
It looks like 0.92 coulombs of
charge was placed on the plates of
this capacitor when charged to 6 volts
The “capacitance” of the capacitor is
C = Q / V = 0.9 coulomb / 6 volts
C = 0.15 farad = 150,000 microfarads
You can also examine the graphs of the
discharge of the capacitor into a
wire resistor.
What will the graphs like for
voltage vs. time
current vs. time
Then use the “curve fit” function of
Logger Pro to fit an exponential decay
type of curve.
The current that flows out of the
capacitor into a fixed resistance is
directly proportional to the voltage
left on the capacitor.
But as charge leaves the capacitor, its
voltage decreases (unlike a battery).
Here is the voltage vs. current graph
for the discharging capacitor