The Vernier Motion Encoder System
allows you and your students to measure
the position of a cart as a function of time
easily and with very high accuracy.
It's used a bit like an ultrasonic motion detector
but doesn't have the accompanying frustrations
of detection of stray objects
and other kinds of interference in the classroom.
For example, if I had a motion detector
at this end of the track and a computer screen here,
the motion detector would be blind
to the cart's motion on most of the track.
The Motion Encoder System
consists of three new pieces.
First, the track has a bar pattern printed on it.
That bar pattern has a 4-millimeter period,
allowing you to measure the position of a cart
to the nearest millimeter.
The cart has a sensor on the underside.
The sensor detects the passage of the bars on the track.
That information is sent by an infrared beam
to the receiver.
The receiver is plugged into an interface.
In this case, I'm using a LabQuest Mini,
but you could also use a LabQuest 2
or a LabPro or even an original LabQuest.
The interface is plugged into a computer,
and I'm going to use Logger Pro
to graph the motion today.
I'm going to move the cart up to the top
and launch the software.
That's establishing my zero position.
And if I let the cart roll down,
you can see on my computer screen
the current position is being shown
in this digital readout.
Let me start data collection and give the cart a push,
and it rolls up and comes back down the track,
moving with constant acceleration.
If I take a look at my position data,
I get a very nice, clean parabola.
There are no spikes, there's no extraneous stuff
that you've got to explain away to students.
The velocity graph is showing a nice linear portion,
of course pointing to when the cart was freely rolling.
I can do some analysis here.
Let me select a region of the graph.
And I'm going to choose to do a quadratic fit here.
And indeed my fit is quite good,
and you see that the position data follow
that expected parabolic form.
I can go to the velocity graph,
select the constant acceleration portion,
and request a linear fit.
And indeed, you can see that the fit is quite good
and gives me a good measure of the value of the acceleration.
Now, one of the things that's hard to do
with a motion detector is to get
high-quality acceleration graphs.
Often they're a bit noisy, too noisy to use with students.
Let's take a look at what the acceleration graph looks like
for the Motion Encoder System.
I'm just going to click on the Y-axis label,
and I'll get an acceleration graph.
And you see that the part of the graph
corresponding to the free-rolling motion of the cart
is approximately constant.
I can actually go one step beyond the acceleration graph,
which is the second derivative of position.
Let's take a look at the graph of jerk
as a function of time.
Jerk is the third derivative of position.
Such a graph is essentially never used
with a motion detector because they're too noisy.
But let me draw that graph and see what it looks like.
Since the acceleration graph is constant,
the jerk graph should be zero during this time interval,
and indeed it is.
That would be tough to do with a motion detector.
The Motion Encoder System can be purchased
as a complete unit with two carts, a track,
the receiver, and other hardware.
You can also buy pieces to upgrade
an existing Vernier Dynamics System
to become a Motion Encoder System.
If you like, you can add a second receiver and cart
to a Motion Encoder System
and monitor the position of two carts,
allowing you to do collision experiments
and do conservation of momentum,
conservation of energy experiments.
So that's the Vernier Motion Encoder System.
If you'd like more information on that,
check out our website.