Measure. Analyze. Learn.
Hello. Our Centripetal Force Apparatus (CFA) allows students
to explore the relationship between centripetal force,
angular speed, radius, and mass.
Using high resolution data collection technology
students can analyze the relationship quantitatively.
There are four things you can measure directly;
the mass, the radius, the velocity, and the force.
We'll measure the mass using these carriages,
which have calibrated masses installed.
There is a fixed carriage,
and one which is allowed to slide freely on the beam.
We'll measure the radius
using the marking on the front of the beam.
There's a slotted wheel which is allowed to pass through
a Vernier Photogate to measure the velocity.
To measure the force, you can use a Dual Range Force Sensor,
or a Wireless Dynamics Sensor System (WDSS).
Now, I'll show you how to assemble the apparatus with sensors.
When you first assemble the Centripetal Force Apparatus,
you will notice that the frame is stored flat.
Also in the package, you will find two carriages
for holding the masses.
One, has thumb screws and it will be fixed to the beam.
And the other one, has bearings, and it will be allowed to slide.
The calibrated masses are 100 grams each.
And, you will also find a string and spool assembly,
which will allow you to connect to the Dual-Range Force Sensor,
and not have any twisting in the string.
In this flat position, you'll notice that the legs are stored
on the structure of the Centripetal Force Apparatus itself.
What we're going to do when we turn it upright,
is we're going to use the holes at the bottom of the beam.
Next, we're going to install the carriages on the beam.
Before we start, there's an important difference to notice.
This center spool is not perfectly in the center.
As you look at the markings,
you'll notice that it is off a little bit to the right.
Be sure to look for the thumbscrews;
this carriage will go on the left side of the beam.
You'll need to use the thumbscrew to remove the end cap.
Find your fixed carriage. That's the one with the thumbscrews.
And, align the tabs to the slot in the beam.
Then, replace the end cap.
We'll repeat the same process at the other end of the beam.
Before we install the sliding carriage, note that one side
of the bottom has bearings, and the other side does not.
It's important that the bearing go toward the center of the beam.
When we replace the end cap, you'll see that this free side
is not allowed to interfere with the end cap,
and the carriage should move freely.
Now, with the carriages installed,
we're ready to install our sensors.
You'll want a Vernier Photogate to measure the velocity,
with the slotted wheel.
You'll see that the thumbscrew for this photogate
is installed in a storage location on this bracket.
Line up the photogate with the wheel.
And, you may want to insert the end of the cord
into the groove on the frame.
With that installed, we're ready to put on our force sensor.
The Dual-Range Force Sensor attaches to a post
on the frame of the Centripetal Force Apparatus.
First, remove the screw.
Then, slide the force sensor onto the post, and use
the thumbscrew on the force sensor to orient the force sensor.
Finally, we're ready to install the spool and string assembly.
Find the carriage that slides freely.
So, go ahead and thread that through,
and hook it to the edge of the carriage.
Next, feed the string along the outside of the upper spool.
Feed it along the outside of the corner spool.
And then, screw it into the Dual-Range Force Sensor.
To set the radius of the free carriage,
adjust the position of the force sensor on the frame.
The next step we're going to take is to level the apparatus.
We'll do that by putting masses on one side of the beam.
And, we're going to give the beam a slow spin.
Now, you may notice that there's a place where the beam
tends to rest, it tends to bottom out,
there may be a low point in your setup.
If that's the case, you can go ahead and loosen one of these feet
on the low side, until you've got it level.
Now, let's run an experiment.
So, I will open the file from the 'Probes and Sensors' folder
of Logger Pro that indicates Centripetal Force Apparatus,
Dual-Range Force Sensor, photogate.
And, I'm going to open the file that is
set up for angular velocities.
This file is preinstalled with Logger Pro.
And, you will see that, when it opens,
I get the views I want, with the graphs I need.
And, I also have a data table set up, ready to collect the data.
Before I begin data collection, I'm going to spin the beam,
and I'm going to aim for a force over 5 Newtons.
You can read the force while you're spinning,
and then you're ready to start.
As data collection proceeds,
you can see I'm collecting a lot of points of data.
As we watch the velocity decrease, we can also see that
the force is decreasing over time.
Now that the experiment is finished,
we can go ahead and take a look at our results.
On page 2 of this experiment file,
there is a new view of the graph.
So, go ahead and click on 'Next'.
And, you'll see that I've got two views of the data here.
I've got the force versus the angular velocity, and I've also got
the force versus the square of the angular velocity.
You'll notice a few things.
First of all, force versus the velocity squared
is more of a linear graph, and also you can see that
it aims directly at the origin.
That's because it's a direct proportionality.
In fact, if I apply a linear fit to these data, I will find that
the slope, matches the product of the mass and the radius.
There are a few other ways you can change this experiment.
One thing we can do is, we can adjust the amount of mass,
in the carriages, on the beam.
Another thing we can do is change the radius.
The way we'll do this is, we'll first adjust the position of
the fixed carriage, using the markings on the beam.
And then, we can adjust the position of the sliding carriage,
by changing the position of this Dual-Range Force Sensor.
Finally, there is one more way you can measure the force.
You can use the Wireless Dynamics Sensor System.
To do so, we will mount the device on the beam.
And, we will be able to eliminate the factors of
friction and stretching in the string.
Those are the basics for setting up a Dual-Range Force Sensor,
a Vernier Photogate, and the Centripetal Force Apparatus.
For information on using the Wireless Dynamics Sensor System,
please see our website and the product user manual.