We wish to investigate the relationship between acceleration, force, and
mass. This investigation should lead
to an understanding of
Materials
You will need a single cart and dynamics track with a pulley and magnetic stop
attached, force sensor, 2 photogates, picket fence, and hooked & slotted masses.
Procedure
·
Set up the track with a pulley and magnetic stop at the end opposite the
permanent bumper.
·
Record the mass of the cart, force sensor and picket fence (combined).
The cord should lay on the table beside the balance.
Record this (and all masses) in kilograms.
·
Attach the photogates as you did in Experiment 4, making sure the cord
of the force sensor will not catch on them.
The picket fence should be put in the force sensor “up-side down” and the
photogates adjusted so the second bar on the picket fence blocks the gates.
·
Level the track, then, with the cart on the track, attach a string to
the hook on the force sensor so that you can attach masses to the string to hang
over the pulley. (The masses hanging
over the pulley will provide the force on the cart.)
Position the pulley so that the string is horizontal and does not drag on
the magnetic stop.
·
Plug the force sensor into “Analog Channel A.”
·
Now set up Data Studio to record
your data as follows.
o
Open the Data Studio application and click on the “Create Experiment”
icon when it appears.
o
Set up the photogates to measure the acceleration of the carts just as
you did in Experiment 4.
o
You will only need two tables
for the acceleration, one for “time in gate 1” and one for the acceleration.
o
Drag a force sensor icon (not force sensor – student icon) to the
interface box. Double click on the
sensor icon attached to the interface to open the force sensor’s “Sensor
Properties” window. Set the sample
rate to 20 Hz.
o
Drag a graph icon from the “Displays” window to the “Force, Ch 1” listed
in the “Data” window.
o
Arrange the two tables so they are “tall and skinny” on the left side of
the window and stretch the “force” to fill the rest of the window.
PART I: FORCE AND
ACCELERATION WITH CONSTANT MASS
·
Zero (tare) the force sensor by pressing and holding the TARE button on
the side of the sensor for at least 5 seconds.
This should be done with no force pulling on the sensor’s hook.
·
Click “Start” and verify that the sensor is tared by checking that the
force graph reads zero. Delete this
data run.
·
Hang a 20-g mass off the end of the string attached to the sensor.
·
Tare the sensor again with slack in the string
·
Click “Start” and gently let the slack out of the string.
·
Release the cart and click “Stop” when the cart reaches the bumper.
Note that one of you will need to hold the track in place while the cart
is running, or its collision with the bumper may shift it off the table.
·
You should see the force data on your graph and the acceleration in your
table. From this information you
will determine the force on the cart and its acceleration as follows.
o
If tared correctly the graph will be zero for some time at the
beginning. If not, delete this data
run and redo it.
o
Click the “Scale” icon in the upper left corner of the graph window to
stretch your data to fill the graph window.
o
Look at your “time in gate 1” table and make note of the time that the
cart entered gate 1, (which is in the left hand column of the table).
Also look at the acceleration table and make note of the time the cart
exited gate 2.
o
Use your mouse to drag a box around the force data that includes all the
points recorded between the two times you noted above.
The data points will be highlighted in yellow.
o
Click on the statistics icon (“Σ▼”) to display the mean value of the
force in newtons.
o
Record this force. (Note
that the sensor records a “pull” as a negative force.
You should simply record the absolute value of the number displayed.)
o
Record the acceleration.
o
Delete this data run.
·
Repeat this procedure for a total of 5 hanging masses:
20 g, 40 g, 60 g, 80 g and 100 g.
You will need to tare the force sensor each time before adding a new
hanging mass. Pay attention to your
data, make sure the force graph starts with zero, and see if you need to repeat
any runs that give unusual data.
PART II: MASS AND
ACCELERATION WITH CONSTANT FORCE
You have a run from Part I with a hanging mass of 60 g.
Record this run in a second table as a run with zero added mass.
Then make 4 additional runs,
adding 200 g of mass to the cart (not hanging over the pulley!) each time.
You will need to lay slotted masses in the tray of the force sensor so
that they do not block the photogates.
You can also hang 200-g hooked masses off the back of the force sensor.
Tare your sensor before each run.
For each run, record the added mass, the total mass (cart & sensor plus
added mass)—in kilograms—and the acceleration.
Also calculate the reciprocal of the total mass for each run and include
it in your data.
ANALYSIS
Use your data from Part I to make a graph of a vs. F for constant mass and
answer these questions.
1.
What
is the shape of your graph? What
does this tell you about the relationship between a and F?
2.
What does the x-intercept of
the graph represent?
3.
Calculate the reciprocal of the
slope of your graph. How does it compare with the mass of your cart & sensor (in
kg)?
Use the data from Part II to construct two graphs, one of a vs. m and another of
a vs. 1/m, then answer this question.
4.
What
do the shapes of these graphs tell you about the relationship between a and m?