Name____________________________________
PHYSICS 124 LAB 4: FORCE TRANSDUCER AND NEWTON’S 2ND LAW
Calibrating the “Dual-Range Force Sensor”
A force sensor measures force. Well, not really. When
the movable arm (see Figure 1) of the force sensor is pushed (or
pulled!) it sends a signal to the computer in the form of a voltage.
The harder the push, the higher the voltage produced. The
combination of the force sensor and the computer, however, can
be used to measure force if it is calibrated; that is, if you instruct
the computer how to convert the measured voltage to a force.
Follow these steps to set up the force sensor:
i) Connect the force sensor to CH 1 of the LabPro. Set the
switch on the force sensor to the ±10 N setting. Connect
the motion detector to the DIG/SONIC1 port.
ii) Start the Logger Pro program and wait for it to start.
The computer will automatically detect the force sensor.
If it works properly, you should see a Force vs. Time
graph. Try clicking on the Collect button and you will see
a line appear. Push or pull on the sensor “arm” to see the effect of a force.
iii) These force sensors should already be calibrated, but they won’t give precise results
unless we make a small adjustment, called “zeroing the sensor.” Place the sensor on the
table, with the movable arm pointing horizontal. Then click on “Experiment” then click
on “Zero…”. After a short delay the sensor is ready to measure forces.
iv) To check that the sensor is measuring force accurately, suspend a 500 g weight and a
50 g weight hanger from the hook on the force sensor. Hold the sensor as still as
possible. Once you have suspended the weight and hanger from the force sensor you will
notice that force is indicated on the screen, indicating that something is indeed pulling
down on the force sensor. The value of the force (i.e., the weight of the 550 g mass)
should be 5.39 N.
Observing and Measuring Forces
At this point it will be good for you to push and pull on the sensor with your fingers to
get an idea of how the thing works, and also to get a feel for what a Newton is. To observe the
value of the force exerted on the sensor as a function of time click the “Collect” button at the top.
You can also change the Force and Time scales as needed to better observe the data. Each
individual in your group should take a moment to try the following:
* With your thumb exert a constant +10 Newton force for 5 seconds.
* With your thumb exert a constant –10 Newton force for 5 seconds.
* Apply a varying force with your thumb.
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* Hang a known weight (different from that with which you calibrated the instrument, but less
than 900 g) from the sensor and check if the sensor is properly reading it in Newtons.
* Put the sensor on its side on the table and check for a zero force again.
* Try to observe the effects of gravity on the force sensor by rotating it by 180 degrees with no
extra weight added. First point it up, and then point it down. You may have to change the scales
on the Force vs. Time graph to observe this effect. Does your observation make sense?
Exercise: Below, estimate the weight, in Newtons, of the movable “arm” of the force sensor
from this data.
The Effect of a Net Force: Newton’s 2nd Law
Next, you will make use of the PASCO track and the cart with the little fan on it. When
the fan motor is switched on you will notice that, when released, the fan causes the cart to
accelerate down the track. Therefore, the fan must effectively be exerting a net force on the cart.
The fan can be rotated to face any direction (it is best to hold the fan near its base to do this).
Newton’s 2nd Law (F = ma) tells you that a net force exerted on a massive object should cause an
acceleration of the object which is directly proportional to the exerted force and inversely
proportional to the object’s mass. We will now check the validity of this assertion by measuring
the net force exerted on the cart and the acceleration of the cart when the fan is set at different
angles.
Before you make any measurements, observe qualitatively the effect that different fan
settings have on the motion of the cart. “Qualitatively” means to observe the effect of different
settings without estimating any actual values of the force. Also, for a given angle, observe the
effect of different fan speeds by running the fan on “high” and then on “low.”
To quantitatively measure (i.e., get an actual number for) the net force exerted on the fan
and the acceleration of the fan cart associated with the different settings, follow this procedure
for each fan setting and enter the measured force and acceleration in Table 1.
i) Set the force sensor on the track so that the movable arm is facing along the track.
Place the fan cart directly in front of the force sensor so that the fan will push the cart up
against the sensor. The sensor may record this as a negative force. Set the time for
observation to 10 sec, and set the vertical (force) scale of the graph from –1.0 to 1.0
Newtons (you may have to use a different scale to suit your particular fan). With the fan
set at the angle of interest (see the table on the next page), switch the fan on to the desired
speed so that it pushes against the arm of the force sensor. Wait for two or three seconds,
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then click on the “Collect” button and observe the measured force for the 10 second
interval. You will notice that a jaggediness, characteristic of any measurement device,
appears. This jaggediness is commonly referred to as “noise” and is an example of
random error associated with the operation of the instrument. It is also due to vibration
from the fan. There is no way to eliminate the noise. So you must work with this data
and use it to estimate the value of the force.
ii) A good way to estimate the value of the force is to find the average of a number of
measurements of the force. If you have the sampling rate set at 50 Samples/second (you
can check this by clicking on “Experiment” then “Data Collection”, then look at the
“Sampling Rate” box), then over the 10 second interval there should be 500 data points.
You must find the average of these points! Fortunately the computer will do this for you.
Using the mouse, select most of the set of data by holding the mouse button and dragging
the cursor (a + symbol) across the horizontal extent of the Force vs. Time graph (it’s OK
if you leave out a few of the data points at the beginning and end). From the “Analyze”
menu, choose “Statistics” and a box will appear indicating statistical information about
the set of values that you selected. (There is also a shortcut STAT button on the main
menu.) The important quantity in this box is the “Mean” value, which is the calculated
average for all the data points selected. (“Mean” is another term meaning “average.”)
iii) You have measured the force exerted on the cart when the fan is set at High 00. Now
for this setting, let’s measure the associated acceleration of the cart. To do this, use your
friend, the motion detector, whom you’ve grown to know and love. Here is a procedure
to follow in order to determine the acceleration of the fan cart.
iv) Position the motion detector at the end of the track. The motion detector must be able
to detect the fan cart as it is accelerating down the track away from the detector. There
should be a bumper at the other end to stop the fan cart.
v) Put your finger in front of the fan cart, with the cart at least 50 cm away from the
detector. Once the fan is switched on and is up to speed, click the Collect button, wait for
the sound of the motion detector, and then pull your finger away so the cart can
accelerate away from the motion detector. Someone should catch the cart!
vi) Measure the acceleration for the fan setting High 00 and record this in Table 1. (Do
you remember how to obtain acceleration from a Distance vs. Time and/or a Velocity vs.
Time graph?) You may have to play with the position of the motion detector to ensure
that you’re actually detecting the fan cart.
vii) Follow this procedure and measure force and acceleration for each fan setting
indicated in Table 1, and record them. (It is best to choose to use angles on one side or
the other, and remember which side you used.)
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Table 1
Fan
Setting
Measured
Force (N)
Measured
Acceleration (m/s2)
High 0
High 30
High 60
Low 0
Low 30
Low 60
With Table 1 completed, you have sufficient data to make a validity test of Newton’s
second law of motion.
* Describe below how you propose to use this data to test the validity of Newton’s
second law. (Hint: You will want to plot something vs. something else. Notice that
F=ma is similar to y=mx so you will need to do a linear fit to a graph of F vs. a using the
values of F and a from the columns of Table 1. Which variable, F or a, goes on the
horizontal axis and which on the vertical axis?)
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* What do you expect your proposed graph to look like? Why?
* Now make the plot you propose in the above description by using the Graphical
Analysis program (or on paper if the program is not available). You can minimize the
LoggerPro window and you will see the Graphical Analysis icon on the desktop. Your
data can be entered into the “Data Set” area in the Graphical Analysis program, by hand,
from the data in your Table 1. To get these to plot correctly, you will need to order the
pairs of data points (F vs. a) in order of increasing a (a is entered into the column
corresponding to the x-axis). Then you can select all the data points, either by dragging
the mouse over the range of the data points on the graph itself, or by putting the cursor on
the first row number in the Data Set and dragging the mouse down the left side of the
data table to select all the rows of data. Then go to the Analyze menu and select Linear
Fit. You can choose Graph Options from the Options drop-down menu and give the
graph an appropriate title.
* What do you expect the slope of this graph to be equal to? Is the actual slope equal to
the expected value (the mass of the fan cart)? You can weigh the fan cart on a pan
balance in the lab to get its mass. When you weigh the fan cart, tilt it on its side to keep it
from rolling off the pan. Different fan carts may have slightly different masses since they
may have different types of batteries in them. If the slope is significantly different from
what you expect or predict it to be, how can you account for the difference? (Did you
plot force on the y –axis and acceleration on the x-axis?)
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* How will you know if you have indeed validated Newton’s second law?
Print out and turn in your graph with the rest of the lab exercise.
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