Newton’s Laws and Modified Atwood’s Machine
Overview
The purpose of this investigation is to validate Newton’s Second Law of Motion and test assumptions about Atwood’s machine. Lab equipment will be used to measure force, mass, and acceleration. Force data will be measured by a wireless force sensor (which must be calibrated). Position data will be measured by a CBR sonic ranging device. Both sets of electronic data will be collected and analyzed by a LabQuest2 device. Mass data will be determined simply with a triple beam balance.
In this lab, a cart of constant mass is pulled by a
weight hanging on a string that passes over a pulley. By changing the weight at the end of the
string, different amounts of force can be applied to the cart. It is important to realize that it is
the tension in the string that is
causing the cart to accelerate.
This tension will be measured by a force sensor attached to the top of
the cart.
1. Connect the CBR to the DIG 1
port found under a rubber flap on the side of the LabQuest2.
2. Attach the force sensor to
the top of the cart. Place the cart
on the track. Adjust the feet of
the track so that it is level – this can be judged by rolling the cart in
both directions.
3. Attach the pulley to the end
of the track and adjust the height of the pulley to match that of the hook of
the force sensor.
4. At the other end of the
track arrange the CBR so that it is at the same level as the cart but separated
by a minimum of 0.4 meters (16 inches).
5. You must connect and calibrate
the force sensor. Turn on the
Wireless Dynamics Sensor System (WDSS).
Then under the Sensor menu
choose WDSS Setup… and scan for the
wireless device. You should see the
name of your sensor that is on the label on its side. For this experiment you will use only
the Force sensor – do not enable any of the three acceleration sensors or
the altitude sensor.
6. Once it is connected, go to
the Sensor menu choose Calibrate and WDSS Force. Then enter
zero for Known Value 1 with nothing
touching the force sensor’s hook (with the sensor in a horizontal position). Then apply a known force to the sensor
by attaching a string to the hook, passing it over the pulley, and hanging a
500 gram mass on the end – note: you must hold the cart in place
to prevent it from moving with this mass on the end of the string. Enter the correct force value for Known Value 2. Remove the 500 gram mass after this
process!
7. Adjust the data collection
parameters and make the duration of the experiment 3 or 4 seconds.
8. Now place a 20-gram mass on
the end of the string passing over the pulley.
9. Give the cart a push toward
the CBR and release such that it rolls one direction and then reverses
direction under the influence of the weight at the end of the string. Collect data for this motion – tap
the “green arrow” button lower left of the screen.
10. You should now be looking at
graphs of position vs. time and force vs. time. The position vs. time graph should be a
smooth curve. If not, you need to
repeat the experiment – simply click on the Collect button to
repeat. You may need to adjust the
direction the CBR is pointing if it is getting errant reflections (normally it
works best when tilted slightly upward).
11. Tap on the word “Position”
and choose to change the graph to “Velocity”, so that you can now see two
graphs showing force and velocity.
It should be apparent where the cart was rolling toward the CBR and
where it was rolling away from the CBR – these are the two distinct intervals
of time that must be analyzed.
12. You may find it helpful to
focus on one graph at a time – go to the Graph menu and then Show
Graph and choose to see only 1 graph.
You can always change what data is shown on a graph by tapping on the y-axis label.
13. On the force graph find the
“plateau” that represents the cart moving “backwards” (toward the CBR). Tap and drag to select this portion of
the graph. Then go to the Analyze menu and choose Statistics to get the mean force. Record this value as the tension in the
table. Repeat the process to find
the mean tension for the cart moving “forwards” (away from the CBR).
14. On the velocity graph find
the linear section that represents the cart moving “backwards” (toward the
CBR). Tap and drag to select this
portion of the graph. Then go to
the Analyze menu and choose Curve Fit to get a linear
regression. Use the result to
determine and record the acceleration in the table. Repeat the process to find the
acceleration of the cart moving “forwards” (away from the CBR).
15. Complete the rest of the
table by adjusting the mass on the end of the string to the values shown.
16. Adjust the appearance of the
graphs to your liking and then print ONE
representative graph of each type including the analysis showing how the values
in the table were determined. Do not print graphs for every trial.
17. Measure the mass of the cart
with the sensor attached (the total mass that was being accelerated by the
tension in the string). And measure
the mass of the string.
Analyses
1. Use the results to produce a
tension vs. acceleration graph. Plot
the independent variable (tension) on the y-axis. Use different symbols and/or colors for
the cart moving backward versus moving forward and include a key or
legend. Determine a line of best
fit and its equation for each of the two sets of data.
2. The mass at the end of
string had the same acceleration as that measured for the cart. Use this acceleration and the mass of
the hanging weight to calculate the
tension at that end of the string.
Create a table and corresponding graph of calculated tension versus
measured tension for the two sets of data backwards and forwards. Again use different symbols/colors and
determine lines of best fit.
1. (a) Make a free body diagram
for the cart moving backward. Write
the equation of motion and solve for the tension symbolically. (b) Make a free body diagram for the
cart moving forward. Write the
equation of motion and solve for the tension symbolically.
2. Consider the lines of best
fit for the graph of Tension vs. Acceleration. (a) What do the slopes represent? (i.e. should
equal what?) Explain your
answer. (b) Assuming the values on
your data sheet are accurate, calculate the percent error in the two slope
values. Show your work.
3. Again consider the lines of
best fit for the graph of Tension vs. Acceleration. (a) What do the y-intercepts represent (i.e.
should equal what?) Explain your answer. (b) Ideally how should the two y-intercepts compare to one another? And if this is not the case how can the discrepancy
be explained?
4. (a) Show one example of how you calculated the
tension in the string based on the hanging mass and its acceleration. (b) Discuss the significance of the
results shown in the calculated tension vs. measured tension graph.
5. Discuss error in this
lab. (Things to discuss: indications and signs of error –
random and/or systematic, the probable and significant cause(s) of the error
that is apparent in the results.
The goal of discussing error is to explain satisfactorily why the
results of your lab are not quite exactly what was expected. Be as specific as possible.
You will almost always have unexpected results in an
experiment. Your task is to write a
discussion that is intelligent, thoughtful, and insightful!)
Atwood’s Machine Data
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Total Mass of Cart plus Force Sensor: |
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Mass of the String: |
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Moving Backwards |
Moving Forwards |
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Mass on End of String (g) |
Tension |
Acceleration |
Tension |
Acceleration |
20.0 |
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50.0 |
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70.0 |
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100.0 |
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120.0 |
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150.0 |
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A complete report (50 pts): (5 or 6 pages in this order)
q Completed data/results
table. (10)
q Example graphs of Force vs.
Time and Velocity vs. Time, including analyses. (10)
q Tension vs. Acceleration
graph with lines of best fit. (10)
q Calculated Tension vs.
Measured Tension table and graph with lines of best fit. (10)
q Answers to questions. (10)