Download Newtons Laws I

Lab 05: Newton’s Laws Part I
Learning Objective:
Students will be able to:
• Design and conduct a controlled experiment to determine a mathematical model from
experimental data
• Apply mathematical model to predict outcome
Lab Records Scoring Rubric (14 pts total)
Excellent (2)
General Clarity
Limited (1)
1. Student name
2. Experiment name & date
3. Lab partner names
4. Course and section #
5. Organization and neatness
Missing (0)
A couple of the parameters
are missing or submissions are
disorganized, difficult to read.
Multiple parameters are
missing or submissions are
highly disorganized or
difficult to read.
I. How does the acceleration of a system change when the applied force changes?
a. Consider the scenario shown at right in which a hanging mass
applies a force to a block, causing it to move to the right. Assume
the friction between the block and the table is negligible. In your
lab records, reproduce and complete the experimental design
template below to address the research question “How does the
acceleration of a system change when the applied force changes?”
Experimental Design Template
Research Question:
How does the acceleration of a system change when the applied
force changes?
Dependent variable (DV):
Independent variable (IV):
Control Variables (CV):
(include actual values once chosen)
Testable Hypothesis:
(should contain IV and DV)
Prediction:
For the prediction, sketch a
graph for acceleration vs.
force as shown at right.
Lab 05 - Newton’s Laws Part I Page 1
b. Before conducting the experiment, the system must be chosen. A system is a collection of two or
more objects that can be treated as a single object. As a group, discuss what will comprise the
system in this experiment and record this as a CV in your experimental design template.
c. As a group, discuss how many trials will be conducted and what values will be used in each.
Checkpoint 1! Have your experimental design checked by your TA before continuing. Your TA
will also check your choice of system and how it will be kept constant as one of the control
variables during the experiment. Be sure your TA also checks your plan for the number of trials
that will be conducted.
Check your lab records for completeness using the rubric below:
Excellent (2)
Experimental
Design
Template
Experimental
Set-up
1. Clearly states research question,
hypothesis and prediction
2. Identifies independent and
dependent variables
3. Lists control variables along with
actual values
1. Makes a sketch of the experimental
set-up or apparatus; essential
features are included and labeled.
Limited (1)
Missing (0)
A couple of the
parameters are missing.
A significant number of
parameters are missing or
are included with too
little detail to be useful.
Some features and/or
labels are missing.
Sketch is missing.
d. Using the provided air track and equipment (including the GOLD cart), conduct the experiment. Your
TA should have already discussed how to measure the acceleration of the cart on the air track.
• Be sure the string passes over the largest diameter pulley on the rotary motion detector.
• Be sure to catch the cart at the end so it does not damage the rotary motion detector.
• Record all data and accompanying uncertainties* in your lab records.
*In order to determine the uncertainty of the acceleration, remember that the rotary motion sensor
measures the cart’s velocity precisely but the acceleration obtained from DataStudio is the slope of
the best-fit line through the velocity vs time points and therefore has randomness. This randomness is
reflected in the standard deviation 𝜎𝜎 of the slope so be sure to record this value. However, note that
DataStudio states the slope to only three figures. Treating this value as an instrumental reading, its
scale error is plus or minus the last digit. The velocity points may be so close to being on the same line
m
that the slope’s uncertainty 𝜎𝜎 is smaller than the scale error of 0.001 2 . If this is the case, use the
s
scale error for 𝑢𝑢(𝑎𝑎) instead of 𝜎𝜎.
e. Enter the collected data into Excel to produce the appropriate graph, with both horizontal and vertical
error bars, to address the research question. Save all data and the graph on a personal storage device.
f. Using the graph, determine the mathematical relationship between acceleration and applied force.
Based on what has been covered in the lecture part of this course, does this mathematical relationship
make sense? If not, why not? This will be explored further in the next section.
Checkpoint 2! Have your graph and mathematical relationship checked by your TA. While
waiting, be sure your lab records are complete using the rubric on the next page.
Lab 05 - Newton’s Laws Part I Page 2
Check your lab records for completeness using the rubric below:
Data
Estimation of
Uncertainties
Excellent (2)
Limited (1)
Missing (0)
1. Organizes all measurements into a
neat handwritten table.
2. Clearly labels values with units.
3. Creates and clearly labels graph.
1. Gives uncertainty estimates for
each type of measurement.
2. Describes how uncertainties were
determined.
Some measurements,
tables or graph missing;
labels or units are missing.
A significant amount or
all data and the graph are
missing.
Several uncertainty values
or the description of how
uncertainties were
determined are missing.
A significant number of
uncertainty values or
description is missing.
II. Connecting Experimental Outcomes to Expected Theoretical Values
g. In the previous section you determined a mathematical model that predicts the acceleration of an
object when a range of forces are applied to a system of constant mass. In reality, your model might
not match what is expected in theory due to a variety of environmental factors, such as friction, or
experimental errors.
Compare your experimental model to the theoretical model. Identify any differences between the
two as well as what any constants in the experimental model represent in the theoretical model.
Show all work in your lab records. Some things to consider:
1. What other forces, other than that due to the hanging mass, may be present in the experimental
context which needs to be considered when comparing to the theoretical model?
2. Where does the mass of the system show up in the experimental model?
3. What possible systematic errors may impact your results?
4. If the string used to connect the small weight to the cart had appreciable mass, would the cart
still undergo uniform acceleration?
Excellent (4)
Comparison of the
Experimental and
Theoretical
Models
1. Provides a thorough comparison
between the two models and takes
into consideration each of the four
points above.
Limited (2-3)
Details of the
comparison are not
complete.
Missing (0-1)
A significant amount
of the comparison is
missing.
h. A lab report is required for this investigation BUT is not to be written until after Lab 06. In the lab
report you will address the research question “How is the acceleration of a system related to the
force applied?” You have enough information to start working on the lab report now BUT you will be
required to include data and findings from other groups to provide support for your own
mathematical model generated during this lab activity. The sharing of this data will occur at the
beginning of the Lab 06 class. This ends the work necessary for Lab 05. Turn in your lab records but
be sure to bring your own copy to class during Lab 06 as this data will be needed again.
Checkpoint 3! Your TA will check your understanding of how to compare an experimental model
with a theoretical model.
Lab 05 - Newton’s Laws Part I Page 3