Pre-Lab 07
Learning Objectives:
Students will be able to:
• Design a controlled experiment to determine a mathematical model from experimental data.
• Recognize assumptions made in an experiment that may affect its validity.
There are two parts to your pre-lab assignment for Lab 07. The first part is the standard of reading this
document before completing the Pre-Lab 07 Quiz on Blackboard. The second part is to print out the last
page, complete it, and hand it in at the beginning of your Lab 07 class. This worksheet is worth up to 12
points towards your Lab Records grade for Lab 07.
The next two sections (Design the Experiment and Characterize a Spring) contain six numbered
subsections that correspond to the six questions or tasks on the worksheet. Read and consider these
before filling out the worksheet.
Design the Experiment - What affects the period of an oscillating spring/mass system?
1. Pulling down and releasing a weight hanging on a spring causes it to bob up and down
at a certain rate. What characteristics might impact the rate?
I.
2. Part of the design process is to complete an experimental design template for each
identified factor. What are the dependent and independent variables? What are the
control variables? What is a testable hypothesis? Predict how the period changes as
you change the factor.
Characterize a Spring
Different springs stretch differently. The spring constant 𝑘𝑘 is a physical property of a spring that
describes its elasticity (also stretchiness or stiffness). It is determined by hanging a known weight on the
spring and measuring how far the spring stretches from a reference point. For the spring in Figure 1, the
unweighted length is 7.5 cm. The resulting length is shown for different added weights.
3. What does the graph of applied force (added weight) versus the resulting stretch look like?
Figure 1 Spring stretched with three weights.
Length of spring = 7.5 cm with no mass attached.
4. What is the slope of the best line drawn through the points on the graph?
5. Hooke’s Law for springs is given by 𝐹𝐹spring = −𝑘𝑘𝑘𝑘 where 𝐹𝐹spring is the force exerted by the spring, 𝑘𝑘 is
the spring constant, and 𝑥𝑥 is the distance the spring has stretched from equilibrium. The negative
Pre-Lab 07 1
sign indicates a restoring force exerted by the spring that is in the opposite direction of both the
applied force and the stretch. An equivalent way of stating this law is 𝐹𝐹 = 𝑘𝑘𝑘𝑘, where 𝐹𝐹 is the applied
force. Using the second equation, what does the slope in 4 represent? How would the equation
change when measuring the stretch from a point that is not the equilibrium point?
6. In the Lab 07 class you will be provided with a set of springs. How would you measure the spring
constant of each?
Making Assumptions
The definition of “assumption” is something which is taken for granted; something that is believed to be
true without proof. All scientific investigations involve assumptions made by the researchers. These are
justified claims that if they are not true, may impact results.
As an example, consider the hypothesis: Substance A impacts bacterial growth.
Researchers predict that: Substance A will stop bacterial growth.
In testing the hypothesis, several Petri dishes are spread with a mixture containing substance A and a
bacterial growth medium, and several others are spread with a mixture containing an inert substance B
and the same bacterial growth medium. Bacteria are spread on all Petri dishes. One day later, the
researchers examine the Petri dishes for any difference in bacteria growth between substance A and
substance B.
Although this test appears straightforward,
it relies on several assumptions. These are
shown in the diagram on the right. Read
through them before reading on.
Note that all of these assumptions are
reasonable. If the researcher was
concerned that some of the assumptions
might influence the results, additional tests
in parallel with the experimental ones
could be run, such as not using marker on
the containers and checking for any
differences. Often assumptions are justified
by past experiences of the researchers and
therefore do not need to be checked. In
[Example adapted from http://undsci.berkeley.edu/article/howscienceworks_13]
this case the assumption that bacteria
will grow on the growth medium likely won’t have to be tested as this particular medium was likely used
many times in the past. Some assumptions might remain untested simply because our knowledge
suggests that the assumption is a safe one (e.g., we know of no reason why bacteria should multiply
faster when their dishes are marked with a red, rather than a green, pen). And last, some assumptions
might not be testable in the lab setting; such as all mice being identical in a pre-clinical drug test.
Pre-Lab 07 2
Regardless, identifying assumptions is an important part of any experimental design. When evaluating
the experimental outcomes, a researcher must reflect back on this list of assumptions and ask:
• Were experimental conditions such that an assumption was incorrect?
• Might this have altered or impacted the final claim made?
• If so, how was the claim impacted?
It is for this reason that you will be expected to include a statement in the conclusion section of your
next lab report about what assumptions were made and whether or not they might have impacted your
results. Once you have identified an assumption, it is appropriate to suggest how the experiment may
be changed or improved if the experiment were repeated to account for the assumption.
There often many assumptions that can be listed in an experiment, and simply put, many of these are
not appropriate for reporting. For example, assumptions that your lab partners correctly used the
equipment, didn’t make any calculation errors, and didn’t write down incorrect numbers, are not worthy
of consideration in a report. Although these things can happen and will certainly impact your final
results, they should be addressed and corrected during the investigation, and should not be included in
a lab report.
Examples (address each before looking at the provided suggested answers)
1. Make a list of assumptions made in the pendulum lab conducted at the beginning of the term.
2. Make a list of assumptions made in the Newton’s Law experiment conducted during Labs 05 and 06.
Pre-Lab 07 3
Answers
The suggested answers are not complete, but will provide examples of assumptions which might be
included in each of the lab investigations:
1. Make a list of assumption made in the pendulum lab conducted at the beginning of the term.
- There is no difference in the period between a planar swing (the shadow of the bob due to a
single bright light directly overhead travels along a line) and an elliptical swing (the shadow
traces out an ellipse).
o We could test this by making two measurements of the period, one from trying to keep
the motion in a vertical plane, the other from trying to get the bob to move in a
horizontal circle. If the two measurements agree with each other, the assumption is
good.
- The pendulum string is massless.
- The pendulum bob behaves like a point mass.
- The geometrical center of the brass cylinder is the center of mass.
- The system is frictionless.
- The string doesn’t stretch.
- The arm of the pendulum support does not bend.
2. Make a list of assumptions made in the Newton’s Law experiment conducted during Labs 05 and 06.
- Changing the mass riding on the cart on the air track does not change the amount of friction
between the cart and the track.
o We could test this by observing how far a differently-massed cart goes on the track with
a small push and no hanging mass. A different frictional force would change how far the
cart could travel.
- The air flow from the holes on the track merely lifts the cart off the track and does not exert any
horizontal forces on the cart.
o We could test for this by placing the cart on the track and noting if it remains at rest
even after the track has been properly leveled.
- If friction is present, it is the same everywhere on the track.
- The track is level
- The track is exactly straight and not curved.
- The string is massless.
- The pulley is massless.
- Each fishing bob has the same mass.
Pre-Lab 07 4
Lab 07: Lab Records (Pre-Lab Worksheet)
Name ______________________________
Date ______________________________
Print this page, fill it out, and turn it in at the beginning of Lab 07.
1. (Refer to section 1 found on page 1.) Name at least three factors that might impact the period of an
oscillating spring/mass system.
2. (Refer to section 2 found on page 1.) Fill out the experimental design template for one of these
factors.
II.
Experimental Design Template
Research Question
What affects the period of an oscillating spring/mass system?
Dependent variable (DV):
Independent variable (IV):
Control Variables (CV):
(include actual values once chosen)
Testable Hypothesis:
(must contain IV and DV to be testable)
Prediction
3. (Refer to section 3 on page 1.) Sketch on the graph below the points of applied force (added weight)
versus the resulting stretch for the spring in Figure 1 above, as well as the best curve through those
points.
Applied
Force (N)
Stretch of Spring from Equilibrium (m)
4. (Refer to section 4 on page 1.) Determine the slope of the best line that passes through the four
points on the graph above (be sure to include units).
5. (Refer to section 5 on page 1.) What does this slope in 4 represent? Does the y-intercept affect the
value of the slope?
6. (Refer to section 6 on page 2.) Describe how you would measure the spring constant of a spring.
Pre-Lab 07 5