Trapeze Inquiry

SWING/TRAPEZE INQUIRY ACTIVITY

End-of-Class Question. What affects Ted’s daughter’s experience going on the swing?

The ends of the ropes were uneven. The longer rope will swing more slowly, and so she’ll pivot slightly. The stretchiness of the rope may cause her to bob up and down, according to Hooke’s law, more than if it were made out of linked chain (and this may just be the model).

1.What questions do you have? Complete the list of your personal questions from doing the pendulums activity. (I couldn’t resist looking up material while I formed my question. I don’t think too many of my students will also feel bad about cheating by studying behind my back, but it was a really interesting thing to feel bad about.)

A.    What variables affect frequency, if not mass?

B.     Why was it important to achieve an angle of 22.5^o? Is that angle significant, other than it is simpler to fold paper than use a protractor?

C.     What accounts for the standing wave pattern we saw in the video? Could I repeat it?

D.    How do these properties of waves relate to sound waves?

E.     What would happen if we tried to vary the motion of the pendulum in different dimensions (not just along the x axis but, say, somehow got it to vary in along the x and y axes of a three-dimensional Cartesian coordinate)?

F.      Could I figure out a way to quantify the work or energy generated by the pendulum swing?

G.    What other variables would be important to take into account for a very pendulum (i.e., what are all of the variables that explain the behavior of a Foucault’s Pendulum? How does the rotational spin of the earth affect the swing of a Foucault’s Pendulum)?

H.    Would we get more consistent results if we reduced the friction of the string against the table? I wouldn’t think that it would matter too much with just a 10 s run-time.

I.       What behavior would the pendulum show if I added additional forces, like a fan going on a low setting at different angles around the pendulum? Would the different forces add constructively and deconstructively like hybrid orbitals?

J.       What if the pendulum were also a spring, so Hooke’s law was also acting on the string’s behavior? Both gravity and the force of the spring would be acting on the spring, and the length of the string would be inconstant.

K.    What would I see if the mass changed midflight (e.g., if Alka-Seltzer were first dipped in water and then clamped to the spring)? Would the frequency still be constant? That is, is frequency is unaffected by mass, or is frequency just unaffected by constant mass?

2.Analyze your questions – Look at your list of question

  a. Which of these questions can be investigate using the activity materials you’ve been using?

Questions A, B, E, could be investigated by brainstorming other possible variables that might affect frequency and incrementally varying them, recording my results.

I’m not sure about C.

  b. Which questions require additional materials? What are they?

I’m not sure about C or F.

Question D requires the SoundMeter app or another method of measuring pitch, although it wouldn’t be interesting unless I could find something to measure with harmonics. Question G requires a Foucault’s pendulum. Question H requires a lubricant, question I requires a fan, question J requires springs, and question K requires Alka seltzer and water. 

  c. Which questions are beyond the scope of this activity to find answers? How would you find those answers?

Questions C, D, and F would require for me to just look up the material. Question G would require for me to go to a museum.

  d. Identify three questions you personally are most interested in investigating.  Why are these questions interesting or important to you?

Question D would be interesting, because I was a music and chemistry major and always wanted to take a class on the physics of sound.

Question F sounds like an interesting challenge.

Question I sounds like it would be engaging to set up and lead to interesting results. The “other forces” component of my question could come in a variety of forms, which would allow me flexibility if one thing I tried didn’t work. I did Science Olympiad a little bit in junior high school, and this question sounds like something we may have built.

3.   Relate this to the NGSS.  Look up and find a specific location standard and copy that to your blog.

The standard HS-PS4-1, Waves and Electromagnetic Radiation, involves using “mathematical relationships” to describe waves (i.e., graphing using variables that affect the behavior of waves). These questions would seek to provide students with the opportunity to explore the relationship among ; the pendulum could be a model for the earthquake or electromagnetic waves described in the standard. The standard states:

Students who demonstrate understanding can: Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

Clarification Statement. Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth.

Assessment boundary. Assessment is limited to algebraic relationships and describing those relationships qualitatively.

My Inquiry

The question I ended up using was related to adding another force in conjunction with the force of gravity acting on the ball AND if the any other properties (energy or work) could be quantified as a pendulum swung. I chose to vary string length for the relative ease of changing this variable, as I had found the relationship: T = 2π(l/g)^0.5.

Specifically, my question was: what relationship, if any, exists between the length of the pendulum and the force it exerts on another object? My prediction was that since a longer pendulum moves more slowly, it will also exert less of a collision force on another object.

Materials: Shoelace string, Android device with the iSeismometer app installed, Kleenex box (to prop up the phone), a small rubber ball to act as a weight, a drawer from which to hang my pendulum, and a piece of paper folded to act as a protractor.

The iSeismometer app shows force applied to the phone in three dimensions. When the phone is upright, +Y is the top of the phone, -Y is the bottom of the phone, -X is the left-hand side of the phone, +X is the right-hand side of the phone, +Z is going towards the user, and –Z is going back behind the phone. On the seisometer screen, the x axis measures cycles (Hz) and the y axis measures in increments of g (-9.8 m/s^2). 

Procedure: A ball was tied at the end of a shoelace folded in half, which was tied to the top of a drawer so that it was able to swing (admittedly, with constant but existent friction). The iSeismometer app on an Android device was propped up so that the end of the pendulum would collide with the phone. The ball was pulled back at a 45^o angle at lengths of 16 cm, 32 cm, or 50 cm and released. Several practice trails were conducted until it seemed like I was getting distinct but relatively consistent data at different string lengths. 

Results and Discussion:

The Supplementary Material has been submitted to the Dropbox in the NGSS category on ICON.

The data were collected with the pendulum at its shortest (S) length, the intermediate length (I), and then the longest (L) length; the clusters of data on the graphs were collected in the order of the pendulum at lengths S, I, and L.

Interestingly, the tentative results showed that the pendulum exerted about twice the acceleration (which should be proportional to force) at the intermediate length (I), while the pendulum exerted a force of about +1 in the Z direction at its shortest (S) and longest length (L).

At length S, the pendulum may have been swinging at a frequency so that it was still gaining in momentum but that the pendulum was swinging at a frequency at length I so that it had gathered more momentum and was able to hit the phone at full swing. At length L, the pendulum was starting to swing in the opposite direction when it hit the phone, and thus its force was weaker. These tentative results indicate that the force exerted by a pendulum is affected by its length in a sinusoidal manner.

Logically, if I were using a consistent procedure, the pendulum would swing and collide with an object in the same position, and it would make sense for the force to come from +Z direction; however, the force experienced in all directions at a length of 50 cm indicates that the Kleenex was also exerting a force on the phone. After an initial collision, the phone hit the Kleenex box, which hit the phone in return.

If I were to do this lab differently, I might take a ring stand from lab to reduce friction. Having three unanchored objects, rather than just two, was a design flaw in my experiment by introducing new variables; if the phone were held in place on a ring stand, it would reduce this variability. Since the NGSS stresses real-world applications of waves and uses such examples as earthquakes, this activity could be a jumping off activity in which students practice analyzing data, thinking about earthquakes as forces in multiple directions, and practice using Excel.

This would be a good physics lab for applying and expanding students' knowledge of g, and I could see further investigations expanding on the use of this type of instrumentation to explore concepts of g. For instance, students could use a sandbox full of different types of material (sand, dirt, concrete, pebbles) and manipulate their iSeisometer to collect data in three dimensions on the acceleration applied when the media in the sandbox is systematically manipulated.

Now that I look online more carefully, there is an engineering ed paper that describes this app much better and provides a much more controlled experimental to be used in an educational setting: http://library.queensu.ca/ojs/index.php/PCEEA/article/viewFile/3623/3637 
Based on the results of Hubbard, et. al., the iSeisometer can be used to get quantitative results, provided one makes approximations on the time cycles.

Based on the SparkNotes physics site (http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section5.rhtml), the forces on a pendulum are: force of tension (the rope), the restoring force (swinging back to equilibrium), and gravity. The pendulum should collide with the app with the most force when its restoring force is highest, which = mg*sin(theta). With a mass of ~0.002 kg for the ball, graphing restoring force vs. angle gives the highest restoring force at 5 degrees and 30 degrees.

This means that if the relationship between pendulum length and restoring force would be studied, the restoring force would be dependent upon the length of the string (since where the pendulum was along the mg*sin(theta) curve is determined by its frequency). THIS means that optimizing string length means having the frequency of the pendulum's oscillation correspond the best with the sinusoidal curve of restoring force, which can go towards explaining the results gathered in this open inquiry.