Level 11 - Tarzan Rides the Merry-Go-Round!

Transcription

1 Group #4 Name: Partner(s): Level 11 - Tarzan Rides the Merry-Go-Round! Side View pivot Top View blue yellow clay ball hot wire green red clay ball The Scenario: Tarzan is being chased (as usual). He must swing from a vine and hit a children's merry-go-round that is at the bottom of the vine in an abandoned jungle playground. After hitting the merry-go-round he will let go of the vine and start spinning around. But the situation is a bit trickier. You see, the merry-go-round is surrounded by deadly boobytraps, except for one narrow escape route. If he tries to jump from the merry-go-round before it has stopped spinning, he will surely set off a deadly booby-trap. Likewise, shifting his weight on the merry-go-round will set off a deadly booby-trap. His only hope is to stop spinning at the location of the escape route, where he will gently get off the merry-goround. But if he stops short or long of the escape route - he is done! Tarzan estimates the rotational inertia of the merry-go-round and then makes his jump. Will he make it? Of course he does - he's Tarzan - King of the Jungle! But how will you fare? Place yourself in this scenario and use your physics and math knowledge to calculate your way to safety!

2 2 Main Objective: Calculate the height from which Tarzan (a clay ball) must jump such that he makes an inelastic collision with the merry-go-round and spins to the predetermined angle of the escape route. Apparatus: A clay ball hanging on a fine cotton thread from a nearly frictionless pivot will be released from rest. When the ball gets to the bottom of its swing, it will make a perfectly inelastic collision with a merry-go-round. Simultaneously, at the bottom of its swing, the thread will be quickly cut with a hot wire. The combination of clay ball and merry-go-round will spin to a predetermined orientation. In order to keep the merry-go-round balanced, a clay ball of equal mass will be placed symmetrically on the opposite side of the merry-go-round. Be sure to account for its effect. rotational inertia of merry-go-round = kgm 2 collision radius = 14.5 inches mass of clay balls = kg each mass of thread = negligible length of thread = 195 cm final height of clay ball at collision = 34 cm Your Group's Assigned Range: Tarzan should end in the "yellow zone" after one complete rotation.

3 3 Theory: The total angular momentum of the system before the collision must equal the total angular momentum of the system after the collision. Assignment (to be completed by next week, before the lab): 1. Use the assigned values above and determine the height (H) from which Tarzan must be released in order to end up in the in the "yellow zone" (after 1 complete rotations). The angular deceleration of the merry-go-round will depend on the average friction present. This value can vary from day to day because of changes in humidity, dust level in the lab room, etcetera.* *The exact deceleration of the merry-go-round will be measured right before your lab. So solve for the height in terms of angular deceleration (α). That way, when the deceleration value (α) is given to you in lab by the instructor, you can quickly "plug and chug" an answer for the release height (H). Attach pages that explain your group's reasoning and show your calculations (attach as many pieces of paper as needed). Put a box around your final answer for H.

4 4 2. Now, using the information above, think things through and predict the angular velocity vs.time graph for your case. Assume a constant angular deceleration of 0.13 rad/s 2 after the collision. Place your "best guess" in the graph below, including a scale along each axis. Assume the merry-go-round starts at position zero. (Hints: First determine the general shape you expect the graph to have. Then use your predicted ω to set the vertical scale. Finally, use the fact that the area** under the displacement you expect. ) ω vs. t graph should equal the total angular ** Remember, units are important. The area under your angular velocity-time graph should be found using the scales you have set up along each axis. ω t

5 5 3. Using the previous information (including your predicted angular velocity graph above), now predict the angular displacement vs. time graph of the merry-go-round. Place your answer in the graph below, including a scale along each axis. Include the entire time from when the collision occurs until the merry-go-round stops turning. θ t

6 6 Analysis - To be completed while in lab after your solution has been tested and data has been collected. 1. Highlight the area under your ω t graph where there is meaningful data (i.e. from the time of the collision to the time the merry-goround stopped turning.) Use the statistics mode of the Science Workshop software to integrate the area. Enter your answer in the chart below. 2. Now use the statistics mode and determine the maximum angular displacement on your angular displacement graph. If the rotational sensor was zeroed properly, this should be the total angular displacement of the merry-go-round. Enter the answer in the chart below. Area Under ω t Graph Total Angular Displacement Your comments about the above chart: 3. Highlight a small interval of data on your angular displacement graph and use the statistics mode to do a linear curve fit. The slope of the curve-fitted line will be indicated with the variable a 2 that shows up in the statistics window. Record this value in the chart below. Also use the analysis feature of the software (i.e. the crosshairs) to determine the approximate time at the center of this interval you have chosen. Record this in the chart below also.

7 7 4. Now use the crosshairs on your angular velocity graph to measure the angular velocity at the same time. Record this value below. 5. Repeat steps three and four choosing new data intervals up and down your angular displacement graph. Record your results in the chart below. Time Slope of θ t Graph Angular Velocity Your comments about the above chart:

8 8 Questions - To be completed after the lab When answering these questions, be sure to refer to your data graphs taken in lab when you ran your solution. 1. How far did the merry-go-round end up turning? Was your attempt successful? Explain: 2. If your attempt was not successful, have you determined what went wrong? What have you narrowed it down to? Explain. Also, show any corrections in your solution below (attach as many pieces of paper as needed).

9 9 3. The tension in the thread was not considered in the lab. At what point would the tension in the thread be greatest? Calculate the maximum tension that would have existed in the thread while the clay ball was swinging in your solution. Show your work below (including a free-body-diagram) and put a box around your final answer: 4. Calculate the kinetic energy in your system right before the collision. Then calculate the kinetic energy right after the collision. Are they the same? Why or why not?

10 10 5. The merry-go-round stopped turning mainly because of friction, but there was also some air resistance. So where did all of the original rotational kinetic energy of the merry-go-round go? Answer in detail including the specific process that occurred on the molecular level. 6. Considering the effect of air resistance in addition to friction, does the merry-go-round's rotational kinetic energy dissipate at a steady rate? If not, when was the merry-go-round dissipating the energy at higher power: at the beginning of the motion or near the end of the motion? Explain:

11 11 7. Overall, how did your predicted graphs match up with the true data graphs? Keep in mind that you assumed an average angular deceleration of 0.13 rad/s 2 when making your prediction graphs, and this was not necessarily the value for during the lab. Rate how well you think they matched using a scale of 1 (terrible) to 5 (fantastic). Angular vel. vs. time Angular pos. vs. time Score