Free fall from SPACE!

Transcription

1 Free fall from SPACE! Description: A major theme in physics is free fall motion. This lesson capitalizes on that fact, and the recent free fall jump made by Felix Baumgartner from 39,045 meters. Computations to find velocity and acceleration are made. An emphasis is placed on thinking about and logically analyzing the results. This applies to high school physics and/or algebra. Background: Felix Baumgartner, a Redbull athlete, recently made a free fall jump from the upper atmosphere. While, at the time of this lesson s writing, the details of his jump were either not entirely available, or inconsistent across various sources, his jump does provide a prime case for analysis of free fall motion. Additionally, the showing of a YouTube video of the jump is a great add-on to this lesson. The following statistics are those used in the included worksheet, and can be used to develop additional questions and discussions beyond what is included here. Starting height: 39,045 m Starting velocity: 0 m/s (although this is not true since Free fall duration: 4 minutes 19 seconds the balloon was actually rising when he jumped) Maximum absolute speed: 1,342.8 km/hr Acceleration due to gravity: 9.81 m/s 2 Speed of sound (at sea level): m/s Time Felix reached the speed of sound: 34 seconds Total flight time: 9 minutes 9 seconds Notice that some unit conversions will be required if the data is taken as given here. Also, a discussion about approximations or assumptions would be a good lead-in to this lesson. The following image is of Felix just after jumping from his capsule. More images are available online.

2 Concepts: The following concepts apply to this lesson: free fall motion, acceleration, velocity, gravity, air drag, model development, and potential model flaws. Vocabulary: These words are interesting and important words or phrases found throughout this lesson. Students may benefit from learning about these prior to the lesson, perhaps as a homework assignment. Free fall motion Motion of an object caused solely by the force of gravity acting upon that object. Acceleration The rate at which the velocity of an object is changing. Velocity The speed and direction of an object, quantified as a vector. Gravity The phenomenon that causes bodies to attract with a force related to their relative locations and masses. Air drag The force (or forces) that act upon a moving object opposite to that object s direction of travel. Unlike friction, air drag (or air resistance) depends upon velocity. Take Away Message: Even something as awesome as Felix s jump requires a deep understanding of physics to properly execute and understand. Lesson: How is free fall motion applicable to exciting activities and events, such as skydiving? This lesson covers (or may cover with minimal addition discussion) the following Wyoming State Standards and requires approximately 55 minutes. SC SC11.2.4, part of SC Materials: Unless a demonstration of free fall motion is desired, this lesson requires only the attached worksheet, pencils, and calculators. Good resources: x=2&feature=plcp About the Author: Rob Streeter is a graduate student at the University of Wyoming. He is currently pursuing a MS of Electrical Engineering. A Wyoming native, Streeter appreciates the need for Wyoming high school graduates to be aware of the extensive opportunities available to them. He genuinely hopes this lesson inspires interest in engineering and the University of Wyoming. Any feedback on this lesson would be appreciated and should be directed to Mr. Streeter (rstreete@uwyo.edu), NSF GK-12 EE- Nanotechnology Fellow, University of Wyoming, Laramie, Wyoming. The following pages include a suggested worksheet and a solution to that worksheet.

3 UW GK-12 Nanotechnology in the Classroom Name: Student Worksheet Felix Baumgartner recently set several world records dealing with free fall motion. What did he do and what records did he set? What important factors may play a role in coordinating a jump like his? Just brainstorm some answers and then justify your choices.

4 Felix jumped from 39,045 meters and, over the course of the 4:19 fall, achieved a maximum speed of 1,342.8 km/hr. Assuming he started from rest, and that the acceleration of gravity is about 9.81 m/s 2 at the equator and sea-level, how long did it take him to reach his max speed (neglect air drag and maneuvering contributions)? Issues like air drag and maneuvering are major factors for a situation like this. How do you think these factors affect the time required to reach the max speed?

5 If Felix reached the speed of sound ( m/s at sea-level) about 34 seconds into the jump, how fast was he accelerating? Does this coincide with the assumption we made in the previous question (that the acceleration from gravity is 9.81 m/s 2 )?

6 UW GK-12 Nanotechnology in the Classroom Name: Student Worksheet Felix Baumgartner recently set several world records dealing with free fall motion. What did he do and what records did he set? Highest free fall jump Fastest vertical speed achieved without a vehicle Longest duration free fall jump What important factors may play a role in coordinating a jump like his? Just brainstorm some answers and then justify your choices. Answers may include, but are certainly not limited to: weather, Felix s health, equipment functionality, safety, physics, math, backup options, etc.

7 Felix jumped from 39,045 meters and, over the course of the 4:19 fall, achieved a maximum speed of 1,342.8 km/hr. Assuming he started from rest, and that the acceleration of gravity is about 9.81 m/s 2 at the equator and sea-level, how long did it take him to reach his max speed (neglect air drag and maneuvering contributions)? Using the equation v f = v i + a * t, and subbing in for v f, v i, and a, the following equation can be written: [km/hr] = 0 [m/s] [m/s 2 ] * t [s] It is immediately clear that a unit conversion must be made. Converting 1,342.8 [km/hr] to [m/s] gives a v f value of 373 [m/s]. Now, using algebra, the result can be rearranged to give: t = 373 [m/s] / 9.81 [m/s 2 ] Thus, the final result is [s] Issues like air drag and maneuvering are major factors for a situation like this. How do you think these factors affect the time required to reach the max speed? These factors would increase the time required to reach the max speed.

8 If Felix reached the speed of sound ( m/s at sea-level) about 34 seconds into the jump, how fast was he accelerating? Using the equation v f = v i + a * t again, but this time subbing in for v f, v i, and t, the following equation can be written: [m/s] = 0 [m/s] + a [m/s 2 ] * 34 [s] It easily follows that, with the assumptions a) that that speed of sound is valid at altitude (which it isn t) and that b) he accelerated at a constant rate (which he didn t), he accelerated at about [m/s 2 ] Does this coincide with the assumption we made in the previous question (that the acceleration from gravity is 9.81 m/s 2 )? Clearly, no. While the result is relatively close, it is not the same and thus some of the assumptions made (as mentioned in the previous question) must be flawed. Researching the local speed of sound sheds some light on how variable the actual speed of sound is.