File:ButterSideUp.gif
ButterSideUp.gif (360 × 360 pixels, file size: 62 KB, MIME type: image/gif, looped, 31 frames, 3.1 s)
Captions
This real time strobed animation, of an experiment done elsewhere in our solar system, illustrates the butter side up version of an angular impulse problem.
Contents
Practical Problem
[edit]At what minimum height h above the edge of a height-H table should you hold a square (side 2R) piece of toast butter side up, so that if its edge clips the table edge when you drop it the toast will land butter side down?
- Does this change if the toast is circular, or if a corner rather than an edge is clipped?
- What if you use margarine instead of butter, or cashew butter with strawberry jam?
- How high would you hold it if you want it to land butter side up after one turn?
- How big must H/R be to allow a double somersault butter side up?
- Do any of these answers depend on the size of g?
- Should this be an event in the kitchen olympics?
Discussion of Data
[edit]If the table is 1 meter high and this strobed animation is in real time, how accurately can you determine:
- (i) the acceleration due to gravity on the experiment site,
- (ii) where in the solar system this data might have been taken,
- (iii) the size of the impulse FΔt/m the toast experiences, and
- (iv) the dimensionless ratio ξ=I/mR2 for the toast?
Discussion of Models
[edit]If the toast is height h above the table, the speed when it hits will be v = Sqrt[2gh]. But how might we model the table's impact? Suppose after collision that the toast center has a downward speed v' and angular velocity of ω=v'/R where R is the edge distance. Then collision impulse FΔt=m(v-v') and angular impulse RFΔt=Iω are linked. Solving for v' gives v'=v/(1+I/mR2). Time to the floor and the amount of rotation can now both be calculated as a function of h, and then h adjusted so that the butter side lands down. Will that work?
See Also
[edit]Footnotes
[edit]
Summary
[edit]DescriptionButterSideUp.gif |
English: Animation of a rotational impulse problem. |
Date | |
Source | Own work |
Author | P. Fraundorf |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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current | 02:04, 5 April 2009 | 360 × 360 (62 KB) | Unitsphere (talk | contribs) | {{Information |Description={{en|1=Animation of a rotational impulse problem.}} |Source=Own work by uploader |Author=Unitsphere |Date=2009-04-01 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> |
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