Donna asks…
Help finding ratio of rotational kinetic energy to total kinetic energy?
A puck rests on a horizontal frictionless plane. A string is wound around the puck and pulled on with constant force. What fraction of the disk’s total kinetic energy is due to the rotation?
Picture to go with problem: http://i284.photobucket.com/albums/ll28/bathtub2008/showmepl-6.gif
KErot/KEtot = ____
………9
adminsta answers:
A nice little problem.
Let F be the applied force, M the mass of the puck, and R it radius.
The force F acts both to accelerate the center of mass of the puck and to provide a torque to increase the angular velocity of the puck.
The equations for linear acceleration are:
F = M Al
Vf = Vi + Al T
D = Vi T + (1/2) Al T^2
Those for rotational acceleration are parallel:
torque = F x R = I Ar
Wf = Wi + Ar T
@ = Wi T + (1/2) Ar T^2
As are the equations for kinetic energy:
El = (1/2)M V^2
Er = (1/2)I W^2
The moment of inertia goes as the square of the radius:
I = k M R^2
where k depends on the geometry of the puck.
So the ratio you want is:
(1/2)I W^2 / ((1/2)I W^2 + (1/2)M V^2)
Since:
Vf = Vi + Al T = 0 + T (F/M)
Wf = Wi + Ar T = 0 + T (F R/I) = T F R/(k M R^2)
You can substitute these back into the desired fraction. As you would expect, the time T, the force F, and the mass M all cancel.
Steven asks…
Information topics on Energy?
Writing an article for my school newspaper and the topic is Energy. I’m not trying to get too specific (limited to my two columns:( and I need a picture). But what I do want to talk about is energy consumption, what energy is of course, why it is important to conserve and alternatives like solar and wind, and little things people can do to conserve energy. Any suggestions and information would help.
Thanks!
adminsta answers:
Hmm, a school news paper well a good idea will be if you just talk about your school like the problems or something last time I made my news paper so mine was like “recycle, and dont waist donate money to the school to make it better” or just like this person and tht person were fighting something like that dont gossip too much or something might happen to you..
Ken asks…
What do you make of these building codes?
I think they should have new building codes that require solar panels, geothermal heating pumps, rainwater collecting cisterns, passive ventilation, thermal super glass, and caulking. If they mandated green switches that shut the power to all appliances but the refrigerator, that would be fine with me. I believe they should even have, broadleaved trees on the south side, to provide shade during the summer. Perhaps they could have eaves to provide extra shading. I believe all commercial and industrial buildings should require wind turbines and skylights on the rooftops. Moreover, I believe all flat-roofed buildings should have green rooftops. Indoor plumbing is included in all building codes. You can no longer have an outhouse outside. If all buildings must have bathrooms and fire exits, why shouldn’t they include these in new codes? If they shall abide by OSHA standards why not make them abide by EPA standards. Plus, they can require other buildings to be retrofitted through time. Imagine how picturesque Wal-Mart and other big box retail chains would look with green rooftops. Picture how much energy they could return to the grid. Any thoughts on this?
adminsta answers:
It seems once again you have been reading my mind! I can’t speak for the big box stores other than to say they would look much better than the ones we have now, they look so industrial and clinical so much so i hate shopping in any of them.
As far as the indoor plumbing goes i think all new homes should be required to have composting toilet systems installed, and of course owner education as to how to use said composting toilet systems. As far as gray water systems i’m not so sure as to the best way to proceed in that area, my idea was to use all gray water in gardening applications ( so long as eco-friendly soaps are used)
David asks…
Does solar activity affect cloud cover?
When the sun is active there is an increase in the suns magnetic field, electrically charged particles (solar wind), energy in the ultra violet spectrum can increase by 100%, and the energy in other spectrums will increase slightly. During The Little Ice Age, the sun entered a period of little or no solar activity called the Maunder Minimum. It was still shining brightly, but there were hardly any solar flares. The decreased solar wind allows more cosmic rays from outside the solar system to enter the atmosphere. Some scientists believe these cosmic rays help to seed clouds. We don’t have any pictures from the Little Ice Age, but there are many paintings from artists of that era. Here are some links to landscape paintings, notice that the skies are overcast in most of the paintings:
http://www.bouman102.info/avercamp_hendrick.htm
http://www.postershop.ch/Brueghel-Piet/Brueghel-Piet-Jaeger-im-Schnee-2600217.html
http://www.masterworksartgallery.com/BRUEGHEL-Pieter-the-Younger/BRUEGHEL-Pieter-the-Younger-Winter-Landscape-with-a-Bird-trap.html
http://www.prints.co.nz/page/fine-art/PROD/Art_History/554
http://www.abcgallery.com/B/bruegel/pieter8.html
http://www.canvaz.com/gallery/2130.htm
http://www.masterworksartgallery.com/MEISSONIER-Jean-Louis-Ernest/MEISSONIER-Jean-Louis-Ernest-Napoleon-and-his-Staff.html
http://www.ibiblio.org/wm/paint/auth/david/st-bernard.jpg
The last 7 decades have been the highest solar activity in the past 8000 years.
http://www.space.com/scienceastronomy/sunspot_record_041027.html
Why would an artist create a dreary totally overcast sky? A blue sky is much prettier, especially with a white fluffy cloud hear and there. Many of the paintings contain blue pigments.
There are at least a dozen paintings of people playing on the ice. They all have dreary overcast skys. I would think the artists would want to convey a blue sky in at least one or two renditions of these joyful moments.
I’ve looked around at other paintings by Brueghel and he used blue in some of the others, especially in people’s clothing and water. I also looked at Rembrandt’s paintings from the same era. He didn’t do a lot of landscapes, but the ones he did were also very cloudy or overcast. These paintings are made to look realistic and I believe they reflect the times. I know it is not proof, but it is not unreasonable to think that the paintings would resemble reality. There are several artists in my family and I know several more. When they paint something, they usually try to duplicate an object or a picture that they took.
The first 14 paintings are by Hendrick Avercamp, the next 4 ar Brueghel, the next two are Meissonier and I believe the last one is Jacques-Louis. You might look a little more carefully. As far as bringing it goes, the CO2 crap is weak.
adminsta answers:
It would be hard to believe that solar activity doesn’t affect cloud cover. The two processes are definately related. I think the quantitative linkage and process may be debated but that there is a linkage hardly can be.
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