The Coolest Commercial, Check it out, it's awsome! |
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The Coolest Commercial, Check it out, it's awsome! |
Apr 15 2003, 02:31 AM
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#1
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Group: Posts: 0 Joined: -- Member No.: 0 |
http://home.attbi.com/~bernhard36/honda-ad.html
yeah, yeah, yeah. It's a honda commercial, but you will enjoy it. trust me. (IMG:style_emoticons/default/mueba.gif) Read this after: http://www.dailytelegraph.co.uk/news/main..../13/ixhome.html |
Jeff Krieger |
Apr 17 2003, 11:10 PM
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#2
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Unregistered |
Oops! This solution is wrong. Check out my later post for the correct solution.
*************************************** Ok, Andy, I'm no physicist so you can correct me where I'm wrong. Let the tire sit just at the bottom of a ramp which has a positive slope. If the tire's center of mass is a distance r from the tire's center and the center of mass is located at the top dead center point on the tire, then it's height (y) above ground is given by y = r*[1+cos(a)] + r*a*sinb. Here "a" is the angle formed between the vertical axis and the tire's (point) center of mass. 12 o clock ---> 0 rads and 3 oclock ---> pi/2 rads etc. "b" is the angle that the ramp makes with the horizontal axis. Since the tire's mass (m) and the acceleration due to gravity (g) are both constant, the critical points of the tire's potential energy (mgh) equation are determined completely by the the height of the tire's center of mass above the ground h = y = r*[1+cos(a)] + r*a*sinb. For fixed r and b, dy/da = r*sinb - r*sin(a). The critical numbers occur when r*sinb = r*sin(a), when a = b or a = [pi - b]. When the ramp makes an angle of b with the ground, the first critical number occurs at an angle of a = b. You can verify that a = b produces a local maximum. Therefore the tire has its maximum potential energy when a = b and as the tire rolls further up the ramp its PE decreases until the angle a = [pi - b] when it reaches a local minimum. Here is a graph for y = r*[1+cos(a)] + r*a*sinb for the specific case when r = 10 and b = pi/3. (In this graph x = a). (IMG:http://persweb.direct.ca/aschwenk/PE.jpg) |
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