I could not find a solution to the following problem:
UNTAMED (I am walking 8 foxes at the top of my head and trying to keep their tails apart ! (*))
I am the one who posted the problem. I vaugely remembering seeing something similar somewhere years ago. But just couldn't solve it.
Has anyone seen anything like that?
Potential energy lost = kinetic energy gained:Originally Posted by oswaldo
.
Radial component of weight just sufficient to provide centripetal acceleration:.
Put those two equations together to get, from which
(independent of m, r and g !).
Good work! Thanks Opalg.
I had the conservation of Energy part before. For the second equation I was thinking of equation of the tangent line at point A, but yours makes more sense.
BUT I still have a question:
"Radial component of weight just sufficient to provide centripetal acceleration
"
Radial component is towards the center, so the equation should be:
which should give a different answer!!! But 3/5 makes more sense!
Would you please clarify?
Thanks.
-O
You're absolutely right! It should be"Radial component of weight just sufficient to provide centripetal acceleration
Radial component is towards the center, so the equation should be:
which should give a different answer!!!, not
. That makes the equation
. I have edited my previous comment to correct it. (I think I was misled by the fact that θ is decreasing from π/2 towards 0, rather than increasing.)
Thank you for the correction Opalg!
gives:
is about 42 degrees.
To me, this is intriguing. I would expect to object remain on course, say until 30 degrees. But apparently my intuition is wrong.
One more details:
holds only at point A, when the object is airborne. Not before nor after. Interesting!
Having the answer not depending on m, g, r makes it more beautiful.
Thanks for a great solution!
-O
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