<p>Hey… I’m working on my physics mid-term exam (a take-home he said we could seek help on), and I think I’ve answered every question correctly. I only have reservations about the following question:</p>
<p>A small monkey is swiming on a vine. The vine is 2.5 m long and fastened at point C. The monkey swings in a circular path sliding on a frictionless plane tipped at an angle of 53.1° from the horizontal. Calculate the minimum speed required at the lowest point, A, if the monkey is to coast through the highest point, B, without leaving the circular path. </p>
<p>If any of you guys are bored, could you please solve this problem and tell me what you did?
(I solved it and got 9.90… The prof said the answer was ‘about 10’… I’m just not quite sure about my method.)</p>
<p>A midterm exam on which you can get outside help?
As in, other people solving the problem for you and telling you the answer?
Riiiiiigggghhhhht… what’s the point of the exam then?</p>
<ol>
<li><p>It allows him to test us on much more involved and difficult material.
(The above is the first and by far the easiest of the bunch.)</p></li>
<li><p>It provides a more realistic situation and fosters team-work. </p></li>
<li><p>It ensures that we grasp the concepts.
(This exam will determine whether most students pass of fail because it is weighted so heavily.)</p></li>
</ol>
<p>He gives us the numerical answers and forces us to figure out the correct method.
I have reached the same answer he did (10), but I am unsure whether my method is correct.</p>
<p>You might say this is ********, but once we complete this section of the exam, we go in and write the testing section.
This portion of the exam deals with similar concepts and is conducted more like a ‘normal’ exam.</p>
<p>EDIT: Please note that the take-home portion isn’t worth any marks.</p>
<p>Sorry, I just had to edit my routing table, it’s back up now.</p>
<p>My solution simply disregards the angle of the plane, and assumes that it is @ 90°.</p>
<p>This is based upon the following two facts:
No work is done by the plane in terms of friction.
A perfect circle is maintained.</p>
<p>Ek + Eg = Ek + Ug + W
(0.5)mv² + mgh = (0.5)mv² + mgh + Fd
(0.5)mv² + 0 = 0 + mgh + 0
v² = 2gh = (2)(9.81)(5) = 98.1
v = sqrt(98.1) = 9.9 m/s</p>
<p>The reason I question the validity of this solution is because the height is not actually 5.0 m.
5 sin 53.1° = 3.998 m</p>
<p>I took this into account before bringing my solution to the table, but my classmates have assured me that I am wrong. The problem is that none of them have reached the correct solution, and I still believe mine to be valid.</p>
<p>My reasoning is that we can totally ignore the angle the plane is tilted at because the circle stays exactly the same and the plane applies no force. If you convert the height, you will also have to convert every other aspect of the forces acting upon it, which will cause you to reach the exact same solution. Is this logic flawed?</p>
<p>interesting. your method isn’t quite correct, but you got the right answer anyway… hm. okay. anyway. i never give people answers, but i <em>do</em> give hints… here are 3 that you should find useful. note that the last one is the most important of the three: </p>
<p>a) the minimum velocity at the bottom of the circle DOES depend on the angle of the plane. you should have a sin(theta) term somewhere in your final equation for v. i think your teacher may have intended this as a sort of trick question - theta equal to approx. 53 degrees is the only angle at which the solution by the correct method and your almost-correct-but-not-quite method give the same value.</p>
<p>b) you’re right that the “h” you should use for calculating energy is 5*sin(53.1 degrees), not 5 m.</p>
<p>c) this is the really important one: the speed of the monkey at the top of the circle is NOT 0 m/s. if its speed is 0 m/s, then the monkey will not keep moving around the circle, and it will instead just start to slide down the face of the plane. the key part of the problem is that it has to go through the top of the circle without leaving the circular path. so you need to figure out what the speed of the monkey at the top of the circle is</p>
<p>(this is sort of tricky, so i’ll give you a bit more on this hint. in order to keep moving in a circle, the total force has some relation to the mass, velocity, and radius - and the velocity is the only one of these that is variable. what is the equation that expresses this relationship? now, what are the two forces acting on the monkey at the top of the circle? there’s only one of them that we can minimize. so what’s the minimum total force on the monkey? set the forces equal and solve - what’s the minimum velocity at the top of the loop?)</p>
<p>NOW you should know enough to solve this problem correctly. if you can’t get it, you can always come back and ask for more hints, but definitely give it a go by yourself before you do.</p>
<p>The trick is to realize that for the minimum speed, the tension at the top of the motion vanishes, and therefore the centripetal acceleration down the plane must equal to the parallel component of the gravitational acceleration down the plane. (The perpendicular component of gravity is balanced by the normal force.)</p>
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