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fishingspree2
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Homework Statement
A simple pendulum whose length is L=2 meters has a mass of m=2kg. When the angle between the pendulum and the vertical is 35 degrees, it has a speed of 1.2 m/s. Find the pendulum's speed when the pendulum is at its lowest height.
Homework Equations
K = 0.5mv2
U = mgh
E = K+U
The Attempt at a Solution
I arbitrarily set that h=0 when theta = 35 degrees
http://img232.imageshack.us/img232/4803/pend1cs5.jpg
NOTE: I have found the right answer by setting h=0 at the pendulum's lowest point, but I can't find the right answer when I set h=0 when theta = 35 degrees. Since h=0 can be arbitrarily set, I would like to know where is the mistake.
Since E = K + U, and U = 0
then E = K = 0.5mv2 = 0.5(2)(1.22)= 1.44 J
Now, at any point E = K + U = mg*-[L-Lcos(theta)] + 0.5mv2 = mg[Lcos(theta) - L] + 0.5mv2
Now, I am pretty sure the error is in what follows:
At the pendulum's lowest point, theta = 0 degrees
then mg[Lcos(theta) - L] + 0.5mv2 = 0.5mv2 = 1.44 J, solving for v gives back the 1.22 m/s, which is clearly not the answer. If i set theta = 35 degrees, I get v = 2.38 m/s, which is also not correct.
The correct answer is 2.9 m/s
Can anyone help?
Thank you
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