# Homework Help: Pendulum, conservation of energy theorem

1. Nov 11, 2008

### fishingspree2

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
K = 0.5mv2
U = mgh
E = K+U

3. The attempt at a solution
I arbitrarily set that h=0 when theta = 35 degrees
http://img232.imageshack.us/img232/4803/pend1cs5.jpg [Broken]
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

Last edited by a moderator: May 3, 2017
2. Nov 11, 2008

### Staff: Mentor

The problem is in your PE term. You need the distance below the start point, which is where θ = 35 degrees. (Why not just calculate that distance for the bottom position? That's what your expression gives if you put θ=35.)

3. Nov 11, 2008

### fishingspree2

hmm this is what I did: Since d = L cos theta and the pendulum's length = L, then the distance below the starting point is the -(distance between the blue sphere and the red horizontal line), which is = -(L - L*cos(theta)). Isn't that what we need?
http://img511.imageshack.us/img511/9596/pend2rj9.jpg [Broken]

Last edited by a moderator: May 3, 2017
4. Nov 11, 2008

### Staff: Mentor

Sure. As long as θ = 35. (θ is your initial angle, not the final angle.)