# Pendulum velocity using energy forumula

1. Mar 7, 2017

### Garrit

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

This problem deals with a pendulum. Imagine you're just letting it dangle (so perpendicular to ground) and you lift it to the side by some angle theta. This point your holding it at will be Point A. You release the pendulum from your grip and want to find out at Point B (where it was originally at, just dangling in a straight line) what the velocity is there.

2. Relevant equations

Since only the work of gravity is being done, I am using Ea = Eb. So the kinetic energy at Point A plus the potential energy at point A equals the kinetic energy at Point B plus the potential energy at point B.
Kinetic = (0.5)(m)v^2 Potential = mgl

3. The attempt at a solution

I did (0.5)(m)(0) + mglcos(theta) = (0.5)m(Vb)^2 + mgl
Vb = sqrt(2gl(cos(theta)-1)))

The problem is, I don't think this is right. My professor did this in class and got a different answer.
He did this 0 - mglcos(theta) = (0.5)m(Vb)^2 - mgl -------> Vb = sqrt(2gl(1-cos(theta)))

Why did he subtract? I thought Eb= Ea was kinetic PLUS potential

Last edited by a moderator: Mar 7, 2017
2. Mar 7, 2017

### Garrit

I don't know why my picture doesnt show. I drew it (its real simple) and uploaded it. If my wording doesnt make enough sense here it is https://imgur.com/YqxEwFH

3. Mar 7, 2017

### Staff: Mentor

Instead of posting a url to some offsite-stored image which can sometimes be "fragile", it's better to upload your image to the PF server. Use the UPLOAD feature (button at the bottom right of the edit window).

This time I'll insert a copy of your image for you.

4. Mar 7, 2017

### Staff: Mentor

The gravitational potential energy decreases with height above the Earth's surface. You've chosen coordinates such that the distance increases downwards, so that you should have ΔPE ∝ -Δh.

It's often worthwhile to look at the change in elevation that occurs and ask yourself whether you should be gaining KE from the change in PE or losing KE to PE. Then make sure that your equation reflects this gain or loss for the given change in elevation.

5. Mar 7, 2017

### Garrit

Ohh ok. That makes sense. Thanks!