# How do I calculate a Pendulums energy loss?

1. Jun 7, 2014

### Lightness

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

How would I go about finding the energy loss of a Pendulum from top (Ep) to Bot (Ek)

Mass= 2.0kg
Length= 0.38m
height= 0.05091m
theta= 30°

2. The attempt at a solution

I know that we could find Ep by going mgh (2.0kg)(9.81m/s)(0.05091m)=1.0J of Ep

But how would I calculate Ek at the bottom and the amount of energy loss from Ep to Ek due to friction?

2. Jun 7, 2014

### Lancelot59

If you ignore friction, your kinetic energy at the bottom of the swing would be equivalent to the gravitational potential. However without a second piece of information you can't determine what any losses are. Ideally you would need the speed of the pendulum at the bottom of the swing, or how high it reached on the other side.

3. Jun 7, 2014

### Lightness

What would I need to do after if I find out how high it reached on the other side?

4. Jun 7, 2014

### Nathanael

The difference in gravitational potential energy between the original height and the new height would be the energy lost to friction.

However that would be the energy lost to friction from the top to the "new top" whereas you wanted to find the energy lost to friction from the top to the bottom.

Ideally you would want to know the speed at the bottom (so you could calculate the kinetic energy)

5. Jun 7, 2014

### Lightness

How would I go about finding the velocity?

I have tried √2gh but that is for no friction and that all Ep tranfers to Ek

6. Jun 7, 2014

### Lancelot59

Yes, for the idealized case. Like I stated you can't solve this problem fully without more information specified. You don't have enough known values unfortunately.

The best you can do is solve it symbolically.

$$E_{kinetic}=E_{friction}+E_{potential}$$

Fill in the blank for potential, and isolate variables as desired.

7. Jun 8, 2014

### haruspex

Is that the whole question? Are you sure you've left nothing out?

8. Jun 8, 2014

### Lightness

It wasnt really a question, more like a problem I came up with. I am suppose to make a device that could transfer close to 1 J of energy from one form to another with a energy loss of 5% of less. I was planing to make a pendulum and with the data I giving I could get 1 J of Ep but cant really calculate the loss of energy at Ek. So I guess this was a failed idea.

9. Jun 8, 2014

### Nathanael

Not necessarily. (You should've said that was your intention from the start.)

You do know one thing: the energy lost to friction from the original height to the height on the other side (which you could calculate, right?) will be more than (or at best, equal to) the energy lost to friction from the top to bottom.

So if the energy lost in the first swing (from original height to the new height) is 5% or less, then the energy lost form the original height to the bottom will be 5% or less (most likely less)

And thus:
if you can show that the pendulum swings to 95% (or more) of it's original height (on the first swing) then you've essentially proven that you have converted gravitational potential energy into kinetic energy with less than 5% energy loss

10. Jun 8, 2014

### Lightness

Yea I should of. Even if I do this this way, could I find out exactly what Ek equals to? or is there really no way of finding the value of Ek in this situation?

11. Jun 8, 2014

### Nathanael

You could approximate it fairly accurately, but I can't think of any way to find an exact value of the kinetic energy without directly measuring the speed.
(If you understand how the friction works, (which I don't tbh,) then you could maybe calculate the kinetic energy. For example, if you somehow know that the same amount of friction is lost per distance that it swings, then you could calculate the frictional loss from original height to new height, then use that to find the friction loss per distance, then use that to calculate the frictional loss from top to bottom, and thus calculate the kinetic energy.)

But as long as all you need to do is prove that it's at least 95% efficient, the method in my last post should suffice (assuming you have some way to measure the height it swings to)

12. Jun 8, 2014

### haruspex

It'll be a frictional torque, proportional to the tension in the pendulum. Ignoring the slight increase from the centripetal force when at bottom of swing, that'll be mg cos(θ) when at angle θ to vertical. Integrating, work is mgr sin(ψ) per quarter oscillation, where ψ is the swing amplitude. Since this reduces the amplitude, we get a recurrence relation on ψn.
5% loss per swing would be a very poor pendulum.