The discussion revolves around calculating the energy loss of a pendulum as it swings from its highest point (potential energy, Ep) to its lowest point (kinetic energy, Ek). The original poster provides specific parameters for the pendulum, including mass, length, height, and angle.
Participants are actively engaging with the problem, raising questions about the necessary information to determine energy loss. Some suggest that if the pendulum reaches a certain height on the other side, it could indicate the efficiency of energy conversion. There is no explicit consensus, but various lines of reasoning are being explored regarding the calculations involved.
The original poster mentions a project requirement to design a device that transfers energy with minimal loss, specifically aiming for less than 5% energy loss. This context adds a layer of complexity to the discussion, as participants consider practical implications of their calculations.
Lancelot59 said: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.
Lightness said:What would I need to do after if I find out how high it reached on the other side?
Nathanael said: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)
Lightness said: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
Is that the whole question? Are you sure you've left nothing out?Lightness said:the energy loss of a Pendulum from top (Ep) to Bot (Ek)
Mass= 2.0kg
Length= 0.38m
height= 0.05091m
theta= 30°
haruspex said:Is that the whole question? Are you sure you've left nothing out?
Lightness said: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 can't really calculate the loss of energy at Ek. So I guess this was a failed idea.
Nathanael said: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
Lightness said: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?
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.Nathanael said:(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.)