How to Find the Velocity | Simple Pendulum
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- Опубліковано 12 вер 2024
- This video quickly goes over an example problem of a pendulum. It uses energy conservation to determine the velocity of a pendulum at its lowest point. The ball starts from rest at maximum potential energy and reaches a max speed at the maximum kinetic energy.
Joules, not newtons!! When I solved for the energies, the units should be joules, not newtons! My mistake.
1 joule = 1 N*m
Thank you to the commenter down below for catching that!
So nice to see energy being converted!
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great video.
what happens to the formulas if we included the friction and air resistance?? + can you do an example on this situation??
Thanks! First I’d solve it in terms of angular velocity. Then a ‘drag’ force is added in, which is proportional to the angular velocity (this is true for something moving slowly like a pendulum. Objects at higher speed the drag force is proportional to velocity squared). So once a sum of forces is done, it’d be a 2nd order linear differential equation (with a couple assumptions - one being small angle theorem so we don’t have any sin or cos in our differential equation). Then the solution to the differential equation would be an angular velocity that is a decaying exponential (e raised to a negative value). Hard to explain in words, but in short it’s more complicated so I’ll do a video on it, hopefully soon
Small mistake. After calculating the PE, the units are joules or newton meters, not newtons
Yep! You are correct - should’ve been Joules or N*m
Your hand writing is so nice! 😮what application do you use to write with? And is it on the iPad?
Thanks! Yes an iPad and an Apple Pencil. I think the app is called good notes
Nice content
Thanks!
Hello brother I am from india🇮🇳🇮🇳
Hello brother! Thank you for watching!
Next time can you include the whole word problem in the video Tyty!
Yes I will!
Helpful, but you should have used "joules" instead of "newtons".
Yes you’re right, good catch!
You can get the same results using v² = u² + 2gh, here u = 0.
So, you get the answer of v ≈ 4.4 m/s
Yep!
Why was PE equated to KE?
At any point, the pendulum’s total energy will equal its PE + KE. And the total energy will be the same throughout the movement (not accounting for air friction losses). At the top of the swing, the pendulum only has PE because it is not moving. And at the bottom of the swing, the pendulum only has KE because it can’t go any lower. And since the total energy at every point is equal, we can set the total energy at the top equal to the total energy at the bottom. And since total energy at top is only PE and since total energy at bottom is only KE, we can say PE at top equals the KE at the bottom. (Again, not accounting for air friction losses in this problem).
Got it ty!! :) great video btw
Are you a chemical engineer? 👀👀
Mechanical!
Hey, I know how to do this.
From Philippines
Hello and thanks for watching!