Ending Velocity of Ball Rolling Down Ramp
 

https://youtu.be/l-5rUadvdlQ?si=hWSwXHb_QWdjrY_d

What was your guess, pause the video before you hear the answer?

I'm a science nerd (especially physics), so I was pretty confident that I knew the outcome.

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it's been a long time since physics but seconds 5-7 within the first 30 seconds gives the answer I think. They'll all be the same velocity I'm pretty sure.

That's what I expected since start and end are all the same. When my son raced pine wood derby cars, the start line was on an angle so it made a big difference on where the weight was: as far back as you can put it without the car doing wheelies.

My guess is same speed. Same vertical drop for all the ramps. I don't picture much difference in friction or wind resistance.

I haven’t read any replies, and my guess is they will all be very similar.

Isn't the ending velocity 0 since it is stopped?

I love this!

It's such a great way to trick "smart" people - who in their awesome "smartness" get all into curves, acceleration and fancy math - who confidently, because they're "smart," answer that they're all different, and that of course none of them is optimum.

The "smart" people are answering a different question.

Remember kids, read and understand the question before answering. Pretty much everyone above, and the video, agree. Same height drop therefore same delta(potential energy) to convert into kinetic energy. Same velocity. Eleventh grade newtonian physics as long as the ball has no rotational inertia and no rolling friction or air resistance.

For which one wins a race between the ramps (fastest overall transit, not fastest finishing velocity) you can rejoin the "smart" people with their cardoids and (checking wiki...) brachistochrone curves.

For super-extra credit, repeat the tests with steel spheres in water. Show your work...

Seconds 5 6 and 7 say it all.

I knew the answer as soon as I saw the problem... I remember a similar problem from physics...

The scatter could be from the balls not starting with zero velocity.. He fiddles with them to get them in motion and they all don't appear to start in the exact same spot.. and then the randomness of the balls path..

I agree...but never studied physics...

:DSmileWavy

mgh =.5 m (v^2)

Hopefully super straight forward to anybody on any sort of technical path. Literally the exact set up of the 1st lab in freshman physics. It does turn into a more interesting question when balls of different mass distribution are used or the question of ranking the transit times.

Edit: shoot! replying to mjohnson but forgot to quote. Anyway cool story.

Cool story about this. The problem is called the brachitochrone. Bournoulli brothers posed it, worked on it, ended up with a 300 page proof including measurements. Then issued a public challenge.

Newton finds out and stays up late coming up with a sweet 3 liner.

Newton posts his solution anonymously and one of the brothers sees solution and says:

I know the lion by his claw, this is the work of newton!

Heres a more accurate recap:

https://en.m.wikipedia.org/wiki/Brachistochrone_curve

this seems like one sided beef you have with somone. no one here was doing this.

energy is a state function. E0 = E1

Oh hardly any beef. Not even veal.

And most here understood the question perfectly correctly.

I love questions that inspire people to talk out of their rears to show how smart they are - when they're not even answering the right question. Or even just the quick obvious answer that upon some thought turns out to be completely wrong.

This is a pretty interesting bit of psychology that's actually very relevant to human factors and the development of systems robust to human error.

da/dt amongst the different curves would be interesting

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i dont think this question inspired anyone to talk out their rears or try to show how smart they are.

its a high school physics question, not even a tricky one.

I still don't see covered anywhere the rotational inertia from the ball - it seems that most of the classic maths assume a point mass that doesn't roll. It'd be fun to see that worked up for a real ball/hoop with nonzero radius. Since it started with no rotation at H1 and ended up rolling with some speed at a lower H2, the speed should be lower that you'd expect based on m*g*(H2-H1) because some of that potential energy went into rotation.

These are dangerous waters... Go too far and you get all into the something which is simultaneously simple and mind-meltingly complicated. I've watched this video numerous times and I get a bit further each time...
https://www.youtube.com/watch?v=Q10_srZ-pbs

[QUOTE=mjohnson;12498136]I still don't see covered anywhere the rotational inertia from the ball - it seems that most of the classic maths assume a point mass that doesn't roll. It'd be fun to see that worked up for a real ball/hoop with nonzero radius. Since it started with no rotation at H1 and ended up rolling with some speed at a lower H2, the speed should be lower that you'd expect based on m*g*(H2-H1) because some of that potential energy went into rotation.

These are dangerous waters... Go too far and you get all into the something which is simultaneously simple and mind-meltingly complicated. I've watched this video numerous times and I get a bit further each time...
https://www.youtube.com/watch?v=Q10_srZ-pbs[/QUOTE]

As Mr Spock would say "fascinating!"