Puzzle Description:

Suppose you had a ball rolling down a spiral ramp. The ramp ends and the ball rolls off. What direction does the ball go?

#1: Belita (belita) on Oct 2, 2021 [SPOILER]

You probably know it's supposed to go straight in the direction it leaves the ramp. But consider this: The ball will be rolling along the outside of the ramp, because inertia makes it want to go straight, and the edges of the ramp are pulling it in. So that will put a sideways spin on the ball. And doesn't a sideways spin make a ball curve? I think it curves in the opposite direction it's spinning. What do you physics nerds think?

I think it continues the curve of the spiral. The curve will begin as tight as the spiral, but it will loosen. I don't know if the direction of the spin is a factor.

Also, the image is not quite accurate. The way I see it, the ball's course is in blue, sitting on top of the black base, so the course is depicted as back and forth rather than a spiral. To be a spiral, the blue should disappear at the curves.

I *think* that's correct; that's how I see it in my head.

But it was a good solve! And you woke my brain up today.

No idea. Easy solve. No guessing. Kinda pretty.

Whether you see the blue on the corners depends on your angle of view. I looked at spirals on google images.

As I was solving I was very confused because I had misread Psychic ;-)

Fun solve

I don't believe that the ball will continue spiraling once it leaves the spring.

I think that assuming that the ball has some centrifugal force and is riding the outside edge of the ramp, instead of shooting straight out the tip of the spring, it go mostly straight, but will angle slightly toward whichever way was the outside edge.

So if looking down on the spring, the ball is rolling clockwise down the spring, it will shoot straight out the tip but slightly angled to the ball's left as it leaves the ramp.
If the ball rolls counterclockwise down the spring, it will angle slightly to the right of straight (from the ball's point of view) as it leaves the ramp

The ball's path out the ramp will be straight, because it will be the hypotenuse of the vector shooting straight out the tip of the ramp and the vector of the centrifugal force.
The ramp isn't imparting "english" like a pool ball to make it curve when it leaves the ramp

My son and I have been discussing this and he initially thought there would be a spin on the ball, but now he's changed his mind and thinks it will go straight. I still think the ramp will put a spin on the ball.

The spin won't matter. Something like a steel ball, with a smooth surface, won't be affected. Something like a golf ball, with a dimpled surface, won't be moving fast enough to be affected. With something light enough and dimpled enough, like a wiffle ball, the spin will be immediately slowed and stopped by the surrounding air, and its trajectory won't be affected.

The ball will go straight unless there are other forces applied to it, and there aren't any except perhaps friction with the air or table, which should be small. So to a first order approximation it will go straight.

If the ball is relatively light and spinning fast enough to have some friction with the air, it may curve a little. If the spiral is clockwise as the ball descends, the ball will be spinning counterclockwise, and there will be higher air pressure on the right side of the ball. Therefore the ball will curve a little to the left, the opposite of the curvature of the spiral.

If there is friction with the table, and if the table is not totally smooth, it could go either way or wander back and forth.

I think I just understood Tea's comment and I agree with it. One thing for sure is that common sense says it will continue to curve, but common sense is wrong in this case. The trajectory also depends on if the cat is chasing it. :)

The trajectory will be straight, and angled outward slightly.

This was intriguing, so I tried to look it up. A spin with a horizontal axis will cause the ball to deviate in the direction of the spin- see link below and lots of links on baseball and ping pong etc.. What I could not find is whether the curved ramp will cause the ball to spin. There are lots of links to balls and ramps and Galileo, straight ramps and ramps that curve vertically, but I couldn't find anything with ramps that curve horizontally- if this link does not work, look up Magnus effect......https://en.wikipedia.org/wiki/Magnus_effect

Thinking more about this, if you slowly and steadily apply pressure to the side of a ball sitting on a table to rotate it, it will stop rotating when you stop moving it. I'm not sure what would happen in a frictionless environment. You would have to give it a "flick" at the end to get it to move off and spin. That is what baseball pitchers do, and apparently tennis players give it a vertical spin with a horizontal axis, and golfers try not to. It seems like the ramp would just give it pressure and not a "flick" but maybe it would be different in a frictionless environment? This has been interesting, please correct me if I am wrong.

In first comment I should have said a horizontal spin with a vertical axis.

I think once the ball exits the ramp it will slowly rise up about 10 feet in the air, circle lazily a few times, then shoot off at dizzying speed, cackling maniacally.

Cuz that's much more fun.

You may have something there, Bill!

If the ball is hugging the side of the spiral, there will be a bit of sidespin. Think of it as having the spin axis not exactly horizontal, and with a bit of friction, it will turn a little bit until the spin axis is horizontal. So there will be a bit of curve initially (let's not assume a frictionless surface here), then straight off. It it's hugging the right edge of the spiral, it will go right for a little bit, then straight. Left edge, well you know.

Bill, that's what a Golden Snitch would do for sure!

"The ball rolls off" Onto what?
A frictionless horizontal surface...straight.
Into a freefall...a parabolic path to the ground.
A horizontal surface with medium friction...perhaps a slight curve like a fancy billiard shot.
A high friction horizontal surface... sudden deceleration like a golf sand trap.

Now, if it is a baseball with laces or a golf ball with dimples, than air resistance comes into play with even more interesting possibilities.

Goto next topic

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