6th Grade Physics Question - Roller Coaster Ramp

Good evening!

In my classroom, we had a single ramp that was about 6 feet high at a 45 degree angle. The track was a marble run type of track that you would find on a skyrail tower. We placed two of these tracks side by side. When the tracks hit the floor, they formed a strait-a-way, similar to an ending trough on a water park slide.

On one track, we placed a hollow plastic golf ball. On the other, a regular standard golf ball. We let them go at the same time and we had the same result.

Going down the tracks, the lighter ball and the heavy ball kept the same pace, but when they got to the straight-a-way, the lighter ball always won. (Even when we switched tracks).

Is this because of Newton's second law that explains that you can kick an empty box further than the same box when it's full of books. Or is it because the friction with the heavier ball will be greater, thus slowing down the speed.

Everyone predicted that the heavy ball would be faster. It was just hard to explain why.

Also, when parks test coaster trains at the start of the day, is their speed greater without passengers.

Would a heaver ball (or coaster car) ever have an advantage?

Thanks for your help and support.

Assuming both balls have the same surface, thus same coefficient of friction, the heavier ball would have more friction, but it's basically negligible since the balls are theoretically rolling and not sliding.

I'd have to consult my mechanics book to remember for sure, but I believe the lighter (hollow) ball has less rotational inertia, thus it can roll faster than the solid ball. Try spinning a basketball vs a bowling ball.

The slope is steep enough that the two balls fall more so than roll until they reach the bottom. And since both balls are the same size and have the same surface area (and again assumming they have the same surface), they have the same air resistance. Once they reach the bottom, rolling takes over.

The fact that the slope is at 45 degrees means the vertical component (sine 45) is equal to the horizontal component (cosine 45). I doubt this is a coincidence, so there's probably a little more to this.

As for the coaster train thing, I guess a train with lighter wheels would have an advantage over a train with heavier wheels. :) *** Edited 3/20/2006 6:57:04 AM UTC by Acoustic Viscosity***

Matt wins. You're seeing the difference in rotational inertia present in a solid body versus a hollow body.

Rotational inertia is certainly not a 6th grade physics lesson. I learned in 12th, but it probably should've been taught in 6th, so let's split the difference and call it a 9th grade lesson. :)

Well, if rotational inertia is the only manipulated variable, then the lighter ball should make it to the bottom of the ramp first, too.

I knew that the rotational inertia was the factor that caused the difference between the two. I guess I did learn something in our physics course.

As for them making it to the bottom of the ramp at the same time, I think because of the acceleration due to gravity, that the difference between their rotational inertia becomes negligible.

On the straight-away, however, there is no longer acceleration due to gravity, so their rotational inertia is the only difference between the two.

If you want the answer with equations, going down the hill, the inertia doesn't matter. All that is a factor here is mgh=.5*(m)v^2. That is why they both reach the bottom at the same time - the masses are cancelled out. On the straight-away, the inertia for the regular golf ball is (2/5)MR^2 and for the hollow ball is (2/3)MR^2. This shows why the hollow ball always wins. Pretty good lesson though for 6th grade.

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Chernabog said:
Matt wins. You're seeing the difference in rotational inertia present in a solid body versus a hollow body.

Rotational inertia is certainly not a 6th grade physics lesson. I learned in 12th, but it probably should've been taught in 6th, so let's split the difference and call it a 9th grade lesson.

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I also learned this lesson this year. 12th grade. It should have been taught when I had 8th grade physics, but we never got that far.

This is starting to get over "my" head. (Which isn't too hard to do)

I should have said that I basically teach a unit on simple machines and Newton's Laws. I was given some Skyrail tracks and connectors to play with. When I set up two identical tracks, it seemed that the lighter ball won the race down the straight-a-way, though the falling of the two balls down the ramp seemed even. Everyone predicted that that heavy ball would travel faster and win the race.

They aren't satisfied with the answer that "It's easer for forces to act on a hollow ball than it is on a heavier one due to 1) Less friction on the lighter ball and 2) Less mass in the lighter ball. (This is also Newton's second law - I think)

The textbook uses the example of a kid kicking a box. When the box is empty it goes a greater distance. When the box is full, it barely moves.

I appreciate everyone's help on this.

BY THE WAY - It's not really ride-related, but at Hofstra University this weekend, several Long Island high schools are competing in a robotics competition. It was highlighted in last week's Sunday Newsday. The robots have to climb an incline and "shoot" a ball at a target. Admission is free.