# Did I just lie about Galileo to a fat kid on a sled? **URL:** \ **Category:** Factual Questions\ **Created:** [February 19, 2015, 1:35am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053 "2015-02-19T01:35:43Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![buddy431](https://avatars.discourse-cdn.com/v4/letter/b/6a8cbe/32.png) [@buddy431](https://boards.straightdope.com/u/buddy431)\ **Post date:** [February 19, 2015, 3:57am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/21 "2015-02-19T03:57:11Z")
> [@Princhester](#): > > I didn’t say that their acceleration would be proportional to their masses. What I said was “the rate of acceleration of the respective kids downhill is proportional to their respective masses, **and the forces on them** ”. > > If you leave out bits of equations, they break and don’t work. Handle them carefully. > > What I said, in sentence form, was F=MA. You can argue that is wrong if you like. Good luck. When you succeed, remind me to congratulate you on your Nobel. Uh, that equation shows that acceleration is inversely proportional to mass… [QUOTE=OldGuy] Pure 1st year Newtonian mechanics ignoring friction, air resistance, etc., he acceleration will be the same for both. Both will be going the same speed at the bottom of the hill. [/QUOTE] Actually, first year mechanics will include friction, and it would also have them going the same distance. However, first year mechanics will assume that friction is proportional to the normal force (for identical materials), which is not quite true. Close, but not quite. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [February 19, 2015, 4:08am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/22 "2015-02-19T04:08:15Z")
> [@buddy431](#): > > Uh, that equation shows that acceleration is inversely proportional to mass… You are correct that I should have said “the rate of acceleration of the respective kids downhill is **dependent upon** their respective masses, and the forces on them”. You described my whole post as “wrong” over this one mis-phrasing (particularly given that based on the rest of the post it was clear I understood the correct position)? ---
**Author:** ![buddy431](https://avatars.discourse-cdn.com/v4/letter/b/6a8cbe/32.png) [@buddy431](https://boards.straightdope.com/u/buddy431)\ **Post date:** [February 19, 2015, 4:09am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/23 "2015-02-19T04:09:10Z")
> [@Princhester](#): > > I didn’t say that their acceleration would be proportional to their masses. What I said was “the rate of acceleration of the respective kids downhill is proportional to their respective masses, **and the forces on them** ”. > > If you leave out bits of equations, they break and don’t work. Handle them carefully. > > What I said, in sentence form, was F=MA. You can argue that is wrong if you like. Good luck. When you succeed, remind me to congratulate you on your Nobel. OK, sorry, I guess I better understand what you’re saying now, and I do agree with you. I don’t think energy’s the best way to think about it though, because it’s not clear at all how the energy lost to friction or air resistance scales with size. You say it’s marginal, but it’s really not, especially for friction. The energy lost to friction scales almost linearly with mass. But I apologize for my earlier remark. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [February 19, 2015, 4:19am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/24 "2015-02-19T04:19:51Z")
Apology accepted. I tend to agree regarding an analysis in terms of energy. I find it much easier and more intuitive to talk about momentum and force etc (which is why I did that too) but IME someone in these threads always analyses in terms of energy, so I thought I’d get in first. ---
**Author:** ![chappachula](https://avatars.discourse-cdn.com/v4/letter/c/d2c977/32.png) [@chappachula](https://boards.straightdope.com/u/chappachula)\ **Post date:** [February 19, 2015, 8:17am UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/25 "2015-02-19T08:17:54Z")
I dont have anything to add about the physics. But I would like to say that the title of this thread deserves a prize-- for a unique combination of words. Nobody in human history has ever used “fat kid” in the same sentence as “Galileo”. I love this place. 🙂 ---
**Author:** ![Kiber](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kiber/32/317_2.png) [@Kiber](https://boards.straightdope.com/u/Kiber)\ **Post date:** [February 19, 2015, 12:19pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/26 "2015-02-19T12:19:51Z")
I just wanted to add a real world example. In luge competition, riders are permitted to wear additional weight based on their initial starting weight. It’s a sliding scale in which riders who weigh less than a certain threshold are permitted to add ballast. The intent is to offset the benefit that heavier riders have over lighter ones. See here for an overview of the [physics](http://adventure.howstuffworks.com/outdoor-activities/snow-sports/luge4.htm) of luge. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 19, 2015, 2:47pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/27 "2015-02-19T14:47:57Z")
First of all, empirically, a sled with a lot of weight on it definitely does go much further than a sled with little weight on it. The kids on top of the hill were correct: He went further because he’s fat. But now we must figure out why that is. If the only force were gravity, mass would not matter. If the only forces were gravity and the normal force exerted by the snow, mass would still not matter. Even if we had gravity, normal force, and dry friction, mass would _still_ not matter. This is because, in such a situation, _all_ of the forces are directly proportional to the mass, and so the acceleration is the same for all (some fraction of g, with the fraction being determined by the steepness of the slope and the coefficient of friction). If mass does matter (as, empirically, we know it does), then there must be some other force at work besides gravity, normal force, and dry friction. **buddy431** has already pointed out one possible culprit: Friction with snow does not behave in the same way as dry friction, and so snow friction is not proportional to mass. Another possible culprit, which is more significant than many folks realize, is air resistance, which is also not proportional to mass. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [February 19, 2015, 3:51pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/28 "2015-02-19T15:51:47Z")
Nice thread. Wasn’t there some humongous physics thread on skiing here not so long ago? ---
**Author:** ![Pixel\_Dent](https://avatars.discourse-cdn.com/v4/letter/p/bc8723/32.png) [@Pixel\_Dent](https://boards.straightdope.com/u/Pixel_Dent)\ **Post date:** [February 19, 2015, 4:13pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/29 "2015-02-19T16:13:30Z")
> [@Leo\_Bloom](#): > > I checked if each kid started from a sitting start–they did. So did the factor of inertia screw me up, and I lied to the hope of America’s future? If the kids were cub scouts they knew all about the forces involved from building their pinewood derby cars. Even among the youngest scouts you’ll see all the cars within .01 ounces of the legal maximum, center of gravity moved just in front of the rear axle of the car to maximize potential energy at the start, and axle nails buffed to a mirror finish to minimize friction. You weren’t going to fool them. 😉 ---
**Author:** ![steronz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steronz/32/11765_2.png) [@steronz](https://boards.straightdope.com/u/steronz)\ **Post date:** [February 19, 2015, 4:33pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/30 "2015-02-19T16:33:59Z")
> [@Pixel\_Dent](#): > > If the kids were cub scouts they knew all about the forces involved from building their pinewood derby cars. Even among the youngest scouts you’ll see all the cars within .01 ounces of the legal maximum, center of gravity moved just in front of the rear axle of the car to maximize potential energy at the start, and axle nails buffed to a mirror finish to minimize friction. You weren’t going to fool them. 😉 I was going to say this, along with soap box derby contestants and any toddler who’s had the pleasure of going down a water slide between his 200lb father’s legs. Shit gets real when you quintuple your mass on water slide. ---
**Author:** ![Fubaya](https://avatars.discourse-cdn.com/v4/letter/f/c2a13f/32.png) [@Fubaya](https://boards.straightdope.com/u/Fubaya)\ **Post date:** [February 19, 2015, 4:53pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/31 "2015-02-19T16:53:58Z")
Here’s an easy way to think about this… > [@Leo\_Bloom](#): > > Me, passing by: "Gravity works the same on feathers and bowling balls, excluding wind and other stuff. Which one is harder to stop? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 19, 2015, 5:03pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/32 "2015-02-19T17:03:24Z")
Despite the advance physicism displayed in this thread I think the fat kid started further up on the hill and had the advantage of less friction on the snow surface from the skinny kids taking their runs. But Leo did the right thing, throw a bone to the fat kid. ---
**Author:** ![August\_West](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/august_west/32/18069_2.png) [@August\_West](https://boards.straightdope.com/u/August_West)\ **Post date:** [February 19, 2015, 6:03pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/33 "2015-02-19T18:03:18Z")
I would have told him to stop sledding into the street. ---
**Author:** ![DrDeth](https://avatars.discourse-cdn.com/v4/letter/d/b487fb/32.png) [@DrDeth](https://boards.straightdope.com/u/DrDeth)\ **Post date:** [February 19, 2015, 6:44pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/34 "2015-02-19T18:44:07Z")
> [@buddy431](#): > > At least for snow, your [assumption about friction is incorrect](http://hyperphysics.phy-astr.gsu.edu/hbase/frict3.html). Assuming all the kids were using the same size sleds, the fatter kid will exert a larger pressure on the snow, which tends to decrease the coefficient of friction. > > And I suspect that the friction force between the snow and the sled is the main factor in determining how far he slides. Right, the heavier kid will go faster in this case. ---
**Author:** ![Drunky\_Smurf](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/drunky_smurf/32/449_2.png) [@Drunky\_Smurf](https://boards.straightdope.com/u/Drunky_Smurf)\ **Post date:** [February 19, 2015, 6:44pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/35 "2015-02-19T18:44:00Z")
> [@TriPolar](#): > > Without gravity he wouldn’t weigh anything. So, gravity makes people fat? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 19, 2015, 6:54pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/36 "2015-02-19T18:54:14Z")
> [@Drunky\_Smurf](#): > > So, gravity makes people fat? Apparently, but I’m not a physicalist so I couldn’t explain why 🙂 ---
**Author:** ![Tangent](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tangent/32/3098_2.png) [@Tangent](https://boards.straightdope.com/u/Tangent)\ **Post date:** [February 19, 2015, 6:59pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/37 "2015-02-19T18:59:36Z")
> [@Leo\_Bloom](#): > > Did I lie? I sentence you to house arrest for the remainder of your life! ---
**Author:** ![Sampiro](https://avatars.discourse-cdn.com/v4/letter/s/2acd7d/32.png) [@Sampiro](https://boards.straightdope.com/u/Sampiro)\ **Post date:** [February 19, 2015, 7:03pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/38 "2015-02-19T19:03:08Z")
Wasn’t “Don’t Lie About Galileo To a Fat Kid on a Sled” one of Briscoe Darling’s favorite songs on _The Andy Griffith Show_? ---
**Author:** ![Omar\_Little](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/omar_little/32/269_2.png) [@Omar\_Little](https://boards.straightdope.com/u/Omar_Little)\ **Post date:** [February 19, 2015, 7:18pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/39 "2015-02-19T19:18:59Z")
Straight Dope users - spreading ignorance to fat kids everywhere, since 1973! ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [February 19, 2015, 8:00pm UTC](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053/40 "2015-02-19T20:00:55Z")
Have you guys never competed in a Pinewood Derby? They have a 5 oz weight limit on the cars for a reason. If they didn’t, the guy with the 20lb car would always beat the guy with the 10lb car; that is until someone’s 30lb car broke the track. In the Pinewood derby, at any sledding hill, and implicitly stated in the OP (assuming that the sidewalk and the street have negligible sideways slant) there is a “steep” downhill portion and a flat (or flatter) runout portion. You may choose to ignore friction in the downhill part, but you cannot on the flat part. Even if you assume all parties have the same speed and friction at the bottom of the hill, the more massive sled will have more momentum and kinetic energy, and therefore a longer runout. I think that practically speaking, friction does increase for a heavier sled, but within the range of masses where friction increases at a slower rate than momentum, the heavies will win. [Previous page](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053.md?page=1) [Next page](https://boards.straightdope.com/t/did-i-just-lie-about-galileo-to-a-fat-kid-on-a-sled/713053.md?page=3)