# Why do heavy people go faster on a zipline? **URL:** \ **Category:** Factual Questions\ **Created:** [September 15, 2011, 1:58am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354 "2011-09-15T01:58:54Z")\ **Posts on this page:** 12\ **Page:** 3
**Author:** ![Heracles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heracles/32/487_2.png) [@Heracles](https://boards.straightdope.com/u/Heracles)\ **Post date:** [September 15, 2011, 6:15pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/41 "2011-09-15T18:15:43Z")
> [@Machine\_Elf](#): > > Problems: > > 1. you cannot assume the cable is tight enough not to deviate from a straight line. The tension will exceed the strengh of the cable. This is why, for example, electrical/telephone cables on elevated poles all have some deliberate sag between support points. I understand that this is theoretical, and that there’s no way to create such a cable (of any significant length) in reality. Let’s consider an incline instead. Do heavier people go faster when rolling down an incline in a given vehicle? > [@](#): > > 1. Acceleration will not be 10 m/s[sup]2[/sup]. if we do assume that the cable is infinitely tensioned so as to provide straight-line movement of the rider (which we can’t - see above), the acceleration of the rider will be 9.81 m/s[sup]2[/sup] times the sine of the angle of the cable with respect to the horizon. In your stated case of a 10m drop over a 100m-long cable, the sine is .1, so the acceleration is a steady 0.981 m/s[sup]2[/sup]; it will take 14.3 seconds for the rider to travel the length of the cable in this scenario, achieving a final speed of 14 m/s. Ah! yes. That makes sense. Otherwise we’d all be moving at relativistic speeds when going down a slight hill on rollerblades. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [September 15, 2011, 6:19pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/42 "2011-09-15T18:19:38Z")
> [@Heracles](#): > > I understand that this is theoretical, and that there’s no way to create such a cable (of any significant length) in reality. Let’s consider an incline instead. Do heavier people go faster when rolling down an incline in a given vehicle? In the absence of aerodynamic drag, no, Fat Guy and Skinny Guy will accelerate at the same rate, just as they would in freefall. That formula I cited earlier, a = 9.81\*sin(theta)? Notice that the mass of the object is not in that equation. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [September 15, 2011, 6:25pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/43 "2011-09-15T18:25:45Z")
> [@Machine\_Elf](#): > > In the absence of aerodynamic drag, no, Fat Guy and Skinny Guy will accelerate at the same rate, just as they would in freefall. That formula I cited earlier, a = 9.81\*sin(theta)? Notice that the mass of the object is not in that equation. But with aerodynamic drag, the Fat Guy will travel faster than the Skinny Guy. Probably just pointing out the obvious, but that’s my job. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [September 15, 2011, 6:45pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/44 "2011-09-15T18:45:31Z")
> [@Machine\_Elf](#): > > The acceleration will be different, but conservation of energy dictates that for a given vertical drop, the final speed will be the same As you note, this is true in the absence of air. Otherwise the final speed that results from an inclined path will be lower, due to a longer path that requires pushing more air molecules out of the way (and the small but non-zero contribution of pulley friction). ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [September 15, 2011, 7:34pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/45 "2011-09-15T19:34:17Z")
**Chronos** , you mentioned actually testing the hill hypothesis in sledding. Do you also attribute the difference to wind resistance? And, for curiosities sake, how big are the differences? ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [September 15, 2011, 8:19pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/46 "2011-09-15T20:19:12Z")
> [@DSeid](#): > > Close to the same formula. Sine is included. Quite right. I should have noted that your formula is the more general form, covering paths at any angle. ---
**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:** [September 16, 2011, 12:05am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/47 "2011-09-16T00:05:39Z")
> [@](#): > > Chronos, you mentioned actually testing the hill hypothesis in sledding. Do you also attribute the difference to wind resistance? > > And, for curiosities sake, how big are the differences? Yes, I attribute the difference to wind resistance, since I can’t come up with anything else that could account for it: All other forces on the sleds would be directly proportional to the masses, and therefore produce a mass-independent acceleration. And as for how big the differences were, there wasn’t any speed-measuring equipment available, nor were the distances along the sled tracks marked, so I don’t have any numbers (and I would probably have forgotten them by now even if I had them). So I can’t say anything more than that it was qualitatively extremely significant. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [September 16, 2011, 12:31am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/48 "2011-09-16T00:31:33Z")
> [@Chronos](#): > > Yes, I attribute the difference to wind resistance, since I can’t come up with anything else that could account for it: All other forces on the sleds would be directly proportional to the masses, and therefore produce a mass-independent acceleration. Was the surface upon which they were sliding snow? I was at some point led to believe (by a ski instructor) that a snow surface actually changes composition (i.e. packs down and melts a bit) when you put weight on it, and therefore doesn’t obey the usual “friction is proportional to normal force” rule. ---
**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:** [September 16, 2011, 1:19am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/49 "2011-09-16T01:19:34Z")
It was a toboggan track, well-used, so any packing that was going to happen had already happened long before either test sled ever touched the track. Though I’ll grant that “friction proportional to normal force” is only ever an approximation for _any_ surface, and it might well be a poor approximation for ice-- I don’t know the practical details on that one. ---
**Author:** ![AaronX](https://avatars.discourse-cdn.com/v4/letter/a/7bcc69/32.png) [@AaronX](https://boards.straightdope.com/u/AaronX)\ **Post date:** [September 19, 2011, 7:47am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/50 "2011-09-19T07:47:38Z")
A piece of news that may be relevant to this thread: Tourist breaks back on Sentosa ride [Tourist breaks back on Sentosa ride](http://sg.news.yahoo.com/tourist-breaks-back-on-sentosa-ride.html) At least he can move his legs now, I thought a broken back is guaranteed paralysis. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 19, 2011, 8:22am UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/51 "2011-09-19T08:22:00Z")
> [@Xema](#): > > If these are valid, the energy that goes into torque is not significant. I did the math and it appears that for fairly typical pulleys, there’s somewhere around 15 joules of energy in the rotating masses @ 50 mph. Assumptions: 50 mph speed, or 22.35 m/s pulley diameter 21 mm (from [here](http://www.ebay.com/itm/Zipline-Cable-Trolley-zip-line-pulley-NEW-/360278808775#ht_1350wt_817)) 2 pulleys of 60 g each (estimated based on 270 g total trolley mass and materials) Energy in a rotating disk is ¼Mr²ω² I get 14.46 J. So yeah, not significant here. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [September 19, 2011, 12:38pm UTC](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354/52 "2011-09-19T12:38:36Z")
> [@AaronX](#): > > …I thought a broken back is guaranteed paralysis. No guarantee. It’s possible to break your spine without damaging your spinal cord; the latter is what causes paralysis. Twelve years ago my brother was in a motorcycle accident in which he broke his back; there was no spinal cord injury though, so he never experienced any paralysis. [Previous page](https://boards.straightdope.com/t/why-do-heavy-people-go-faster-on-a-zipline/596354.md?page=2)