My high school physics class drilled in to us that objects fall at the same speed regardless of weight (at least, ignoring air resistance). Contrary to intuition, heavy objects do NOT fall faster than light objects. There’s a famous video of astronauts on the moon dropping a hammer and a feather at the same time, and they both fall to the moon at the same speed. This is still true, right? The laws of physics haven’t changed since I was in high school, have they?
But I went zip-lining last week and there was one heavy guy. Every single time, he zoomed down the line WAY faster than anyone else. The guides said this would be the case in advance, and they were right.
So if objects fall at the same speed regardless of weight, how come the heavy guy was consistently faster on the zip line than anyone else?
He pulls the line down at more of angle. So, initially he has to move faster. Someone will have pull out some math to show that, even though he slows down faster at the end, the overall average velocity will be higher than someone who accelerates/de-accelerates slower.
My guess: His greater weight means he overcomes the friction of the zip line easier, and his eight means he’s starting at more of an angle as K364 says. He’s not truly falling, after all.
Its due to air resistance. A heavier person will cut through the air much easier than a lighter person. Think of someone hanging on a perfectly horizontal zip line and a constant wind parallel to the zip line. A heavier person will be less affected by the wind than a lighter person.
Another example would be an empty plastic bottle and a full plastic bottle. Same size and shape but one will fall faster than the other due to air resistance.
But most of the time there is air, which causes drag and complicates things. Among other effects, it quite often means the heavier object does fall faster.
Still true on the moon. Here on Earth, the presence of air means the hammer falls faster.
For the math of this:
The net force on an object falling through air is given by: Force = (Mass * Gravity) - Drag
Acceleration is Force divided by Mass, so: Acceleration = Gravity - (Drag / Mass)
This clearly shows that when air drag is present, more mass yield more acceleration. It also shows that when drag is zero, acceleration no longer varies with mass - it’s always equal to Gravity.
In the case of a zipline, I think K364 is correct about initial acceleration.
No, but he’s moving under the influence of gravity, as is a truly falling object. The effect of gravity is always G times the sine of the descent angle (e.g., the angle of the zipline below horizontal).
Heavy people are almost never the same size and shape as light people. I think you have the right idea but you have to take into account the ratio of mass to reference area, not just mass.
I doubted this at first but on thinking about it, the cable will hang in a parabolic arc due its own weight when there is no rider. The cable’s shape will approach the shape of the bottom two legs of a triangle as the weight of the rider approaches infinity, so this should be a significant difference between a very heavy and a very light rider. The math analysis to model the acceleration/velocity through the entire ride is out of reach of my rusty brain.
Picture a cube 1’ across compared to a cube 2’ across. If the first has a mass of 1 and a surface area facing forward of 1’ sq, the second has a mass of 8x and s surface area facing forward of 4’ sq. Mass always increases more than surface area, generally square versus cube.
No, assuming a spherical cow of uniform density ( the only kind for a three line response). Air resistance goes up as the square of radius, weight goes up as the cube of radius. As you get into non spherical people I think you will find that air resistance goes up faster than the square of height increasing the heftier peoples lead.
I am not sure about the drag due to the wheels in the zip line. I would be interested to know if roiling resistance or air resistance dominates.
I think the effect of friction is greater than air resistance. Specifically, friction does not scale up as quickly with weight:
Light person: weight - 1, friction 0.1. Net force = (1-0.1) = 0.9, acceleration = 0.9
Heavy person: weight - 2, friction 0.15. Net force = (2-0.15) = 1.85, acceleration = 0.925
I don’t think it’s because of change of shape of the rope, because this also happens in go-karts.
If heavy people had less drag compared to weight force, wouldn’t their terminal velocity be higher?
IANA physics or fluid dynamics expert, but something tells me that when we’re scaling wind resistance calculations up to adult people-size, and not talking about perpendicular freefall, then air resistance won’t matter as much as the combined factors of increased weight overcoming rolling resistance, and increased angle of descent. But that’s just my WAG.
It would take a poor bearing for this to be true. Such a bearing would necessarily be hot at the end of a zipline run.
Various Googling (e.g. this site) suggests that within reasonably wide limits friction is basically linear with load. (There will be a tiny component of no-load friction as well.)
Not only is he initally descending at a steeper angle, he also descends farther, converting more gravitational potential energy to kinetic energy.
An accurate model of the zip line system has to account for the fact that the rope is not weightless. Just eyeballing this particular zipline, I’d guess the entire length of rope weighs a good 50 pounds or so. Imagine suspending a very small child (~20 pounds?) from the center of the span; the rope on each side would be a catenary curve, rather than a straight line, and the child would be suspended at a height greater than you would expect if the ropes were actual straight lines. As the weight of the suspended person increases, the two lengths of rope remain as two catenary curves, but become straighter and straighter, and the person suspended at mid-span hangs lower and lower. The theoretical extreme involves someone whose mass is very, very large compared to that of the rope, i.e. the ratio approaches infinity; in this case the two lengths of rope are indeed straight lines.
The steeper initial descent is also for the same reason. When the rider is very close to one end of the rope, nearly the entire mass of the rope is off to one side of him, forming that catenary curve. The more the rider weighs, the closer he can pull that long length of rope to a straight line; his support pulley ends up more below the start platform instead of next to it.
Did a zip line in Costa Rica about 2 years ago. Well, a bunch of them. We were told to get in a position that minimizes air resistance. Sort of a feet forward tuck.
Indeed one light kid did not make it and had to hand over hand to finish, after that a guide went with him to increase the weight.
And these where some zip lines. Speeds about 50 miles an hour and 600 feet in the air. ¼ - 1/3 mile long.
