# A Science Question About Gravity

#### Electric Skeptic

##### Well-known member
"Dynamic positioning of mass" means that the crew lean in on curves. In yacht racing, crewmen are picked for their size because they can then affect the stability by moving about. Ask AN for further details. Okay, I'm familiar with the idea of crewmen on yachts leaning and moving, particularly when turning - images of several of them with their feet on the edge (right term?) of the boat, their entire weight leaning out over the water as they hold onto ropes, come to mind. But believe me, if the idea wasn't familiar to me, I'd certainly ask our resident commodore all about it But I wouldn't have thought that that would apply in bobsledding since all the curves are banked. If you're riding a motorbike and you turn left, then you lean left and the bike tilts to the left. But in bobsledding the sled is tilted to the left by the bank of the snow/ice; you don't need to lean. Or that's how it seems to me - I'm quite prepared to believe I have it very wrong #### Electric Skeptic

##### Well-known member
On the general topic of sports and physics, I remember once hearing Erich Segal (author of Love Story, but also a classics professor) commenting on the Olympics and saying that the ancient Greek long jumpers would carry a couple of lead weights and then throw them behind them when they were in mid-air, giving them a kind of "rocket" type boost. And I thought, wait a minute... wouldn't the extra weight handicap their liftoff at least as much as the discard would help them? If that sort of thing could work, couldn't you use the same principle to create a perpetual motion machine? So was Segal botching the physics, or was I missing something?
I'd agree with you - TANSTAAFL. Whatever benefit you get from throwing the weights in mid-air would be exactly balanced by the detriment of the extra weight at liftoff.

A similar thing I've heard before - the bloke driving a truck full of birds approaches a bridge. His truck weights 1 ton; the birds between them all weigh a hundred pounds. The bridge is rated for 1 ton only. He knows that since his truck (laden as it is) weighs 1 ton + a hundred pounds, the bridge isn't safe for him. So he (magically, with some apparatus that weighs nothing, lol) gets all of the birds to fly inside his truck for the duration of the trip over the bridge. Since they're all in the air, their weight doesn't actually 'count', and the truck makes it safely across. But, like the long jumpers, whatever benefit you gain from having the birds in the air is exactly balanced by the 'weight' of the thrust they must use to stay in the air. Every wing flap, they are exerting a force equivalent to their weight on the floor of the truck - so no net gain, and the truck goes crashing into the gorge with all those poor birds. I think.

#### Temujin

##### Well-known member
Okay, I'm familiar with the idea of crewmen on yachts leaning and moving, particularly when turning - images of several of them with their feet on the edge (right term?) of the boat, their entire weight leaning out over the water as they hold onto ropes, come to mind. But believe me, if the idea wasn't familiar to me, I'd certainly ask our resident commodore all about it But I wouldn't have thought that that would apply in bobsledding since all the curves are banked. If you're riding a motorbike and you turn left, then you lean left and the bike tilts to the left. But in bobsledding the sled is tilted to the left by the bank of the snow/ice; you don't need to lean. Or that's how it seems to me - I'm quite prepared to believe I have it very wrong What we need here, more than a physicist, is someone who has ridden a bobsleigh. Interesting topic, but with all this non-expertise on offer, I feel we may be getting slightly bogged down.

#### Electric Skeptic

##### Well-known member
What we need here, more than a physicist, is someone who has ridden a bobsleigh. Interesting topic, but with all this non-expertise on offer, I feel we may be getting slightly bogged down.
Good point. And that person who's ridden a bobsleigh ain't me.

#### LifeIn

##### Well-known member
We all know that (barring wind resistance) objects fall at the same speed, regardless of their weight.

So why is putting extra weight in things like bobsleds illegal? Adding weight to them won't make gravity pull them any faster.
You said it at the very beginning. Wind resistance. Wind resistance is a limiting factor in the speed of the bobsled, especially at the speeds they travel. Wind resistance does not depend on weight. It depends only on the profile presented to the wind and the speed.

The effect of wind resistance on acceleration (and hence velocity) is a smaller fraction of the force from gravity if the force from gravity is greater. So a very heavy sled would behave more like it would in a vacuum, whereas a very light sled would behave --- like a feather.

We should also consider the friction of the runners. To some extent, that is proportional to weight, the proportionality constant being the "coefficient of friction". So it neither helps nor hurts the speed to have a heavier sled, if runner friction was all that one had to contend with. It is the air resistance that makes the difference.

As for why it is illegal, it is probably a safety issue, or maybe because without the restriction the competition would degenerate to the point where every sled was filled with a several tons of lead, and then the structure of the course itself might be at risk.

#### Electric Skeptic

##### Well-known member
You said it at the very beginning. Wind resistance. Wind resistance is a limiting factor in the speed of the bobsled, especially at the speeds they travel. Wind resistance does not depend on weight. It depends only on the profile presented to the wind and the speed.

The effect of wind resistance on acceleration (and hence velocity) is a smaller fraction of the force from gravity if the force from gravity is greater. So a very heavy sled would behave more like it would in a vacuum, whereas a very light sled would behave --- like a feather.
If that were the case, then a 16 lb bowling ball would fall to the ground significantly faster than an 8 lb bowling ball (in our atmosphere). Is that the case?

Above you say that "[w]ind resistance does not depende on weight. Yet in your second paragraph, you seem to contradict this. What am I not understanding?

We should also consider the friction of the runners. To some extent, that is proportional to weight, the proportionality constant being the "coefficient of friction". So it neither helps nor hurts the speed to have a heavier sled, if runner friction was all that one had to contend with. It is the air resistance that makes the difference.

As for why it is illegal, it is probably a safety issue, or maybe because without the restriction the competition would degenerate to the point where every sled was filled with a several tons of lead, and then the structure of the course itself might be at risk.
I cannot agree with your last paragaph. If extra weight helps increase speed, then it would be illegal because it would be cheating. But if extra weight doesn't help increase speed, nobody would bother to do it, so why bother to make illegal?

#### LifeIn

##### Well-known member
If that were the case, then a 16 lb bowling ball would fall to the ground significantly faster than an 8 lb bowling ball (in our atmosphere). Is that the case?
That depends on what you mean by "significant". When an object is falling straight down, the entire force of gravity is acting on it. In comparison to that force, the force of wind resistance would have a very small affect between 8 lb. and 16 lb. But when an object is sliding down a bobsled track with an incline of, maybe, 8% to 11%, the force of gravity acting to accelerate the object is the component of gravity in the direction of travel. That would be about 0.08 to 0.11 of the force of gravity. So the 8 lb vs 16 lb object would be moving as if it were falling straight down, but weighed 0.8 lb. vs 1.6 lb (assuming a 10% slope on the bobsled track). That would make the relative effect of wind resistance ten times greater than if the objects were falling down at their full weight. Also, remember that bobsleds are not as dense as bowling balls - even a 8 lb ball. So the determination of what is "significant" is a little complicated. Also, at the highest level of competition, it only takes a slight boost to make the difference between gold medal and "also ran".
Above you say that "[w]ind resistance does not depende on weight. Yet in your second paragraph, you seem to contradict this. What am I not understanding?
Wind resistance, as measured in pounds (or more accurately, newtons, since pounds is not a unit of force), does not depend on weight. But the effect in terms of acceleration of a given amount of wind resistance force does depend on the weight of the object being accelerated.
I cannot agree with your last paragaph. If extra weight helps increase speed, then it would be illegal because it would be cheating.
Not if everyone was allowed to do it. Then it would not be cheating. But it would make the sport less interesting for the reasons I stated.

• Whateverman

#### LifeIn

##### Well-known member
, as measured in pounds (or more accurately, newtons, since pounds is not a unit of force),
Whoops! I goofed. I mixed up pounds and slugs. Of course pounds is a unit of force. But the time to edit my post has expired.

#### Whateverman

##### Well-known member
More momentum?
Yup. It keeps the sled moving in a straight line.

Throw a rubber ball at some sheetrock, and it'll bounce off. Throw a cannon ball at that same sheet rock, and it'll pass through like a hot knife though buttah.

edit: of course, more weight on a sled would also increase friction...

#### Temujin

##### Well-known member
If that were the case, then a 16 lb bowling ball would fall to the ground significantly faster than an 8 lb bowling ball (in our atmosphere). Is that the case?

Above you say that "[w]ind resistance does not depende on weight. Yet in your second paragraph, you seem to contradict this. What am I not understanding?
Instead consider a feather, and a replica feather made of brass. In a vacuum they fall at the same rate. Not so in the air.

#### Cisco Qid

##### Active member
Suppose we had a flat stretch of ice, two sleds with different weights, and two machines set to give each an identical push towards the finish line. (I think this is a fair analogy to the bobsled acceleration, since the push the sledders give to the heavier sled would be equal to the push they'd give to the lighter sled: in each case, they will be giving it all the force they can.) If more mass -> greater momentum -> longer period at high speed vs. friction, then we would expect the heavier sled to reach the finish line first, wouldn't we? But that can't be right, because then a sled weighed so heavily that the machine could barely get it started would also finish first.

(I'm also not a physicist, in case that wasn't obvious.)

A physicist wouldn't know either unless he performed the measurements and solved the differential equation. Or just simply raced the damn things.

(I am a physicist - but only if you consider someone with a BS in engineering physics a physicist)

#### LifeIn

##### Well-known member
Suppose we had a flat stretch of ice, two sleds with different weights, and two machines set to give each an identical push towards the finish line. (I think this is a fair analogy to the bobsled acceleration, since the push the sledders give to the heavier sled would be equal to the push they'd give to the lighter sled: in each case, they will be giving it all the force they can.) If more mass -> greater momentum -> longer period at high speed vs. friction, then we would expect the heavier sled to reach the finish line first, wouldn't we? But that can't be right, because then a sled weighed so heavily that the machine could barely get it started would also finish first.

(I'm also not a physicist, in case that wasn't obvious.)
There is one way in which this scenario is significantly different from a bobsled race. The initial push in a bobsled race is not the only force on the sled. There is also the force of gravity acting through a 8-11 % slope. In that case the heavier sled would receive the greater force. Depending on the length of the race, this may or may not be enough to make the heavier sled win. In the flat ice scenario, gravity does not act on the sled at all, except indirectly by friction, which is proportional to the weight of the object (sort of). Also, you do have to consider air resistance to make any meaningful application to the real world.

#### Electric Skeptic

##### Well-known member
I've seen some very intesting points and arguments made on this thread, so thanks all. I think I've learned some physics, but I'm not sure I'm any the wiser as to the question in the OP #### Komodo

##### Well-known member
There is one way in which this scenario is significantly different from a bobsled race. The initial push in a bobsled race is not the only force on the sled. There is also the force of gravity acting through a 8-11 % slope. In that case the heavier sled would receive the greater force. Depending on the length of the race, this may or may not be enough to make the heavier sled win. In the flat ice scenario, gravity does not act on the sled at all, except indirectly by friction, which is proportional to the weight of the object (sort of). Also, you do have to consider air resistance to make any meaningful application to the real world.
But the greater force of gravity is exactly counteracted by the greater resistance to acceleration, due to mass. This of course is why objects of different weights fall at the same pace, discounting air resistance; why would that be different with a 10% slope than it is with a direct drop?

#### LifeIn

##### Well-known member
But the greater force of gravity is exactly counteracted by the greater resistance to acceleration, due to mass. This of course is why objects of different weights fall at the same pace, discounting air resistance; why would that be different with a 10% slope than it is with a direct drop?
The scenario I was commenting on was not the direct drop. It was the flat ice (0% slope). In that case gravity does not provide any push at all. The only push comes from the person pushing it. Assuming the person can only push with a limited amount of force, he can get a small weight going faster than a large weight. If their were no friction (either from the ice or from air resistance), the smaller weight would continue going faster than then large weight after the pushing was over, and small weight would always win.

But when you add air resistance, the question becomes more complicated. Just try throwing a nerf ball and baseball from the pitcher's mound. Even if you could get the nerf ball going at 90 MPH, it would not continue at that speed for more than a couple of feet. It might not even make it to home plate. But the baseball will continue at almost 90 MPH all the way. Even if the nerf ball was the same size as the baseball and therefore had the same air resistance, that air resistance would have a bigger effect on the very small weight of the nerf ball.

Did your comment refer perhaps to my earlier comment where I did compare the 10% slope to the direct drop? If so the difference is the air resistance. As you correctly noted, without air resistance, all objects sliding down a bobsled track would slide at the same rate. It is only the air resistance that makes the difference.

#### Komodo

##### Well-known member
The scenario I was commenting on was not the direct drop. It was the flat ice (0% slope). In that case gravity does not provide any push at all. The only push comes from the person pushing it. Assuming the person can only push with a limited amount of force, he can get a small weight going faster than a large weight. If their were no friction (either from the ice or from air resistance), the smaller weight would continue going faster than then large weight after the pushing was over, and small weight would always win.

But when you add air resistance, the question becomes more complicated. Just try throwing a nerf ball and baseball from the pitcher's mound. Even if you could get the nerf ball going at 90 MPH, it would not continue at that speed for more than a couple of feet. It might not even make it to home plate. But the baseball will continue at almost 90 MPH all the way. Even if the nerf ball was the same size as the baseball and therefore had the same air resistance, that air resistance would have a bigger effect on the very small weight of the nerf ball.

Did your comment refer perhaps to my earlier comment where I did compare the 10% slope to the direct drop? If so the difference is the air resistance. As you correctly noted, without air resistance, all objects sliding down a bobsled track would slide at the same rate. It is only the air resistance that makes the difference.
No, I was referring to your statement that "There is also the force of gravity acting through a 8-11 % slope. In that case the heavier sled would receive the greater force" which might be "enough to make the heavier sled win." My point was that this greater gravitational force should not have any effect on the race, since it's exactly counterbalanced by the larger mass's greater resistance to acceleration. We're all familiar with the fact that this accounts for why (resistance aside) the heavier object falls at the same acceleration as the lighter one in a direct drop, despite the greater gravitational force, so I'm wondering why the heavier sled would be accelerated more than the lighter sled on a slope, because of the greater gravitational force.

Air resistance (if I remember correctly) is dependent on the surface area, not on weight, so the weight shouldn't be a factor. Aren't sleds all essentially identical in shape and thus in ability to get through air resistance?

#### LifeIn

##### Well-known member
No, I was referring to your statement that "There is also the force of gravity acting through a 8-11 % slope. In that case the heavier sled would receive the greater force" which might be "enough to make the heavier sled win." My point was that this greater gravitational force should not have any effect on the race, since it's exactly counterbalanced by the larger mass's greater resistance to acceleration. We're all familiar with the fact that this accounts for why (resistance aside) the heavier object falls at the same acceleration as the lighter one in a direct drop, despite the greater gravitational force, so I'm wondering why the heavier sled would be accelerated more than the lighter sled on a slope, because of the greater gravitational force.

Air resistance (if I remember correctly) is dependent on the surface area, not on weight, so the weight shouldn't be a factor. Aren't sleds all essentially identical in shape and thus in ability to get through air resistance?
Yes, the force of air resistance is the same on a light sled as on a heavy sled. But that force represents a larger fraction of the force due to gravity in the case of the light sled. The force of air resistance cancels some of the force of gravity. The total acceleration is dependent on the ratio between the force and the mass. As long as air resistance was assumed to be zero, force and mass were proportional. But when a constant air resistance is added, acceleration is affect more in the light sled. To see this in formulas:

Let f1 and f2 be the force of gravity acting on the light sled of mass m1 and the heavy sled of mass m2, respectively. Then we have the acceleration in a vacuum given by

a1 = f1/m1 = f2/m2 = a2

That is, both sleds will accelerate at the same rate in a vacuum. Now subtract from f1 and f2 a constant force, r, due to air resistance. The accelerations are now:

a1 = (f1-r)/m1
a2 = (f2-r)/m2

It is not hard to see that if f1/m1 = f2/m2, and if m1<m2, that a1<a2

#### 4tune8chance

##### Member
We all know that (barring wind resistance) objects fall at the same speed, regardless of their weight.

So why is putting extra weight in things like bobsleds illegal? Adding weight to them won't make gravity pull them any faster.
My two cents. All things being equal (speed, friction, cross sectional area etc) the mass of the object will make a difference to the terminal velocity! I used to work on bombing computers and the equations used do calculate that a heavier bomb falls faster, as it is less affected by the medium it is passing through.
So the same would apply to sliding down an ice sheet.

I think where the conceptual problem lies is in how much the weight affects the different parameters. Extra mass will slow the initial acceleration, it will also affect friction, BUT BY HOW MUCH? I suspect the disadvantages are outweighed by the increase in momentum that has built up allowing it to "punch through" the frictions, and thus able to maintain speed that friction would rob from the lighter sled.

#### LifeIn

##### Well-known member
I think where the conceptual problem lies is in how much the weight affects the different parameters. Extra mass will slow the initial acceleration, it will also affect friction, BUT BY HOW MUCH?
Exactly. If the bobsled course were only 20 meters long, I suspect the lighter sled would win every time, since it is easier to accelerate it up to speed by the initial human pushing. But as the course gets longer, the effect of gravity and wind resistance becomes more significant than the initial push. That would favor the heavier sled.

#### Komodo

##### Well-known member
Yes, the force of air resistance is the same on a light sled as on a heavy sled. But that force represents a larger fraction of the force due to gravity in the case of the light sled. The force of air resistance cancels some of the force of gravity. The total acceleration is dependent on the ratio between the force and the mass. As long as air resistance was assumed to be zero, force and mass were proportional. But when a constant air resistance is added, acceleration is affect more in the light sled. To see this in formulas:

Let f1 and f2 be the force of gravity acting on the light sled of mass m1 and the heavy sled of mass m2, respectively. Then we have the acceleration in a vacuum given by

a1 = f1/m1 = f2/m2 = a2

That is, both sleds will accelerate at the same rate in a vacuum. Now subtract from f1 and f2 a constant force, r, due to air resistance. The accelerations are now:

a1 = (f1-r)/m1
a2 = (f2-r)/m2

It is not hard to see that if f1/m1 = f2/m2, and if m1<m2, that a1<a2
Got it. But when we try to account for the effect of air resistance, do we do so by subtracting r from f or by subtracting r from a? Why is the equation, a=(f-r)/m, rather than a=(f/m)-r?

Suppose, for example, the force wasn't constant, as with gravity, but just an initial push (as with two sleds on a flat surface). The air resistance wouldn't affect the force, then, but it would affect the acceleration. (To maybe make the point clearer, let's say the sleds got the initial push, then went through a vacuum, then encountered air resistance.) Would it still make sense to subtract r from f?

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