Physics question

[ybbor]

This isn't for homework or anything, I was just wondering about it the other day.

a)two separate objects will fall to earth at the same speed. (assuming no air resistance) so drop a full water bottle and an empty water bottle from the same height and they will hit at the same time.

b) the heaviest part of an object will hit the ground first, even if not dropped that way. so an empty water bottle with a lead weight at the bottom will have the part with the weight hit the ground first.


so how can these two be reconciled? does anyone have a good [ideally concise] article on this? and does 'b' still occur in a vacuum?

 

[Babbler]

a)two separate objects will fall to earth at the same speed. (assuming no air resistance) so drop a full water bottle and an empty water bottle from the same height and they will hit at the same time.

They will fall with the same acceleration (if no air resistance), so object of different masses will land at the same time.

b) the heaviest part of an object will hit the ground first, even if not dropped that way. so an empty water bottle with a lead weight at the bottom will have the part with the weight hit the ground first.

I guess that is because the heavy part of the object will rotate to hit first.

 

[plarq]

I guess that is because the heavy part of the object will rotate to hit first.

If the bottle was placed with an angle, it will rotate.

 

[Fetus4188]

B doesn't occur in a vacuum and A only occurs in the vacuum.

 

[Shaihulud]

The proper answer is "center of gravity". When the COG is at the base, there is a bias for the bottle to tilt so that the point closest to the COG hits the ground first.

 

[Zwelgje]

I think tilting of objects in a fall is caused by air resistance so in your hypothetical situation the heaviest part won't hit the ground first. (like Fetus said... that guy is smart man, you have no idea. )

 

[ybbor]

They will fall with the same acceleration (if no air resistance), so object of different masses will land at the same time.


I guess that is because the heavy part of the object will rotate to hit first.

If the bottle was placed with an angle, it will rotate.

The proper answer is "center of gravity". When the COG is at the base, there is a bias for the bottle to tilt so that the point closest to the COG hits the ground first.

well I knew all that that's what the OP states

@Zwelgje; Fetus4188:

okay, that answers my question. could you point me to a good article expalining why an object rotates the way it does, or summarize it yourself?

 

[sanabas]

well I knew all that that's what the OP states

@Zwelgje; Fetus4188:

okay, that answers my question. could you point me to a good article expalining why an object rotates the way it does, or summarize it yourself?

The really basic answer is because that's the most stable position for it. The almost as simple answer is that if you do have air resistance, mass does matter. The higher the speed, the higher the air resistance, so the more mass matters. The heavier part will drop slightly faster, hence the rotation so that the heavier part is the lowest.

 

[Perfection]

Man is a visual beast! Let's give Ybbor a picture!

Okay, let's do a simple example illustrating why the center of mass is often the lowest point

let's say we drop a sphere with a smaller weight inside:

In a vacuum gravity pulls on it the same all over.

In an atmophere part of the gravity on the outside is counteracted by air resistance. So there is less net pull on the outside then the weight (which is unnaffected), so it falls faster until it reaches as far as it can go (the weight at the bottom) and than falls with the rest of the weights.

This is a gross oversimplification, but it should give you a general idea.

 

[Tenochtitlan]

If you assume both bottles are perfectly spherical, the full bottle will hit the ground first. That's because the force of gravity between the earth and the full bottle will be slightly higher than that of the empty one. The difference however, will be so small and immeasurable.

 

[Babbler]

I stand corrected.

 

[sanabas]

If you assume both bottles are perfectly spherical, the full bottle will hit the ground first. That's because the force of gravity between the earth and the full bottle will be slightly higher than that of the empty one. The difference however, will be so small and immeasurable.

That's sort of misleading, and easy to misunderstand. The force from gravity will be much, much higher for the full bottle. Force = mass * acceleration. Acceleration is the same for both bottles, ~9.8m/s. Mass for a full bottle of water is many times that for an empty bottle, so force is also that many times greater. At the same velocity, force from air resistance is the same on both bottles. The total force on the bottles is force from gravity minus force from air resistance. Because the gravitational force on a full bottle is much larger, the air resistance force is a much smaller percentage. The acceleration on the bottle is total force/mass. So the full bottle falls faster, because air resistance slows it down slightly less, rather than because force from gravity is slightly more.

If it makes it easier, rewrite the equation to say that Acceleration (bottle) = Acceleration (gravity) minus (air resistance)/(mass). Air resistance/mass is more for the empty bottle, as mass is less. Therefore the empty bottle falls slower when air resistance matters.

And if actual numbers make it easier: Assume acceleration from gravity is 10m/s. Assume mass of the empty bottle is 1kg. Assume mass of the full bottle is 10kg. Assume force from air restance is 1 N.

So for the full bottle, force from gravity is 100N, total force is 99N, so acceleration is 9.9 m/s.

For the empty bottle, force from gravity is 10N, total force is 9N, so acceleration is 9m/s.

So the heavy bottle falls faster.

 

[ybbor]

okay, so since in an atmosphere with air resistance, the 'air molecules' hitting the empty part of the bottle will have to overcome less force than the part of the bottle with a weight, due to more force, the air resistance will push up on the empty part more. is this summary correct?

 

[Leifmk]

That's sort of misleading, and easy to misunderstand. The force from gravity will be much, much higher for the full bottle.

I think what he's actually alluding to is the bottle's gravitational pull on the Earth. Which, though negligible, is indeed higher for the heavier bottle.

 

[sanabas]

I think what he's actually alluding to is the bottle's gravitational pull on the Earth. Which, though negligible, is indeed higher for the heavier bottle.

Fair enough. Though if the full bottle is 10 times heavier, the full bottle's gravitational pull on earth is still 10 times as much as the empty's.

okay, so since in an atmosphere with air resistance, the 'air molecules' hitting the empty part of the bottle will have to overcome less force than the part of the bottle with a weight, due to more force, the air resistance will push up on the empty part more. is this summary correct?

Sounds close enough for science, and a reasonable way to visualise it. Although it's not that the air molecules are pushing with more force on the empty bottle, they're pushing with the same force against a lower mass, so they affect acceleration more.

If you throw a tennis ball and a bowling ball with the same motion, the tennis ball doesn't go further because you've applied more force. You apply the same force both times, the tennis ball goes further because the same force results in more acceleration for the lighter object.

 

[Mise]

Right, lets make this perfectly clear.

The object WILL NOT ROTATE if there is no air resistance.

Even if you drop it with an angle, it will not rotate. Why the hell should it??

If you drop it with an initial angular rotation, the rotation will persist, and the mass of the object will NOT affect which part of the object hits the ground first.

This:
"b) the heaviest part of an object will hit the ground first, even if not dropped that way. so an empty water bottle with a lead weight at the bottom will have the part with the weight hit the ground first."
Is NOT true.

Air resistance is so rediculously negligable that unless you're jumping off an aeroplane with a parachute it will make zero difference to any calculation you do on two ends of the same body.

 

[ybbor]

"b) the heaviest part of an object will hit the ground first, even if not dropped that way. so an empty water bottle with a lead weight at the bottom will have the part with the weight hit the ground first."
Is NOT true.

Air resistance is so rediculously negligable that unless you're jumping off an aeroplane with a parachute it will make zero difference to any calculation you do on two ends of the same body.

actually, no. I'm assuming we're talk about the plaent earth here; but tape a wieght to a pencil (make sure it's heavy enoughm; a battery should work well). turn it so it's parralel to the groud. now stand on a chair and drop it. the side with the battery will hit the groud first. this is why when you drop a piece of penut butter toast from high enough, your penut butter is promptly covered with carpet hairs.

 

[oagersnap]

this is why when you drop a piece of penut butter toast from high enough, your penut butter is promptly covered with carpet hairs.

But if you drop the toast from twice the height, it will rotate 360 degrees and land with the peanut butter side up.

 

[ionimplant]

actually, no. I'm assuming we're talk about the plaent earth here; but tape a wieght to a pencil (make sure it's heavy enoughm; a battery should work well). turn it so it's parralel to the groud. now stand on a chair and drop it. the side with the battery will hit the groud first. this is why when you drop a piece of penut butter toast from high enough, your penut butter is promptly covered with carpet hairs.

try doing this in vacuum and do you think it still happens that way?
(i actually am not very sure about this. but air does make a lot of difference. put a feather in vacuum and it falls so fast...)

 

[nonconformist]

Won't the mass rotate until its centre of mass is central to the object?