science buff question: two balls of equal volume and different density...

[MrDudeMan]

fall from an equal point above the earths surface. if ball 1 is 100000x heavier than ball 2, does ball 1 fall faster?



edit:

thanks to dullard, here is a link to NASA's thought on the matter...

Text



==============

proof using math from about 40 posts down

F=ma, a=32ft/sec, m= whatever the mass of the object is. The acceleration is always the same IF you ignore air resistance.

If you don't ignore air resistance, then the shape of the object has to be taken into account. The shapes were given as 2 spheres of equal volume. So the shape is out as far as affecting the rate at which they will fall.

All that's left is the mass of each object being different.

Since the force on the objects can be shown as F=ma without air, with air resistance it would be F=ma-r (r stands for resistance (air resistance but I can't write ar or you'll think it's acceleration times r, which it's not)

F=ma-r, a =g, the constant for gravity

so therefore F=mg-r, and mg-r=ma
solve for a, you get a= g-r/m (divided both sides by m)
this gives us what the acceleration will be with wind resistance.

as you can see, if the mass is large, r/m becomes small and wind resistance won't affect it much. but if m is small, the 2nd term r/m starts to become significant. This will "subtract" more from the acceleration. get it?

==============



the last part makes perfect sense if you read it carefully...

everyone down below is right...this will be debated to no end like the other thread where people tried to say .99999 doesnt = 1 (which it does...if you dont think so, refer to basic calculus and stfu)

 

[simms]

They will have different mass. Mass is proportional to wind resistance, so yes, 1 will fall faster.

Unit check: Volume = cm3 ... Density is measured in g/cm3. multiply to get mass.

logically, a ball of feathers will have a volume of say 10cm3, pick a number in the air and say density is 1g/cm3. multiply, get mass of 10g.

a ball of lead has the same volume of 10cm3, density is 10000x that, so it's 100kg/cm3. multiply, get mass of 1000kg (no calculator, but you see my point)

logically a heavier mass will have less wind resistance, so lead will go down first.

if you had said a pound of feathers and a pound of lead, it would be the same (mass:mass). but volume:volume does not mean they will fall equally.

 

[BurnItDwn]

In a vacuum they would fall the same speed.
However, you did specify Earth, and since the atmosphere on earth is not a vacuum there will be air resistance and wind. Ball 1 will fall faster.

 

[hdeck]

burnitdwn has it right.

 

[MrDudeMan]

Originally posted by: BurnItDwn
In a vacuum they would fall the same speed.
However, you did specify Earth, and since the atmosphere on earth is not a vacuum there will be air resistance and wind. Ball 1 will fall faster.

thats what i thought...thanks for clearing that up

 

[glen]

Originally posted by: simms
They will have different mass. Mass is proportional to wind resistance, so yes, 1 will fall faster.

Unit check: Volume = cm3 ... Density is measured in g/cm3. multiply to get mass.

logically, a ball of feathers will have a volume of say 10cm3, pick a number in the air and say density is 1g/cm3. multiply, get mass of 10g.

a ball of lead has the same volume of 10cm3, density is 10000x that, so it's 100kg/cm3. multiply, get mass of 1000kg (no calculator, but you see my point)

logically a heavier mass will have less wind resistance, so lead will go down first.

if you had said a pound of feathers and a pound of lead, it would be the same (mass:mass). but volume:volume does not mean they will fall equally.

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

 

[Daishiki]

darn, be me to it

 

[MrDudeMan]

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

 

[hdeck]

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

grab a book and a pencil. outstretch your arms. drop them both to the floor. they hit at the same time.

 

[simms]

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

I'm a chemist, not a physicist. Yes it was sloppy, but I figured he needed an answer fast.

The mass is a factor in wind resistance when the shape of the object are the same. All things being the same, mass is the only difference, so that property indirectly makes it fall faster.

Can I still get part marks?

 

[MrDudeMan]

Originally posted by: hdeck

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

grab a book and a pencil. outstretch your arms. drop them both to the floor. they hit at the same time.

i dont know how it works for different objects...but i specifically stated very strict conditions. maybe it is wrong after all, but i cant figure out how it could be. reread my initial question.

 

[glen]

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

You specified they have equal volume.
We can reasonably assume that they have equal shape.
Therefore, they have equal wind resistance.

 

[jagec]

Originally posted by: simms

logically a heavier mass will have less wind resistance, so lead will go down first.

if you had said a pound of feathers and a pound of lead, it would be the same (mass:mass). but volume:volume does not mean they will fall equally.

um?

So you honestly think that if I dumped a pound of feathers and a pound of lead out the window, they would fall at the same rate? Not, say, the feathers float down and the lead plummet?

Sorry, you got it backwards...Newtonian physics dictates that if they are both the same size (and since they are assumed to be perfect spheres of the same volume, they fulfill this), they'll fall at the same rate.

Remember Galileo's experiment with a wooden and iron cannonball? http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm

Obviously if one ball is VERY light minor gusts of wind will mess it up. If the difference in weight is ENORMOUS, other factors come into play, but they will still fall at close to the same rate.

 

[glen]

Originally posted by: simms

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

I'm a chemist, not a physicist. Yes it was sloppy, but I figured he needed an answer fast.

The mass is a factor in wind resistance when the shape of the object are the same. All things being the same, mass is the only difference, so that property indirectly makes it fall faster.

Can I still get part marks?

The wind resistance is the same.
The Force UP (wind resistance) is therefore the same.
The Force DOWN is different.

 

[MrDudeMan]

Originally posted by: glen

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

You specified they have equal volume.
We can reasonably assume that they have equal shape.
Therefore, they have equal wind resistance.

so what is your answer to my question then? im not trying to argue...i want to know the real answer.

 

[simms]

Originally posted by: hdeck

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

grab a book and a pencil. outstretch your arms. drop them both to the floor. they hit at the same time.

Take a bowling ball. take a feather, and crumple into a ball. drop them both to the floor.

I'm such a devil's advocate.. :evil:

Honestly, I don't know. I'm here to learn too

 

[MrDudeMan]

Originally posted by: jagec

Originally posted by: simms

logically a heavier mass will have less wind resistance, so lead will go down first.

if you had said a pound of feathers and a pound of lead, it would be the same (mass:mass). but volume:volume does not mean they will fall equally.

um?

So you honestly think that if I dumped a pound of feathers and a pound of lead out the window, they would fall at the same rate? Not, say, the feathers float down and the lead plummet?

Sorry, you got it backwards...Newtonian physics dictates that if they are both the same size (and since they are assumed to be perfect spheres of the same volume, they fulfill this), they'll fall at the same rate.

Remember Galileo's experiment with a wooden and iron cannonball? http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm

Obviously if one ball is VERY light minor gusts of wind will mess it up. If the difference in weight is ENORMOUS, other factors come into play, but they will still fall at close to the same rate.

close to does not equal exactly...read my question and state your answer based on my strict and clearly defined circumstances.

 

[glen]

Originally posted by: MrDudeMan

Originally posted by: glen

Originally posted by: MrDudeMan

Originally posted by: glen

In the nicest, non flaming way, I want to tell you that you totally got just about every bit of physics involved wrong or really sloppy.

Mass is not proportional to wind resistance.

he is right though that ball 1 would fall faster because it weighs more. im not sure about that wind resistance thing, however.

You specified they have equal volume.
We can reasonably assume that they have equal shape.
Therefore, they have equal wind resistance.

so what is your answer to my question then? im not trying to argue...i want to know the real answer.

The denser object falls faster in air, but the same in a vaccum.
But, physics is so difficult sometimes even phd professors make mistakes in simple problems.

 

[RaynorWolfcastle]

edit 3: see my post below for the calculations, it turns out that the accelerations (and thus the velocities) are not equal.


I'm no expert on the subject, but I believe that wind resistance is exclusively a function of shape and speed. IIRC, we used to get a rough estimate for the frictional forces using v^2.
With that in mind weight makes almost zero difference for an object falling towards Earth.

Newton's law states that Fg = G*M*m/r^2
It turns out (obviously) that r, the radius of the Earth is much much larger than the distance most objects drop and we can approximate r as being a constant. Thus we can group G*M/r^2 for all objects and call that a_grav. As you can see now, neither air friction nor the falling acceleration are dependant on mass. As such, two objects of same shape falling from a same height will fall at the same speed, regardless of their mass. I hope that clears things up a bit

glen, correct me if I went wrong anywhere in that description.

edit 2: glenn points out that buoyancy causes another force acting on the objects and the lighter object would be more buoyant than the heavy one, that makes sense. I'm not too familiar with buoyancy however, so I'm not too sure how to properly calculate it's effect on the whole situation.

 

[MacBaine]

This thread should have been like 2-3 posts long at most... what have you done

 

[glen]

Think about dropping a medicine ball and volleyball of the same size into a swimming pool.
If it were empty, they would fall at the same apparent speed, and in a vacuum exactly the same speed.
Now, fill the pool up with water.
You now have a buoyancy problem as well pushing the ball up.
If they are the same size, the buoyancy is the same.
but, in the volley ball, the force down is less than the buoyant force up, so the ball floats.

 

[RaynorWolfcastle]

Originally posted by: glen
Think about dropping a medicine ball and volleyball of the same size into a swimming pool.
If it were empty, they would fall at the same apparent speed, and in a vacuum exactly the same speed.
Now, fill the pool up with water.
You now have a buoyancy problem as well pushing the ball up.
If they are the same size, the buoyancy is the same.
but, in the volley ball, the force down is less than the buoyant force up, so the ball floats.

Hmmm... I'll have to edit my post, we always used air friction on the horizontal plane so buoyancy wasn't an issue, I can see how it might affect objects falling on the vertical though.

 

[glen]

Originally posted by: MacBaine
This thread should have been like 2-3 posts long at most... what have you done

wind resistance
change in the force of gravity as the oject moves closer to earth
is the object spining?
buoyancy

 

[jagec]

Originally posted by: MrDudeMan

Originally posted by: jagec
Obviously if one ball is VERY light minor gusts of wind will mess it up. If the difference in weight is ENORMOUS, other factors come into play, but they will still fall at close to the same rate.

close to does not equal exactly...read my question and state your answer based on my strict and clearly defined circumstances.

Fine, it comes down to

We Can't Know, because there are too many factors. The heavier ball would be less affected by wind gusts, but all that tells you is that on a hot day the heavy ball would fall faster, on a cold day the light ball would fall faster.

 

[fredtam]

They will hit at the same time given that they are the same shape and size to rule out wind resistance.

End of thread