A question of physics

[The Bellman]

Sorry to bore you, but this question has nothing to do with creation or evolution - it's purely about science. I'm posting it here because this at least used to be a science forum, and I know there'll be several here who can answer it.

Two bodies of unequal mass fall at exactly the same rate (ignoring wind resistance). Virtually everyone knows this. In a vacuum, a cannon ball and a feather fall at the same speed.

But...imagine this. Two cannon balls, exactly the same size (so the same amount of wind resistance). One is hollow, so it weighs 1/5 the amount the other one weighs. Drop them both from a height. They hit the ground at precisely the same time. Or do they? Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth? Obviously, the difference would be imperceptible (if it's true) - so it's purely a theoretical question, something I've wondered about for a while. Bodies fall toward the earth based on the earth's gravitational attraction...but doesn't the bodies' gravitational attraction (infinitesmal though it is in comparison to that of the earth) play a part, too, making heavier objects fall very slightly faster?

 

[Jet Black]

Sorry to bore you, but this question has nothing to do with creation or evolution - it's purely about science. I'm posting it here because this at least used to be a science forum, and I know there'll be several here who can answer it.

Two bodies of unequal mass fall at exactly the same rate (ignoring wind resistance). Virtually everyone knows this. In a vacuum, a cannon ball and a feather fall at the same speed.

But...imagine this. Two cannon balls, exactly the same size (so the same amount of wind resistance). One is hollow, so it weighs 1/5 the amount the other one weighs. Drop them both from a height. They hit the ground at precisely the same time. Or do they? Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth? Obviously, the difference would be imperceptible (if it's true) - so it's purely a theoretical question, something I've wondered about for a while. Bodies fall toward the earth based on the earth's gravitational attraction...but doesn't the bodies' gravitational attraction (infinitesmal though it is in comparison to that of the earth) play a part, too, making heavier objects fall very slightly faster?

yes you are right. the ball with the higher mass would fall more quickly. this is pretty obvious if we take it to extremes i.e. if the ball were the mass of jupiter, then it would fall very quickly indeed (actually the earth would fall towards the ball, but that is a side issue, because the earth falls towards the other ball too, but less.)

 

[Logic]

Fg=G(m1*m2)/r[SUP]2[/sup]

G~6.67*10[SUP]-11[/sup] Nm[SUP]2[/sup]/Kg[SUP]2[/SUP]
m1=mass of one of the objects in consideration.
m2=mass of the other object in consideration.
r=distance between the two objects.

So, yes, if one of the object's masses is greater, the force of gravity between the two objects will be greater.

***edit***

ME~5.97*10[SUP]24[/SUP]Kg

The mass of the other object, on the earth, whether it be a marble or an ocean freighter is negligible. The force of gravity between the objects will change by such a small fraction of a Newton, that unless you need very precise measurements, will produce no observable effect.

 

[Aeschylus]

Yes ther are two forces (every action must have an equal and opposite reaction) If we look at it from the (accelerated frame of refernce of the) Earth:

so F = GMm/r^2

so a = G(M + m)/r^2

So when m is small compared to M, we can ignore it.

 

[Chi_Cygni]

Just a word of advice.

Think about accelerations not forces in problems such as this. Thinking about force is what often leads people to conclude wrong answers.

Remember, your acceleration is independent of your mass, as long as you assume the equivalence principle.

 

[JohnR7]

Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth?

When we were kids, my sister and I use to ride skate boards. I weighed more than my sister and when we were going down a hill my skate board would always go faster. So fast it was kinda scary, but my sister did not have any problem at all, because her board did not go as fast.

That was back when we use to take the wheels off of rollar skates and put them on a board, back before they had factory made skate boards.

 

[ForeRunner]

You went faster for a completetly different reason.

By weighing more you have more energy while up on a hill than your sister. When you both release your energy by going down the hill you have more to overcome the resistance of air and friction. Without air resistance or friction you would go (perceptably) the same speed.

 

[Aeschylus]

So far we've assumed two point masses, but even in this highly idealized situation we're not even getting the exact (Newtonian) answer as the force bewteen the two objects is also dependt on r, not just the mass of the two objects. So even for two isolated point masses being accelarted by gravity radially towards each other, to find the precise time as given by Newtonian physics, you're going to need a differential equation.

Air resistance is mainly dependent on surface area (and velocity) so for two objects of the same shape and different masses, the heavier object will fall faster as the force exerted by air resistance is the same on both.

 

[Norseman]

Sorry to bore you, but this question has nothing to do with creation or evolution - it's purely about science. I'm posting it here because this at least used to be a science forum, and I know there'll be several here who can answer it.

Two bodies of unequal mass fall at exactly the same rate (ignoring wind resistance). Virtually everyone knows this. In a vacuum, a cannon ball and a feather fall at the same speed.

But...imagine this. Two cannon balls, exactly the same size (so the same amount of wind resistance). One is hollow, so it weighs 1/5 the amount the other one weighs. Drop them both from a height. They hit the ground at precisely the same time. Or do they? Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth? Obviously, the difference would be imperceptible (if it's true) - so it's purely a theoretical question, something I've wondered about for a while. Bodies fall toward the earth based on the earth's gravitational attraction...but doesn't the bodies' gravitational attraction (infinitesmal though it is in comparison to that of the earth) play a part, too, making heavier objects fall very slightly faster?

Another thing to consider would be how close the balls are to the equator. As you get closer to the equator the centrifugal force goes up, and the ball would drop slower because the net force would be lower.

 

[Mistermystery]

Sorry to bore you, but this question has nothing to do with creation or evolution - it's purely about science. I'm posting it here because this at least used to be a science forum, and I know there'll be several here who can answer it.

Two bodies of unequal mass fall at exactly the same rate (ignoring wind resistance). Virtually everyone knows this. In a vacuum, a cannon ball and a feather fall at the same speed.

But...imagine this. Two cannon balls, exactly the same size (so the same amount of wind resistance). One is hollow, so it weighs 1/5 the amount the other one weighs. Drop them both from a height. They hit the ground at precisely the same time. Or do they? Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth? Obviously, the difference would be imperceptible (if it's true) - so it's purely a theoretical question, something I've wondered about for a while. Bodies fall toward the earth based on the earth's gravitational attraction...but doesn't the bodies' gravitational attraction (infinitesmal though it is in comparison to that of the earth) play a part, too, making heavier objects fall very slightly faster?

When I was still in school and we came to the topic about wind resistance we did a couple of tests with these things... like a feather and a ball in avaccuum... etc.. But when 2 objects are of an equal shape but diffrent in mass it hits the earth at the exact same time under exact the same coinditions.

You can try this out by useing an empty cokebottle and a full one and let them fall to the ground.. I think that they will hit at the exact same moment if all forces on them are exactly equal. I hope this awnsers your question...

 

[Ampoliros]

Ah, I see what you're getting at - that the ball exerts a force on the earth, pulling it toward the ball - so the mass of the ball would infact change the acceleration.

For something taking place on the outer part of the earth and all, you'd need a pretty large mass to start getting something that might even be measurable.

 

[The Bellman]

When I was still in school and we came to the topic about wind resistance we did a couple of tests with these things... like a feather and a ball in avaccuum... etc.. But when 2 objects are of an equal shape but diffrent in mass it hits the earth at the exact same time under exact the same coinditions.

You can try this out by useing an empty cokebottle and a full one and let them fall to the ground.. I think that they will hit at the exact same moment if all forces on them are exactly equal. I hope this awnsers your question...

But according to what others have said (and what I thought) this is wrong. They won't hit the earth at exactly the same time. The heavier will hit first (although the difference in time will be imperceptible).

 

[Mekkala]

Sorry to bore you, but this question has nothing to do with creation or evolution - it's purely about science. I'm posting it here because this at least used to be a science forum, and I know there'll be several here who can answer it.

Two bodies of unequal mass fall at exactly the same rate (ignoring wind resistance). Virtually everyone knows this. In a vacuum, a cannon ball and a feather fall at the same speed.

But...imagine this. Two cannon balls, exactly the same size (so the same amount of wind resistance). One is hollow, so it weighs 1/5 the amount the other one weighs. Drop them both from a height. They hit the ground at precisely the same time. Or do they? Does not the heavier one fall faster because its greater mass exerts a greater gravitational pull on the earth? Obviously, the difference would be imperceptible (if it's true) - so it's purely a theoretical question, something I've wondered about for a while. Bodies fall toward the earth based on the earth's gravitational attraction...but doesn't the bodies' gravitational attraction (infinitesmal though it is in comparison to that of the earth) play a part, too, making heavier objects fall very slightly faster?

EDIT: Doing some calculations. Be back shortly.

Ok. Yes, you guys are right. There would be a very slight difference in acceleration.

[Acc of m] = (M/m + 1)G/R^2

So, you can see that if m is very small, its acceleration will be very high. Conversely, if it is very large, the acceleration will be very low. However, when m is very small compared to M, relatively small differences in the size of m will not matter significantly.

FINAL EDIT: Actually, no. I was pretty sure that when we say that the acceleration is always the same no matter what, we don't mean it's almost the same, but when I solved for acceleration, I found that you guys were right about that -- if the formula I used was correct, which it wasn't. I forgot that the correct formula is G(Mm/r^2), in which case the masses cancel out when solving for acceleration.

And Aeschylus, I understand what you mean now. You're saying that if the two objects fall at the same time and in the same place, the acceleration of the Earth towards both objects will be the same -- whereas if you, say, dropped one object on one side of the Earth and one on the other side, the acceleration of the Earth towards each would be different, and they would not both land at the same time. Good point, that.

 

[Mistermystery]

But according to what others have said (and what I thought) this is wrong. They won't hit the earth at exactly the same time. The heavier will hit first (although the difference in time will be imperceptible).

I don't think so.. And I think this is a question that you can find out for yourself. You do have 2 coke bottles, right? fill one up with something heavy (like sand), and throw them both out of an elevated platform. Perhaps you can throw it from a really high building with someone else monitoring which bottle hits the ground first... If I recall my tests correctly they both hit the ground at the same time.

 

[Aeschylus]

But according to what others have said (and what I thought) this is wrong. They won't hit the earth at exactly the same time. The heavier will hit first (although the difference in time will be imperceptible).

Yep this is true:

a) due to the reaction force

b) due to the fact that air resiatnce means in general that heavier objects fall faster.

 

[Aeschylus]

*though of course if you drop them at exactly the same time both objects will have the advatnge of each other's reaction force.

 

[Mistermystery]

I don't think so.. And I think this is a question that you can find out for yourself. You do have 2 coke bottles, right? fill one up with something heavy (like sand), and throw them both out of an elevated platform. Perhaps you can throw it from a really high building with someone else monitoring which bottle hits the ground first... If I recall my tests correctly they both hit the ground at the same time.

I tried out the test with someone else taking pictures (they failed horribly btw) but I have not seen any evidence that one bottle hits the ground faster... allthough perhaps you should look at this one yourself...

 

[Mekkala]

*though of course if you drop them at exactly the same time both objects will have the advatnge of each other's reaction force.

Huh? What do you mean, "each other's reaction force"?

 

[Aeschylus]

For every action there must be an equal and opposite reaction.

The reaction force is the force that the object exerts on the Earth.

 

[Mekkala]

For every action there must be an equal and opposite reaction.

The reaction force is the force that the object exerts on the Earth.

I'm still confused as to what you mean. How will the objects benefit from each others' "reaction force"? I'm not sure you understand what Newton meant when he said that.