? 2 Cannon balls are dropped at the same time...

[travis575757]

So i have a question, 2 Cannon balls are dropped at the same time, they are both made of iron, BUT 1 is bigger (more mass and greater surface area) than the other, which one hits the ground first.

I have heard this and would think that the smaller one would hit the ground first because it encounters less air resistance. Would this be correct because i have been hearing that they would hit the ground at the same time because they are both facing the same acceleration due to gravity 9.81 m/s. But one is larger and would face more friction thus going slower right?

[Skyler4856]

The smaller one will hit the ground first, albeit by a marginal amount.

[travis575757]

Thanks i needed to make sure.

[Tex]

Of course, in a vacuum, they would fall at the same rate regardless of mass, size, and so forth. This actually can be proven by dropping a brick and a feather in a vacuum- they both fall at the same rate. SCIENCE.

[Whirligig Girl]

Of course, in a vacuum, they would fall at the same rate regardless of mass, size, and so forth. This actually can be proven by dropping a brick and a feather in a vacuum- they both fall at the same rate. SCIENCE.

In a vacuum, the large would hit first because it's bigger and the edge would touch the floor first. If instead they were both the same size but different masses, they would hit the ground at the same time as well.

[K^2]

In air, larger one will fall a little bit faster. It has larger area, but also more mass. Area increases as square of the size, but mass is going to increase as a cube. So a weight-to-drag ratio is higher for larger cannonball, giving it faster fall speed.

[RogueMason]

This is a subject that took me a little while to get my head around a few years back, but I'll try to explain it.

In air, 2 objects with 2 different masses will have their own terminal velocities resulting from air resistance. The more massive object will not reach terminal velocity before the less massive object and so will continue to accelerate towards the Earth 's centre of gravity until it too reaches terminal velocity; therefore, the more massive object will hit the ground first.

This I could accept; it made sense. A vacuum used to be more confusing but it's actually easy to understand if you think about it. Let's take those two different masses from the atmosphere and stick them a hundred metres above the Moon. Both will fall at exactly the same rate due to the negligible atmosphere at the Lunar surface and the equal gravitational pull on each object. The way I visualise this is a bit unusual but helpful. Consider the effect of gravity on all of the individual atoms of each mass; each atom is identical and merely clustered together with others of their kind, all of them being equally affected by the gravitational field, so a larger cluster of these atoms won't fall at a greater rate than a smaller cluster. This is a bit of an odd explanation and I'm sure someone else has something better, but it's the way I can understand it; even two masses composed of different elements (say... lithium and osmium) would fall at the same rate despite their differing densities.

You can test the vacuum portion in KSP (aerodynamic model of the game is questionable); probably the best contrast would be a small fuel tank compared to a jumbo tank (I'll leave the logistics to you ) descending to the surface of Mun. You'll see both fall at the same rate.

Hope this helped

[Nibb31]

Replace one of the iron balls with a feather and you will get your answer.

[Skyrunner27]

Already experimented.

[Mr. Entropy]

In vacuum, the two balls would fall at the same rate. This was experimentally proven by Apollo 15, where a hammer and feather were dropped on the surface of the moon. An atmosphere tends to throw a wrench in the system.

But this is science, you can experiment and find out for yourself. I imagine water balloons would be easier to acquire than cannonballs and yield similar results. We can talk theory all we want here, but let's get some real data to work with.

Edited February 21, 2014 by Mr. Entropy

[lodestar]

But this is science, you can experiment and find out for yourself.

Yep... unfortunately, over the years there are a bunch of anomalous results: elongated objects were observed to fall slightly faster than compact objects, even in a vacuum; objects with the same mass but made from metals with different atomic weights were observed to fall at different rates; objects falling over a mass of water were observed to fall faster; etc. Sure, in most cases the results couldn't be replicated and assumed to be an error after that, but there's still a few unexplained weird cases left. Eventually, they pile up enough that people start talking about a fifth force again, but then the weirder cases are explained (like the Pioneer anomaly), and the issue cools down again.

[Sillychris]

Air drag is proportional to cross sectional area which is proportional to r^2

Gravitational force is proportional to mass which is proportional to volume which is proportional to r^3

r^3 goes up faster than r^2 with increasing r, thus gravitational force goes up faster than drag force in your scenario.

Yes, the larger ball would fall faster.

[rpayne88]

In pure mechanical (I guess that is the right word) physics, ALWAYS ignore factors such as air resistance. That falls under aerodynamics, not physics.

[Capt. Hunt]

now, one way we could properly demonstrate this on Earth, would be to drop two cannon balls that were the same size but different weights, say one's made of iron and the other Uranium. You would see that they would still fall at the same rate.

I would not want to be the person holding the Uranium cannonball though.

[Sillychris]

Uranium cannonball would fall quicker in an atmosphere. Greater density=greater acceleration with drag present. If not convinced in the case of a uranium and iron cannonball, throw a nerf ball into the experiment and see if you are convinced then.

[falofonos]

So if I took 1kg of iron and placed it an a magical sphere of zero mass and 2kg of feathers and compacted them into an identical magical sphere and dropped them in atmosphere, the feathers would land first?

I don't think so.

[N_las]

So if I took 1kg of iron and placed it an a magical sphere of zero mass and 2kg of feathers and compacted them into an identical magical sphere and dropped them in atmosphere, the feathers would land first?

I don't think so.

But it would be the case. If one wouldn't consider air resitance, they would fall with the same accelaration, because only gravity works on the objects, and so the masses cancel.

m*a = m*g

a = g

The mass doesn't play in. But with air resistance:

m*a = m*g - F_AirResistance

a = g - F_AirResistance / m

Since the air resistance is independent of mass, the mass of the object doesn't cancel from the equation. So Objects with greater mass fall faster in Atmosphere.

[LordOfTheOrbits]

now, one way we could properly demonstrate this on Earth, would be to drop two cannon balls that were the same size but different weights, say one's made of iron and the other Uranium. You would see that they would still fall at the same rate.

I would not want to be the person holding the Uranium cannonball though.

Wrong. The kinetic energy of an object is speed times mass. Air resistance only cancels out the same amount of kinetic energy from both cannon balls and because the iron ball has a larger mass and therefore more kinetic energy, it will lose the same amount of energy, but less speed.

[K^2]

Wrong. The kinetic energy of an object is speed times mass. Air resistance only cancels out the same amount of kinetic energy from both cannon balls and because the iron ball has a larger mass and therefore more kinetic energy, it will lose the same amount of energy, but less speed.

Energy is not the best way to think about this. This isn't strictly wrong, but the object that falls faster is going to experience greater resistance, and therefore, have more work done by it by drag than the slower object. So energy loss to drag is not equal. Because energy and drag are both monotonic functions of velocity, and in fact, both are roughly quadratic, the object with more mass still ends up traveling faster despite losing more energy, and so you're not wrong, but it's needlessly complicated.

It's much easier to just look at accelerations. Given equal sizes and shapes, heavier object experiences higher acceleration, and so ends up falling faster.

[Tex]

In a vacuum, the large would hit first because it's bigger and the edge would touch the floor first.

Whoops, sorry. I'm assuming the cannon balls were dropped from the same height or were the same size but had differing masses. In any case, they would fall at the same rate in a vacuum.

[DonLorenzo]

why not make three cannonballs, all the same size, but different mass

1. iron

2. osmium (even denser than uranium! yay!)

3. lighter-than-air foam

They all experience the same g, so they should all hit the ground first right? Who still isn't convinced that that is in fact NOT the case?

[Red Iron Crown]

Wrong. The kinetic energy of an object is speed times mass.

Wrong. Kinetic energy is 1/2 mass times speed squared. You're thinking of momentum, which is related but not the same.

[falofonos]

why not make three cannonballs, all the same size, but different mass

1. iron

2. osmium (even denser than uranium! yay!)

3. lighter-than-air foam

They all experience the same g, so they should all hit the ground first right? Who still isn't convinced that that is in fact NOT the case?

Except the lighter than air foam ball would float....

[DonLorenzo]

Except the lighter than air foam ball would float....

no kidding!

[Sillychris]

So if I took 1kg of iron and placed it an a magical sphere of zero mass and 2kg of feathers and compacted them into an identical magical sphere and dropped them in atmosphere, the feathers would land first?

I don't think so.

I am not sure exactly what you mean by magical spheres, but I think what you mean is to take the 2kg of feathers and compact them until they occupied the same volume as 1 kg of iron. In your situation, the feather ball would have twice the density of the iron ball and would accelerate more quickly in an atmosphere.

Let's do some grade 11 physics: ΣF=ma. Your sum of forces are Gravity and air resistance. There are various methods of modelling air resistance, but the largest term is always proportional to cross sectional area. Stick a constant in front and we've got an equation of F(drag)=CA where C is the modelling constant and A is the cross sectional area. F(gravity), as established by Newton is quite easy near the surface of the Earth. F(grav)=mg where g is 9.8m/s^2

Ok, let's put together the equation of motion for these spheres in freefall. ΣF=F(Grav)+F(drag) and if we define down as positive then this becomes ΣF=|F(Grav)|-|F(drag)|=mg-CA=ma. Let's divide everything by m to make it easier to read: a=g-CA/m The cross sectional areas being equal, you can see quite plainly by inspection that a larger mass in the denominator in the second term makes CA/m smaller, and thus more of g is "left" to go towards the object's acceleration.

Note: The above argument is only valid for objects of identical shape and size with differing masses in the presence of an atmosphere.