# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EvaH on 15/09/2020 11:53:54

Title: What falls faster: heavy or light objects?
Post by: EvaH on 15/09/2020 11:53:54
Emily asks:

Why do heavy objects fall to the ground faster than light objects? If light objects are easier to pull, shouldn't gravity pull them down faster than heavy objects?

Can you help?
Title: Re: What falls faster: heavy or light objects?
Post by: Halc on 15/09/2020 12:15:00
Quote from: Emily
Why do heavy objects fall to the ground faster than light objects? If light objects are easier to pull, shouldn't gravity pull them down faster than heavy objects?
Gravity accelerates all objects at the same rate, so an object of twice the mass is pulled with twice the force, which is why massive things weigh more.  So in the absence of friction, all objects should fall at the same rate regardless of their mass or shape.

Friction changes that story, so a small pebble will fall faster than a person with a parachute, an example that shows that heavy objects don't necessarily fall to the ground faster than a light one. It's all a matter of ratio of gravitational force in one direction to the force of friction in the other.  At some speed (the terminal velocity), the two cancel out and further acceleration ceases.
Title: Re: What falls faster: heavy or light objects?
Post by: alancalverd on 15/09/2020 14:02:20
Galileo proposed a very simple reductio ad absurdam.

Suppose a big rock falls faster than a small one. Now tie them together. The small one slows down the big one. But the big one accelerates the small one.

Torricelli is credited with demonstrating that a pebble and a feather fall at the same rate in a vacuum, and the experiment has been replicated on the moon.
Title: Re: What falls faster: heavy or light objects?
Post by: Janus on 15/09/2020 16:24:52
Galileo proposed a very simple reductio ad absurdam.

Suppose a big rock falls faster than a small one. Now tie them together. The small one slows down the big one. But the big one accelerates the small one.

Torricelli is credited with demonstrating that a pebble and a feather fall at the same rate in a vacuum, and the experiment has been replicated on the moon.
And on a larger scale here:
Title: Re: What falls faster: heavy or light objects?
Post by: myuncle on 20/09/2020 01:21:13
To notice the difference in a vacuum, you would need to compare the fall of a feather versus something as big as Ariel or Umbriel. Am I right?
Title: Re: What falls faster: heavy or light objects?
Post by: Halc on 20/09/2020 01:48:22
Two different masses falling at the same rate assumes both objects are small in comparison to the object pulling them gravitationally.

Therefore a feather dropped from a stationary position 380,000 km above a moonless Earth would take significantly longer to fall to the surface than would the moon (from a stationary position). The difference is that the moon would have a significant effect on the Earth itself, pulling it over 4000 km upward as the moon falls, thus increasing the gravitational pull on the moon and shortening the distance it has to fall.
So if measured down to the femtosecond, the rock really does fall faster than the feather.
Title: Re: What falls faster: heavy or light objects?
Post by: evan_au on 20/09/2020 09:55:16
Quote from: Halc
So if measured down to the femtosecond, the rock really does fall faster than the feather.
Not if you dropped them together.

The mass of (rock+feather) would attract the Earth equally to rock and feather.
Title: Re: What falls faster: heavy or light objects?
Post by: alancalverd on 20/09/2020 10:42:48
And if you dropped them separately they would accelerate towards the barycenter of the (earth + object) system at the same rate. It's only because "practical " objects are so much smaller than the planet that we don't notice shifts in the barycenter as we move stuff around.
Title: Re: What falls faster: heavy or light objects?
Post by: Bored chemist on 20/09/2020 11:06:27
To notice the difference...
What difference?
Title: Re: What falls faster: heavy or light objects?
Post by: myuncle on 20/09/2020 11:22:26
To notice the difference...
What difference?

difference in speed. In a vacuum I suppose any heavier object falls faster than a light object, but we can't detect it.
Title: Re: What falls faster: heavy or light objects?
Post by: Halc on 20/09/2020 13:12:26
In a vacuum I suppose any heavier object falls faster than a light object, but we can't detect it.
This is not correct. This contradicts Newton's laws of motion. The acceleration of a particle due to the gravity of a presumed fixed object (Earth say) is GM/r², which is not a function of the mass of the particle at all.
You speak not of acceleration, but of speed. Those laws say little of the speed that something falls since initial speed must be known. The laws speak only of acceleration, which again, is not a function of the mass of the accelerating thing.

Quote from: Halc
So if measured down to the femtosecond, the rock really does fall faster than the feather.
Not if you dropped them together.

The mass of (rock+feather) would attract the Earth equally to rock and feather.
If the two are dropped together from very close together, then I agree.  The feather hits the ground sooner than it would by itself. It is aided by the presence of the rock next to it.

As you separate the two, the effect lessens, and then actually becomes negative.
So for example, I simultaneously drop a feather and rock, but on opposite sides of Earth. The feather will now take longer to hit Earth than it would have falling by itself.

If 90° apart, neither will effect the other much, but the race will probably be won by the object which has the moon on the horizon. Tidal forces definitely outweigh (pun intended) the sort of difference due to the tiny masses of the objects I'm dropping.
Title: Re: What falls faster: heavy or light objects?
Post by: alancalverd on 20/09/2020 16:24:40
To notice the difference...
What difference?

difference in speed. In a vacuum I suppose any heavier object falls faster than a light object, but we can't detect it.
See Galileo's response at reply # 2 above.
Title: Re: What falls faster: heavy or light objects?
Post by: alancalverd on 20/09/2020 16:42:17
This is not correct. This contradicts Newton's laws of motion. The acceleration of a particle due to the gravity of a presumed fixed object (Earth say) is GM/r², which is not a function of the mass of the particle at all.
You speak not of acceleration, but of speed. Those laws say little of the speed that something falls since initial speed must be known. The laws speak only of acceleration, which again, is not a function of the mass of the accelerating thing.
Let's be pedantic, just for fun

There's no objection to anything contradicting a law of physics. Indeed that's how physics advances! The "laws" are not prescriptions of how things should behave, but descriptions of how they have been observed to behave. Which is why Newtonian mechanics describes the behavior of mesoscopic objects at low speeds but not when v → c.

Whilst we observe that gravitational acceleration is independent of the test mass m if m << M, there's no obvious reason why it should be. It happens that as close as we can measure, inertial mass mi = gravitational mass mg,  which is why a = F/mi = GmgM/mir2 = GM/r2, but that's a real oddity: the electric and magnetic fields of particles and bodies are not related to their mass, so why should the gravitational force be so precisely proportional to inertial mass?
Title: Re: What falls faster: heavy or light objects?
Post by: myuncle on 20/09/2020 22:52:27
Two different masses falling at the same rate assumes both objects are small in comparison to the object pulling them gravitationally.

Therefore a feather dropped from a stationary position 380,000 km above a moonless Earth would take significantly longer to fall to the surface than would the moon (from a stationary position). The difference is that the moon would have a significant effect on the Earth itself, pulling it over 4000 km upward as the moon falls, thus increasing the gravitational pull on the moon and shortening the distance it has to fall.
So if measured down to the femtosecond, the rock really does fall faster than the feather.

Ok, the moon would have a significant effect on the Earth increasing the gravitational pull and shortening the distance it has to fall. But even a pebble in theory has some gravitational pull, too tiny to detect obviously, but not absent. No?
Title: Re: What falls faster: heavy or light objects?
Post by: Halc on 21/09/2020 00:02:26
But even a pebble in theory has some gravitational pull, too tiny to detect obviously, but not absent. No?
If a pebble weighs 1 Newton near Earth, then the Earth weighs 1 Newton on the pebble due the gravity of the pebble. It must accelerate towards the pebble in response to that equal and opposite force. So indeed, not absent. The planet accelerates more towards the pebble than it does towards the feather, unless (as Evan points out) both the pebble and feather are there together and the attraction is due to their combined mass.
Obviously 1 Newton isn't going to accelerate something as massive as Earth in any macroscopic way.

The pebble doesn't fall any faster. It just hits the ground sooner because the ground comes up to meet it a tiny bit.
Title: Re: What falls faster: heavy or light objects?
Post by: Yahya A.Sharif on 01/10/2020 17:34:51
This is how it works:
1) inertia of small objects
2) inertia of bigger objects
The small objects must  fall faster because of its small inertia
3)) force of gravity on small objects
4)force of gravity on bigger objects
The small objects must  fall slower because of small gravity force
a=F/m
In this equation:
Acceleration" a" increase for a small mass m , but at the same time gravity force F decreases for smaller m then " a "is constant
In the same equation:
Acceleration decreases for bigger mass m , but at the same time force of gravity F for the bigger mass  increases then "a"is constant
This constant acceleration "a" is 9.8 m/s² makes two different masses with same height fall at the same time.
Title: Re: What falls faster: heavy or light objects?
Post by: alancalverd on 01/10/2020 23:01:23
This is all very true, but merely experimental observation. It doesn't explain why inertial mass = gravitational mass.
Title: Re: What falls faster: heavy or light objects?
Post by: hamdani yusuf on 09/10/2020 04:15:35
Emily asks:

Why do heavy objects fall to the ground faster than light objects? If light objects are easier to pull, shouldn't gravity pull them down faster than heavy objects?

Can you help?
This is what ordinary experience tells us. That's why Aristotle thought so. The same substance seems to fall at different rate when falling to the ground. Heavy rain falls faster than light rain, although they are both water. Big sand grains fall faster than sand dust.
Downward gravitational force in falling object depends on the its mass, which is proportional to its volume. On the other hand, upward air friction that resist downward movement depends on the object's surface area. It also depends on the speed through air. So when the object fall, it will accelerate downward until reaching its terminal velocity. Its speed stops increasing because downward gravity force is canceled by upward air friction.
Assuming that the objects are spherical, downward force is proportional to R³, while upward force  is proportional to R². Consequently, larger objects will have higher terminal velocity compared to smaller ones, assuming they have the same shapes and compositions.
Title: Re: What falls faster: heavy or light objects?
Post by: Halc on 09/10/2020 13:49:21
The small objects must  fall slower because of small gravity force
Today's F minus:
(https://assets.amuniversal.com/416f7e70e17e01382605005056a9545d)
Title: Re: What falls faster: heavy or light objects?
Post by: Petrochemicals on 09/10/2020 22:11:34
Galileo was wrong and the aristotlewas correct, his balls did hit the floor at different times,it's just not really percept able.

What falls faster a neutron star or the comet that killed the dinosaurs?
Title: Re: What falls faster: heavy or light objects?
Post by: Bored chemist on 09/10/2020 23:56:45
Galileo was wrong
Please explain that in terms of his thought experiment.