Heavier objects actually not falling at the same speed?

[Juan Carlos]

I know, I know. It's a fact that two objects with different masses will fall to the surface of the Earth at the same speed, considering that they were in a vaccumm. Newton knew that and everybody knows that.

 

But something doesn't make sense to me and I'd like to understand it.

 

Objects fall because the Earth (or whatever planet they might be at, for that matter) applies a force of gravity on them (I know gravity isn't a force, but in the Newtonian physics, it is). The gravity of Earth is 9.81 m/s^2 and it applies the same to all objects.

 

However, the force of gravity is directly proportional to product of the mass of the objects and inversely proportional to the squared distance between them. If mass is a factor on the equation of gravity, then objects with more mass should have a stronger pull towards Earth.

 

I know that fhe difference in gravity between a hammer and a feather would be miniscule, even negligible, but not an absolute zero. It could have important consequences in terms of the speed at which planets fall (or, more formally, gravitate) around the sun.

 

Am I right that they actually don't fall at *exactly* the same speed?

[swansont]

The force is larger for the larger mass, but F = ma, so the acceleration is the same. Falling side-by-side they will have the same speed and hit at the same time.

[Externet]

Not in vacuum, but in the real airy planet, find two very identical balloons and inflate one with air and the other with water to the exact same volume and drop them from a height simultaneously...

[J.C.MacSwell]

I know, I know. It's a fact that two objects with different masses will fall to the surface of the Earth at the same speed, considering that they were in a vaccumm. Newton knew that and everybody knows that.

 

But something doesn't make sense to me and I'd like to understand it.

 

Objects fall because the Earth (or whatever planet they might be at, for that matter) applies a force of gravity on them (I know gravity isn't a force, but in the Newtonian physics, it is). The gravity of Earth is 9.81 m/s^2 and it applies the same to all objects.

 

However, the force of gravity is directly proportional to product of the mass of the objects and inversely proportional to the squared distance between them. If mass is a factor on the equation of gravity, then objects with more mass should have a stronger pull towards Earth.

 

I know that fhe difference in gravity between a hammer and a feather would be miniscule, even negligible, but not an absolute zero. It could have important consequences in terms of the speed at which planets fall (or, more formally, gravitate) around the sun.

 

Am I right that they actually don't fall at *exactly* the same speed?

Same speed but heavier object will hit in (negligibly) less time, if dropped at different times under identical conditions otherwise, due to planets reaction, if that is what you are getting at.

[StringJunky]

Same speed but heavier object will hit in (negligibly) less time, if dropped at different times under identical conditions otherwise, due to planets reaction, if that is what you are getting at.

If two objects of different masses simultaneously start falling towards the planet they will arrive at the same? If the same two objects were dropped at different times the reaction of the planet would make a difference to the measured times i.e, they would be different because the reaction between the larger object and the planet would be greater; the planet will move towards the larger object a little more/faster than the smaller one? Hope that makes sense.

Edited November 14, 2016 by StringJunky

[J.C.MacSwell]

If two objects of different masses simultaneously start falling towards the planet they will arrive at the same? If the same two objects were dropped at different times the reaction of the planet would make a difference to the times i.e, they would be different because the reaction between the larger object and the planet would be greater?

That's right. ..and it would need to be identical...the first mass dropped changes the planets mass, where is the moon, etc...not that it would be a measurable difference in any case

Edited November 14, 2016 by J.C.MacSwell

[StringJunky]

That's right. ..and it would need to be identical...the first mass dropped changes the planets mass, where is the moon, etc...not that it would be a measurable difference in any case

Right. Thanks.

[Sriman Dutta]

Newton's Law of Universal Gravitation-

[math] F = G \frac{mM}{S^2} [/math]

Newton's Second Law of Motion-

[math] F = ma [/math]

Combining them-

[math] G \frac{mM}{S^2} = ma [/math]

If [math]m[/math] is mass of object falling towards the ground and [math]M[/math] is the mass of the planet, then-

[math] a = \frac{GM}{S^2}[/math]

If a is the acceleration due to gravity, then-

[math] g = \frac{GM}{S^2}[/math]

By the equations of motion-

[math] S = ut+\frac{1}{2}gt^2 [/math]

If the falling body's initial velocity is 0, then the above equation simplifies to-

[math] S = \frac{1}{2}gt^2 [/math]

Substituting the value of [math]g[/math] in the above equation-

[math] S = \frac{1}{2} \frac{GM}{S^2}t^2 [/math]

So,-

[math] S^3 = \frac{1}{2}GMt^2 [/math]

Edited November 14, 2016 by Sriman Dutta

[DrKrettin]

The force is larger for the larger mass, but F = ma, so the acceleration is the same. Falling side-by-side they will have the same speed and hit at the same time.

 

 

Smartarse comment: If they are falling side-by-side, then the larger one will hit just before the smaller one because it has a larger diameter.

[swansont]

 

 

Smartarse comment: If they are falling side-by-side, then the larger one will hit just before the smaller one because it has a larger diameter.

 

 

I didn't say anything about size. One must assume they have the same size, and a different density, since one assumes that the experiment is not being done carelessly. i.e. one is doing a good experiment.

Newton's Law of Universal Gravitation-

[math] F = G \frac{mM}{S^2} [/math]

Newton's Second Law of Motion-

[math] F = ma [/math]

Combining them-

[math] G \frac{mM}{S^2} = ma [/math]

If [math]m[/math] is mass of object falling towards the ground and [math]M[/math] is the mass of the planet, then-

[math] a = \frac{GM}{S^2}[/math]

If a is the acceleration due to gravity, then-

[math] g = \frac{GM}{S^2}[/math]

By the equations of motion-

[math] S = ut+\frac{1}{2}gt^2 [/math]

If the falling body's initial velocity is 0, then the above equation simplifies to-

[math] S = \frac{1}{2}gt^2 [/math]

Substituting the value of [math]g[/math] in the above equation-

[math] S = \frac{1}{2} \frac{GM}{S^2}t^2 [/math]

So,-

[math] S^3 = \frac{1}{2}GMt^2 [/math]

 

You are using S for two different variables. In Newton's gravitation equation it's the distance to the center of the mass. In the kinematics equation, it's the distance of travel. Using g, you are implicitly assuming you are outside the planet and limited to motion where you can assume g is constant. They cannot represent the same distance.

[Sriman Dutta]

Oh yes yes.... Good point swansont. I totally missed it out.

If [math]R[/math] is the radius of planet and [math]h[/math] is the distance of the object from the planet's surface and [math]S[/math] is the distance between their centres, then [math] S = R+h [/math]. Using this we get-

[math] h(R+h)^2 = \frac{1}{2}GMt^2 [/math]

[AshBox]

we can also say in anoother way that gravity has to pull harder on a heavy object than a lighter one in order to speed them both up by the same amount. However, in the real world, we have things like air resistance, which is why sometimes heavy things do fall faster.

 

However gravity is determined by a number known as the "acceleration of gravity" and on our earth surface it is 9.81 m/s^2 which means within one second velocity will be increased by 9.81 m/s beacuse of gravity. This defines how gravity works.

 

Although in the reality such things, like air resistance. For example, if you drop a feather and you drop a rock, the rock will land first since the feather is slowed down more by the air. If you did the same thing somewhere where there is no air, the feather and the rock would land at exactly the same time.