Concept of Free Fall in question

In summary: Objects with different masses feel different forces due to the law of gravity, but they all accelerate at the same rate due to the force being proportional to the mass.
  • #1
fruit_cake4all
1
0
OK so let me apologies if I don't seem to fully understand the concept of free fall and am making a far fetched connection.

I've been recently reviewing some of my old course material such as vector calculations, Newtonian mechanics,etc, and while reading up on basic vector calculation the book made a reference to Newton's second law while setting an example for scaling a vector by a constant. Saying that you can change the length of a vector without necessarily changing its direction. That is B = cD.

Now having read that, when I reached the topic of free fall, it occurred to me that although the mass is irrelevant in increasing or decreasing the objects acceleration, does it not even have an effect on the gravitational force?

So to sum it up, do objects of different masses also feel the same gravitational force while in free fall? And if they don't feel the same gravitational force, how come they all accelerate at the same rate. ( I know that when an object acts as a projectile the gravitational force is in the opposite direction as acceleration until it reaches its maximum height, and has the same direction afterwards, but what about the magnitude of the gravitational force, doesn't it change with varies masses?)

Once again my apologies if something is missing in my understanding of these concepts, will appreciate it if someone can clear things up for me!

Thank you!
 
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  • #2
fruit_cake4all said:
So to sum it up, do objects of different masses also feel the same gravitational force while in free fall?

No, they feel different forces. The easiest way of seeing this is to look at Newton's equations for the gravitational force between two objects: ##F=Gm_1m_2/r^2##. Clearly if you increase either mass, the force increases commensurately.

There's FAQ at the top of this forum: https://www.physicsforums.com/showthread.php?t=511172 [Broken]
 
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  • #3
fruit_cake4all said:
And if they don't feel the same gravitational force, how come they all accelerate at the same rate?

As Nugatory said, objects of different masses feel different gravitational force. Now, I think your confusion is, if masses feel different magnitudes of gravitational force how come they accelerate at same rate? Right?
In other words you are asking if F is different how can g be same?

You know here F = mg or g = F/m. So you see, as m changes F also changes certainly, but their ratio will always be the same. Thus, objects of different masses feel different gravitational forces but they accelerate (free fall) at same rate.

EDIT: Here I am considering the free fall of a small object (of small mass, compared to the mass of earth) under Earth's gravitational force. The above link gives a more general discussion.
 
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  • #4
What Nugatory said.

The force F = Gm1m2/r2

If the small mass is m2 then the acceleration of m2 is...

a = F/m2 (from Newtons f=m2a)

So

a = Gm1m2/r2m2

m2 cancels so a is independent of m2

a = Gm1/r2
 
  • #5
The mass is not irrelevant, but the difference in results in this situation are negligable and so are ignored, simplifying the maths.

Consider the equation for (total ) acceleration (a) between two bodies :

a = ( G * ( m1 + m2 ) ) / d ²

To keep the maths easy, and exaggerate the difference, let :
G = 1
m1 = 100
d = 10

For experiment 1, let m2 = 1
So, a = 1.01

For experiment 2, let m2 = 2
So, a = 1.02

So, altering the mass of m2 does alter the total acceleration rate.

If you apply this to the Earth and variable masses the values for a are all but identical, but do exist.Comments ?
deanbarry365@yahoo.com
 
  • #6
dean barry said:
The mass is not irrelevant, but the difference in results in this situation are negligable and so are ignored, simplifying the maths.
...
Comments?

This subtlety is covered in great detail in the FAQ I linked to.
 

1. What is the concept of free fall?

The concept of free fall refers to the motion of an object under the sole influence of gravity. In free fall, the object is only subject to the force of gravity and no other forces, such as air resistance or friction.

2. What is the acceleration of an object in free fall?

The acceleration of an object in free fall is always constant and equal to the acceleration due to gravity, which is approximately 9.8 meters per second squared on Earth. This means that the object's velocity increases by 9.8 meters per second every second it is in free fall.

3. How does mass affect an object's free fall?

The mass of an object does not affect its free fall. All objects, regardless of their mass, will experience the same acceleration due to gravity when in free fall. However, a more massive object will have a greater force of gravity acting on it, which can affect its impact upon hitting the ground.

4. What is the difference between free fall and terminal velocity?

Free fall refers to the motion of an object under the sole influence of gravity, while terminal velocity refers to the maximum speed a falling object can reach when the force of air resistance becomes equal to the force of gravity. In free fall, the object is accelerating, while in terminal velocity, the object is falling at a constant speed.

5. Can an object experience free fall in the absence of gravity?

No, an object cannot experience free fall in the absence of gravity. Free fall is defined as the motion of an object under the sole influence of gravity, so without gravity, there would be no force causing the object to accelerate. Other forces, such as air resistance, may act on the object, but it would not be considered free fall without gravity.

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