Why does the last term detract from acceleration?

In summary, The force of gravity is proportional to mass, but acceleration due to gravity is independent of mass. In a vacuum, all objects have the same acceleration of g regardless of their mass. With air resistance, the force of gravity is still proportional to mass, but the acceleration is affected by the force of air resistance, which is dependent on the mass of the object. As the mass of the object increases, the force of air resistance becomes smaller, resulting in a smaller detracting force on the acceleration due to gravity. This is why all objects, regardless of their mass, fall at the same rate in a vacuum. In the presence of air resistance, the acceleration may vary slightly depending on the mass of the object, but it will
  • #1
Peter G.
442
0
I'd like to start off by saying that all I want is explanations. My head forces me to think in a way that goes against what I "know" is right:

Firstly: I "know" all objects fall at the same speed in a vacuum. What I understand from a vacuum is the absence of air, thus, absence of air friction - air resistance, in other words, an absence of the force pulling things upwards. The force pulling us down, as shown in several parachute cartoons is weight: W = m x g. If there is no force pulling us upwards and the only force acting on us is our weight, dependent on mass, why don't heavier objects fall faster in a vacuum?

The same concept confuses me when air resistance is involved. I remember taking my IGCSE's and facing a question regarding two balls, one made of aluminum and another one made out of plastic. Both had the exact same shape, but naturally, different weights. The answer said that both balls would fall at the same rate. But, once again I am confused. Having the same shape, they have the same aerodynamic properties, meaning the air resistance acting on them will be the same at corresponding speeds, but, one ball is heavier than the other, meaning the force pulling it down is greater. So, shouldn't it fall faster?

I hope what I wrote is clear.

Thanks,
PeterG
 
Physics news on Phys.org
  • #2
Peter G. said:
I'd like to start off by saying that all I want is explanations. My head forces me to think in a way that goes against what I "know" is right:
The force of gravity is greater for a more massive object, but acceleration due to gravity is independent of mass.
The force due to gravity is F = mg. By Newton's second law, F = ma or a = F/m = mg/m = g.
 
  • #3
Peter G. said:
I'd like to start off by saying that all I want is explanations. My head forces me to think in a way that goes against what I "know" is right:

Firstly: I "know" all objects fall at the same speed in a vacuum. What I understand from a vacuum is the absence of air, thus, absence of air friction - air resistance, in other words, an absence of the force pulling things upwards. The force pulling us down, as shown in several parachute cartoons is weight: W = m x g. If there is no force pulling us upwards and the only force acting on us is our weight, dependent on mass, why don't heavier objects fall faster in a vacuum?
In a vacuum, all objects have the same acceleration. Given the force, how do you find the acceleration? Use Newton's 2nd law, F = ma. In this case, the force is the weight = m x g. So set that force equal to m x a. Thus: m x g = m x a. The masses cancel and you get a = g, independent of mass.

In words: Yes, the force of gravity is proportional to mass. But the acceleration for a given force is inversely proportional to mass. It cancels nicely.


The same concept confuses me when air resistance is involved. I remember taking my IGCSE's and facing a question regarding two balls, one made of aluminum and another one made out of plastic. Both had the exact same shape, but naturally, different weights. The answer said that both balls would fall at the same rate. But, once again I am confused. Having the same shape, they have the same aerodynamic properties, meaning the air resistance acting on them will be the same at corresponding speeds, but, one ball is heavier than the other, meaning the force pulling it down is greater. So, shouldn't it fall faster?
Sure, the heavier object will have the greater acceleration if you include air resistance. (No idea why the 'answer' said different, unless they were ignoring air resistance.)

Again, use F = ma to see this. For a given velocity, the force of air resistance will be the same; let's call it Fair. The net force on the ball will be F = mg - Fair. The acceleration will thus be F/m = g - Fair/m. The bigger the mass m, the greater the downward acceleration. (The second term will be smaller.)

Make sense?
 
  • #4
Thanks a lot both of you!

Regarding the acceleration in a vacuum, it is very clear.

This is the only thing that confuses me: F/m = mg/m = g, therefore: g - Fair/m. I don't understand where the m comes from :uhh:

Edit: Sorry, read your post. Got it now! Thanks for the patience! :smile:

I am tired of my books saying this and that and not explaining it! It basically, implicitly asks us to memorize stuff when I like to learn!
 
Last edited:
  • #5
Peter G. said:
With air resistance though, the only thing that is confusing me is this: " F/m = g - Fair/m"
Can you pinpoint what's confusing you about it?

Here's how it's derived:
Forces on ball: mg down & Fair up
Net force on ball: ΣF = mg - Fair (taking down as positive)
Applying ΣF = ma: mg - Fair = ma
Solving for a: a = (mg - Fair)/m = g - Fair/m

That last term, Fair/m, detracts from the acceleration due to gravity. The smaller it is, the closer the acceleration is to g. And the bigger the mass m is, the smaller is Fair/m.
 

1. What is freefall acceleration?

Freefall acceleration is the rate at which an object falls towards the Earth's surface due to the force of gravity. It is typically denoted by the symbol "g" and has a constant value of approximately 9.8 meters per second squared.

2. How is freefall acceleration calculated?

Freefall acceleration can be calculated using the formula g = 9.8 m/s^2. This means that for every second an object is in freefall, its velocity will increase by 9.8 meters per second.

3. Does freefall acceleration change depending on the mass of the object?

No, freefall acceleration is independent of the mass of the object. This means that all objects, regardless of their mass, will accelerate towards the Earth's surface at the same rate.

4. Can freefall acceleration be affected by air resistance?

Yes, air resistance can affect the acceleration of an object in freefall. As an object falls, it will encounter air resistance which will oppose its motion and cause it to accelerate at a slower rate than g. However, in most cases, the effect of air resistance on freefall acceleration is negligible.

5. Can freefall acceleration change on different planets?

Yes, freefall acceleration can vary on different planets depending on their mass and radius. For example, on the Moon, the freefall acceleration is about one-sixth of that on Earth, while on Jupiter it is over twice the value on Earth. This is due to the different gravitational forces on each planet.

Similar threads

  • Introductory Physics Homework Help
2
Replies
47
Views
3K
  • Introductory Physics Homework Help
Replies
31
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
1K
Replies
9
Views
788
  • Introductory Physics Homework Help
Replies
8
Views
7K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Mechanics
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
3K
Back
Top