Is Newton's Law of Universal Gravitation Proven Wrong by a Simple Experiment?

[Jeff Weisberger]

[SOLVED] Newton Open Ended Question

Homework Statement

According to Newton's Law of Universal Gravitation, the force exerted by the Earth on an object is directly proportional to the objects mass

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the force being exerted on it.

Therefore, it may be concluded that if 2 objects are dropped simultaneously from the same height, the heavier object, having a greater acceleration, will reach the ground first.

Using mathematical equations, verify or refute the above conclusion

Homework Equations

The Attempt at a Solution

I have a strong feeling the statement needs to be refuted, just not sure what equations to use in the process, besides F=MA for Newton's Second Law

 

[Kurdt]

When you drop two object what force accelerates them?

 

[Jeff Weisberger]

Gravity, right? but I am just unsure of whether more mass constitutes greater acceleration...

 

[cristo]

Do you know how to calculate the gravitational force between two objects?

 

[Jeff Weisberger]

multiply the 2 masses, then divide by the distance squared

 

[Jeff Weisberger]

ooh so the mass of the objects would not affect their acceleration, and therefore they would reach the ground at the saem height, correct?... but that doesn't seem right to me, since a feather would take longer than a bowling ball, or does that have to do w/ weight?

 

[cristo]

Close; you need the gravitational constant. So, the force of gravity exerted by the Earth (mass M) on an object (mass m) at a distance r is $$F=-\frac{GMm}{r^2}$$ Now, use this in Newton's second law.

 

[Jeff Weisberger]

So, 2 objects dropped at the same time would hit the ground at the same time, since the force being exerted on the objects is the same.

 

[Kurdt]

ooh so the mass of the objects would not affect their acceleration, and therefore they would reach the ground at the saem height, correct?... but that doesn't seem right to me, since a feather would take longer than a bowling ball, or does that have to do w/ weight?

A feather takes longer than a bowling ball because of the feathers relatively large surface area to weight ratio which means that air resistance has a significant effect on it compared to the bowling ball.

A rather famous experiment was done on the moon where an Apollo astronaut dropped a feather and hammer at the same time. Of course the moon has no atmosphere. Check out the vid below:

 

[hover]

You don't have to use Newtons law of gravity unless you want to find out how fast the 2 objects are accelerating towards Earth or some other object. Keep it simple with
F=ma

On the surface of the Earth things accelerate at 9.8 m/s or 32.2 f/s (assuming no air resistance) so input that.
F=m*9.8m/s

M= mass so the mass can be 1 gram or it could be a kilogram if you like. No matter what the mass is, it isn't going to change the acceleration (9.8 m/s) of an object. The only thing mass changes is the force.

 

[cristo]

So, 2 objects dropped at the same time would hit the ground at the same time, since the force being exerted on the objects is the same.

Sorry, I didn't read this properly first time (after reading PhantomJay's post, it was apparent that I hadn't read it correctly!) The objects will hit the ground at the same time, but the force exerted on each body is not the same.

 

[Jeff Weisberger]

alright I am going to bed in 5 minutes and this is due tommrow: so, they will arrive at the same time bc they are both affected by the gravitational constant?

 

[Jeff Weisberger]

oh sweet thank you all for the help

 

[PhanthomJay]

So, 2 objects dropped at the same time would hit the ground at the same time, since the force being exerted on the objects is the same.

No, that is incorrect. Do you see why they are different? What is that force on each object?

 

[hover]

No, that is incorrect. Do you see why they are different? What is that force on each object?

Newtons law of gravitation doesn't come into play unless both objects touch. What he ment was that both objects are accelerated at the same speed and will hit the groung at the same time.

 

[PhanthomJay]

Newtons law of gravitation doesn't come into play unless both objects touch. What he ment was that both objects are accelerated at the same speed and will hit the groung at the same time.

What does that mean? Gravity acts at a distance...any distance, great or small. The force of Earth's gravity on 2 objects of different masses are different, and in each case is equal to the objects weight.

 

[Kurdt]

Newtons law of gravitation doesn't come into play unless both objects touch.

What? This is nonsense.

The acceleration on both objects is the same but the forces are different for each one and the force is due to gravity.

 

[hover]

What? This is nonsense.

The acceleration on both objects is the same but the forces are different for each one and the force is due to gravity.

I tend to only think in the form of relativity. When an object moves through space and towards a massive object like Earth it won't feel anything. It will only notice that it is accelerating towards the massive object. When it comes in contact with the massive object then it will feel a force.

Am i missing something??

 

[ranger]

I tend to only think in the form of relativity. When an object moves through space and towards a massive object like Earth it won't feel anything. It will only notice that it is accelerating towards the massive object. When it comes in contact with the massive object then it will feel a force.

Am i missing something??

Newtons laws of gravitation doesn't require the objects to be in contact to work. If you look at the formula, you'll notice that the attractive force between the two objects is inversely proportional to the square of the distance. What do you mean by "object moves through space and towards a massive object like Earth it won't feel anything"? Are you saying that the force of gravity does not affect the object that is moving towards earth? Mayb you are missing a fundamental point here, that when gravity acts on a mass, that object now has weight. And also why do you think the object comes spiraling towards earth? Is it not influenced by some force.

 

[Kurdt]

I tend to only think in the form of relativity. When an object moves through space and towards a massive object like Earth it won't feel anything. It will only notice that it is accelerating towards the massive object. When it comes in contact with the massive object then it will feel a force.

Am i missing something??

Well firstly I said that the statement that Newton's laws of gravity only come into play when objects touch was nonsense. Secondly where in the original post was relativity mentioned. The whole point of the exercise is to realize the equivalence principle through Newtonian physics.

 

[hover]

Newtons laws of gravitation doesn't require the objects to be in contact to work. If you look at the formula, you'll notice that the attractive force between the two objects is inversely proportional to the square of the distance. What do you mean by "object moves through space and towards a massive object like Earth it won't feel anything"? Are you saying that the force of gravity does not affect the object that is moving towards earth? Mayb you are missing a fundamental point here, that when gravity acts on a mass, that object now has weight.

I thought objects in free fall won't feel anything. The object will begin to accelerate towards the Earth but won't feel anything, like they are out in deep space.

What am i screwing up??

I never said i WAS right

 

[hover]

Well firstly I said that the statement that Newton's laws of gravity only come into play when objects touch was nonsense. Secondly where in the original post was relativity mentioned. The whole point of the exercise is to realize the equivalence principle through Newtonian physics.

Gravity acts at a distance i believe that. I screwed up my wording. An object won't feel a force until it hits the ground. Its like having 2 elevators, one in space and one falling to earth. Since both don't feel a force both could say that they are out in deep space or both could say they are in free fall.

 

[ranger]

I thought objects in free fall won't feel anything. The object will begin to accelerate towards the Earth but won't feel anything, like they are out in deep space.

What am i screwing up??

I never said i WAS right

Ah yes, I see where you are confused. What you are talking about is apparent weight, which is the [upward] normal force exerted on an object by the surface. When an object is in free fall, it is true that it has no apparent weight becuase there is no normal force. But the object still has actual weight, which is the [downward] force exerted upon the object by gravity.

Confusing aint it :tongue2:

 

[Jeff Weisberger]

isnt the point to help me w/ my question, not to argue over senseless minutiae in order to prove ur point?? ...(coming from a high school junior)

 

[hover]

isnt the point to help me w/ my question, not to argue over senseless minutiae in order to prove ur point?? ...(coming from a high school junior)

I was hoping that this thread would end. We did help you, its just that i got confused some bit and others tried to help me on this thread, that's all.

 

[cristo]

isnt the point to help me w/ my question, not to argue over senseless minutiae in order to prove ur point?? ...(coming from a high school junior)

Jeff, your reply in post #13 implies that your problem has been solved. Do you have any more questions about this?

 

[Jeff Weisberger]

nah I am good, just wanted to use the word minutiae...thanks for the help