# Newton Open Ended Question

1. Jan 21, 2007

### Jeff Weisberger

[SOLVED] Newton Open Ended Question

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

Last edited: Jan 21, 2007
2. Jan 21, 2007

### Kurdt

Staff Emeritus
When you drop two object what force accelerates them?

3. Jan 21, 2007

### Jeff Weisberger

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

4. Jan 21, 2007

### cristo

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

5. Jan 21, 2007

### Jeff Weisberger

multiply the 2 masses, then divide by the distance squared

6. Jan 21, 2007

### 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?

7. Jan 21, 2007

### cristo

Staff Emeritus
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.

8. Jan 21, 2007

### 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.

9. Jan 21, 2007

### Kurdt

Staff Emeritus
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:

Last edited by a moderator: Sep 25, 2014
10. Jan 21, 2007

### 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.

11. Jan 21, 2007

### cristo

Staff Emeritus
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.

Last edited: Jan 21, 2007
12. Jan 21, 2007

### Jeff Weisberger

alright im 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?

13. Jan 21, 2007

### Jeff Weisberger

oh sweet thank you all for the help

14. Jan 21, 2007

### PhanthomJay

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

15. Jan 21, 2007

### hover

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.

Last edited: Jan 21, 2007
16. Jan 21, 2007

### PhanthomJay

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.

17. Jan 21, 2007

### Kurdt

Staff Emeritus
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.

18. Jan 21, 2007

### hover

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??

19. Jan 21, 2007

### ranger

Newtons laws of gravitation doesnt 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.

Last edited: Jan 21, 2007
20. Jan 21, 2007

### Kurdt

Staff Emeritus
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 realise the equivalence principle through Newtonian physics.