[SOLVED] Newton Open Ended Question

Jeff Weisberger

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

Kurdt

When you drop two object what force accelerates them?

Jeff Weisberger

Gravity, right? but im 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 [tex]F=-\frac{GMm}{r^2}[/tex] 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

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:

http://www.youtube.com/watch?v=5C5_dOEyAfk

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

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 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?

Jeff Weisberger

oh sweet thank you all for the help

PhanthomJay

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

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.

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.

Kurdt

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.