Gravity on a Small Scale: Coyote vs Boulder Debate Explained

[sciencequest]

My teacher and I had a slight disagreement over gravity (I'm in the 8th grade). She said that if you were to drop a coyote and a boulder off of a building, they would hit at the same time if you discounted air resistance. I responded that the boulder, naturally being more massive, would hit first, because gravity is the fictious force of two objects pulling on each other. The boulder would pull the Earth toward itself more so then the lighter coyote, meaning the boulder would land first.

Who is correct, and what equations can you use to calculate gravity on such a small scale?

Thanks in advance.

 

[Doc Al]

My teacher and I had a slight disagreement over gravity (I'm in the 8th grade). She said that if you were to drop a coyote and a boulder off of a building, they would hit at the same time if you discounted air resistance. I responded that the boulder, naturally being more massive, would hit first, because gravity is the fictious force of two objects pulling on each other. The boulder would pull the Earth toward itself more so then the lighter coyote, meaning the boulder would land first.

Who is correct, and what equations can you use to calculate gravity on such a small scale?

I believe you are concerned with the acceleration of the Earth due to the pull of the boulder. Assuming the boulder is 'normal-sized'--with a mass tiny compared to that of the earth--the acceleration of the Earth that it produces will be ludicrously small. You can calculate it using Newton's 2nd law: You know the force (the weight of the object); to get the Earth's acceleration divide by the mass of the earth. (See this post where I compare the Earth's acceleration due to a bowling ball and a feather: https://www.physicsforums.com/showpost.php?p=343562&postcount=16)

So you have a point: The acceleration of the Earth due to the boulder will be greater than that due to the coyote. But we're talking about two vanishingly tiny numbers.

Nonetheless, if you drop both together, even accounting for the acceleration of the earth, they will hit together since they both pull up the Earth together.

So I'd say: For all practical purposes, your teacher is correct. And for nit-picking purposes that include the acceleration of the Earth (but not other WAY more important factors), she's still correct.

(And are you seriously considering gravity as a fictitious force in 8th grade? That's the view from general relativity, but I wouldn't go there quite yet. Plain old Newtonian gravity is all you need here.)

 

[Oldblood]

I think you are right. If the Earth was stationary they would hit the ground at the exact same time according to Newtons laws. However, its not and it will be affected by the smaller mass. Call the 2 smaller masses m1 and m2 and the larger mass (planet) M. m1 > m2. If we first look at the interactions between m2 and M. M would give m2 and acceleration due to its garvitational field. Since the field is independent of the small mass being in the field it would give m1 the same aceleration. That is what happens at the start. But, m2 and m1 draws on M too. m2 generating a smaller field on a distance r at the start would generate the force GMm2/r^2. m1 would generate GMm1/r^2 on the same object. Since m1 > m2 the aceleration of M is greater when m1 is pulling it. So basically m1 and m2 has the same acceleration at the start but M if pulled harder by m1 then m2. Thus the objects collide faster when the smaller object is heavier. So youre right and your teacher is wrong. However for all practical uses and taking account to other factors the pull from the lighter object wouldn't have an effect worth mentioning on the earth.

 

[Doc Al]

So youre right and your teacher is wrong.

If boulder and coyote are dropped together (side by side), then the acceleration of the Earth would be due to their combined mass. And they would hit together.

Nonetheless, it's fun and instructive to think about these things.

 

[Oldblood]

If boulder and coyote are dropped together (side by side), then the acceleration of the Earth would be due to their combined mass. And they would hit together.

Nonetheless, it's fun and instructive to think about these things.

Well if you say they are droped from the same height at the same time. Then you would have an angle between them. By angle I mean the the central angle. (if one is droped on the north pole and one on equator the central angle is 90 degrees). If the object were close this angle would be very small offcourse, and would have no practical effect. So its easier to imagine let's say they were droped at the same height at the same time by far away from each other. Wouldnt the heavier small object draw the Earth more in its direction then the lighter mass would? This draw againt the heavier object would "increase" the distance between the smaller object and the earth. So still if they are droped at the same time the teacher would be wrong I guess.

 

[Doc Al]

Sure, things would be different if they were dropped from the same height at opposite ends of the earth. But the statement was: "if you were to drop a coyote and a boulder off of a building, they would hit at the same time".

 

[Oldblood]

well my point was, we would still have a sepearation by this center angle, even thoug it would be extremely small in that case. The reason I mentioned the north pole and equator was so its easy to see that the separation in space matters, no matter how small it is. Its just easier to picture when its big.

 

[sciencequest]

Thanks for the answers guys... If anyone could provide a third opinion it would be appreciated.

 

[QMessenger]

8th grade and already publicly questioning scientific authority? heh, you are wise beyond your years. It would seem that at very tiny scales gravity cannot be detected, or so I have read. Maybe you should also investigate what Einstein was doing the last years of his life. Perhaps your intuition would be more valuable to the body of knowledge if you didn't go with the status quo. As far as sticking with Newtonian mechanics, Einstein wasn't satisfied with what everyone else thought, so he developed his own theory. You have far greater access to experimental results and alternate theories than he ever dreamt, and he put his pants on one leg at a time to boot. Don't let anyone hold you back but be careful what you state as fact. The fun is in the search so good luck.