- #1

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What I never understood ... was WHY this happened. What causes the two objects to hit the floor at the same moment.

Thanks in advance.

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- Thread starter BL4CKCR4Y0NS
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- #1

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What I never understood ... was WHY this happened. What causes the two objects to hit the floor at the same moment.

Thanks in advance.

- #2

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To simplify issues, we approximate the earth's gravitational field to be uniform such that the value of g remains constant. The gravitational force acting on a body of mass m on earth is then [tex]F_{g} = mg[/tex]. From the simplified version of Newton's Second Law, we have [tex]F = ma[/tex]. Combining, we see that the acceleration a of the body is simply g - independent of its mass.

- #3

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Oh yeah .. that makes sense.

Thanks. :)

Thanks. :)

- #4

HallsofIvy

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In more detail, The gravitational force between two bodies is [itex]F= GmM/r^2[/itex] where G is a universal constant, m and M are the masses of the two bodies and r is the distance between their centers. Take the earth to be one body and the object to be dropped to be the other. The radii of two different objects are so small compared to the radius of earth that "r" can be taken as a constant for any object dropped at the surface of the earth. As Fightfish said, the second law is F= ma so for any object we have [itex]GmM/r^2= ma[/itex] and can cancel the two "m"s: [itex]a= GM/r^2[/itex] for any object dropped at the surface of the earth.

Since two objects always have the same acceleration and start with speed 0 ("dropped" not "thrown down"), the always have the same speed at any time and so always drop the same distance in the same time.

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