if you drop two objects that are the same exact size and shape but one
weighs more than the other, which one will fall faster?

Hi!!


Previous note:
Your question states a problem for regarding two different objects
with different weights. For all practical purposes, at least in this
problem, different weight implies different masses and viceversa.

To answer your question we need to use the Newton's Gravity Law:
"Every particle in the universe attracts every other particle in the
universe with a force that is proportional to the product of the
masses and inversely proportional to the square of the distance
between the particles."

If two objects with masses (M1) and (M2) are separated by a distance
(R) the magnitude of the gravitational force (F) between them is:

            M1 x M2
F = G x  -------------
              R^2

G is called the universal gravitational constant.



We also know that for an object, given its mass (m) and the force (F)
applied on it, the acceleration (a) due the force is:

a = F / m    

This come from the known raltionship between force, mass and acceleration:
F = m x a


When we consider that force applied to an object with mass M due the
gravitational attraction, the acclereation that results from the above
formula is the gravitational acceleration g:

g = F / M

For this object, if Me is the mass of the Earth and R is the distance
from the object to the center of the Earth we have that:

F = G x Me x M / R^2

Combining the last two formulas we have:

g = F / M =
  = (G x Me x M / R^2) / M =
  = (G x Me x M) / (R^2 x M) =
  = G x Me / R^2

As you can see the mass of the object had disappeared from the
formula, this means that the acceleration due to the earth's
gravitational field is independent of the mass of the object.

Then if we ignore the effects of the air resistance every object will
be accelerated in the direction to the center of the Earth with the
same acceleration magnitude.
Because the shape and size of the two objects are the same, the
effects of the air resistance will be the same for both, so we can
ignore in this case the air resistance. Then they will land at the
same time if they are dropped at the same height.


For additional reference see:
"Newton's Law of Gravity":
http://zebu.uoregon.edu/~soper/Orbits/newtongrav.html

"The Law of Universal Gravitation":
http://www.curtin.edu.au/curtin/dept/phys-sci/gravity/intermed/inter.htm

"Newton's Law of Gravity":
http://www.astronomynotes.com/gravappl/s1.htm

"The Force of Gravity":
http://www.school-for-champions.com/science/gravity.htm

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Search strategy:
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I hope that this helps you. Please feel free to request for any
clarification needed before rate this answer.


Regards.
livioflores-ga

You may find this article interesting:

http://solarsystem.nasa.gov/scitech/display.cfm?ST_ID=505

In theory, if the conditions are the same (i.e. all the variables are
the same, wind speed, etc..) a 10lb weight will land the exact same
time as a 20lb weight.

If you drop the objects with the atmosphere present, the heavier one
will fall faster (assuming that they have the same air resistance,
which is related to surface area). Also, if you roll the two objects
down a hill that levels out at the bottom, the heavier one will have
more momentum and reach the end first. But if you drop the two objects
in a vacuum, they will fall exactly the same.

In Newtonian terms the rate off fall will be identical but General
Relativity will give you a different answer -- though incredibly
small. In earth gravity, with objects you can carry, the difference
will be vastly less than the radius of an atom. Huge bodies however,
especially if moving fast, distort space and time. By similar token,
the angles of an equilateral triangle are not quite 60 degrees, not
that one could ever measure the deviation though.

Best