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Date: 05/07/99 at 06:07:41
From: Salma Al-Sayyad
Subject: Gravity: Which ball will hit the ground first

Dear Sir,

Which ball will hit the ground first (and why), the heaviest one or 
the lighter, if:

1. they are dropped from the same level.
2. they are rolling across the slope.

Thanks from Egypt,

Date: 05/07/99 at 08:09:45
From: Doctor Jerry
Subject: Re: Gravity: Which ball will hit the ground first

Hi Salma,

If air resistance is ignored, the balls will hit the ground at the 
same time if they are dropped from the same level or if they are 
rolling down an inclined plane.

The reason is that the net force on a ball of mass m is

   F = (G*M*m/R^2)*u,

where G is the universal gravitational constant, M is the mass of the 
earth, R is the radius of the earth, and u is a unit vector directed 
from the ball toward the center of the earth.  Also, using Newton's 
second law, the net force and the acceleration of the ball are related 

   F = m*a

Equating these two expressions we find

   (G*M*m/R^2)*u = m*a

and the mass m of the ball cancels from both sides, giving

   a = g*u

where, in the metric system, g = 9.8 m/s^2.

So, the mass of the ball doesn't matter. The acceleration (of gravity) 
is the same for heavy or light balls. On an inclined plane, it's much 
the same, except only part of the accleration of gravity acts. Here we 
would ignore friction.

If you try to take into account friction or air resistance, the 
problems become much harder.

- Doctor Jerry, The Math Forum   
Associated Topics:
High School Physics/Chemistry

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