GravityDate: 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, Salma 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 by 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 http://mathforum.org/dr.math/ |
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