Why do two bodies of different masses fall at the same rate (in the absence of air resistance)?I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.BUT Newton's second law states that a = F / m, with a the acceleration of a particle, m its mass and F the sum of forces applied to it.I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don't comprehend why the mass, which is seemingly affecting the acceleration, does not affect the "time of impact".Can someone explain this to me? I feel pretty dumb right now :)

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Why do two bodies of different masses fall at the same rate (in the absence of air resistance)?I&#039;m far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.BUT Newton&#039;s second law states that   a  =  F      /    m, with   a the acceleration of a particle,   m its mass and   F the sum of forces applied to it.I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don&#039;t comprehend why the mass, which is seemingly affecting the acceleration, does not affect the &quot;time of impact&quot;.Can someone explain this to me? I feel pretty dumb right now :)

cartonarepcpo4 · Accepted Answer

it is because the Force at work here (gravity) is also dependent on the massgravity acts on a body with mass m with  F  =  m  gyou will plug this in to  F  =  m  aand you get  m  a  =  m  g  a  =  gand this is true for all bodies no matter what the mass is. Since they are accelerated the same and start with the same initial conditions (at rest and dropped from a height h) they will hit the floor at the same time.This is a peculiar aspect of gravity and underlying this is the equality of inertial mass and gravitational mass (here only the ratio must be the same for this to be true but Einstein later showed that they&#039;re really the same, i.e. the ratio is 1)

Dominick Blanchard · Accepted Answer

Newton&#039;s gravitational force is proportional to the mass of a body,   F  =            G      M              R      2        ×  m, where in the case you&#039;re thinking about   M is the mass of the earth,   R is the radius of the earth, and   G is Newton&#039;s gravitational constant.Consequently, the acceleration is   a  =      F    m    =            G      M              R      2      , which is independent of the mass of the object. Hence any two objects that are subject only to the force of gravity will fall with the same acceleration and hence they will hit the ground at the same time.What I think you were missing is that the force   F on the two bodies is not the same, but the accelerations are the same.

Why do two bodies of different masses fall at the same rate (in the absence of air resistance)? I'm

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