A very dumb question (about different masses and accelerations)

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Different masses fall to the ground with the same acceleration due to the cancellation of mass in the equations of motion. According to the universal law of gravitation, while the force acting on each mass differs, the acceleration remains constant because it is determined by the gravitational force divided by the mass. This is expressed in the equation a = F/m, where the mass cancels out when substituting the gravitational force. Thus, all objects, regardless of mass, experience the same acceleration due to gravity. The principle illustrates that gravity affects all masses equally in a vacuum.
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Why do different masses released at the same time fall to the ground with the same acceleration. Isn't the universal law of gravitation F=G*M(e)*m/r^2? i.e. if masses are unequal the force on both the objects will be different and hence acceleration will be unequal...
 
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physio said:
Why do different masses released at the same time fall to the ground with the same acceleration. Isn't the universal law of gravitation F=G*M(e)*m/r^2? i.e. if masses are unequal the force on both the objects will be different and hence acceleration will be unequal...

Please start by reading the FAQ subforum in the General Physics forum

Zz.
 


physio said:
Why do different masses released at the same time fall to the ground with the same acceleration. Isn't the universal law of gravitation F=G*M(e)*m/r^2? i.e. if masses are unequal the force on both the objects will be different and hence acceleration will be unequal...

F=ma
a=F/m ...(1)
From your post,
F=G*M(e)*m/r^2

Subtitute in equation (1)

a= F/m=(G*M(e)*m/(r^2m)= G*M(e)*/r^2
You see m is missing in final equation.
Acceleration due to gravity does not depend on the mass.
 


physio said:
Why do different masses released at the same time fall to the ground with the same acceleration. Isn't the universal law of gravitation F=G*M(e)*m/r^2? i.e. if masses are unequal the force on both the objects will be different and hence acceleration will be unequal...


Increasing the mass does indeed increase the force but increasing the mass also reduces the acceleration (f=ma so a=f/m).

Overall the mass cancels as per the answer by azizlwl.
 

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