A very dumb question (about different masses and accelerations)

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In summary, the universal law of gravitation states that the force between two masses is proportional to the product of their masses, but the acceleration due to gravity does not depend on the mass. This means that objects of different masses released at the same time will fall to the ground with the same acceleration, as the effect of mass on the force is canceled by the effect on acceleration. This is supported by the equation a= G*M(e)/r^2 where the mass is missing, indicating that acceleration due to gravity is independent of mass.
  • #1
physio
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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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  • #2


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.
 
  • #3


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.
 
  • #4


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.
 
  • #5


This is actually a very valid question and it shows that you are thinking critically about the concepts of mass and acceleration. The universal law of gravitation does state that the force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. However, when we talk about objects falling to the ground, we are dealing with a different force known as the force of gravity. This force is actually a special case of the universal law of gravitation, where one of the masses is significantly larger than the other (in this case, the mass of the Earth).

The reason why different masses fall to the ground with the same acceleration is because the force of gravity is acting on both objects with the same acceleration due to the mass of the Earth. This can be explained by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, the force of gravity is the net force acting on the objects, and since the mass of the Earth is significantly larger than the masses of the falling objects, the acceleration due to gravity is essentially constant for all objects.

In summary, while the universal law of gravitation does state that the force between two objects is directly proportional to their masses, when we are dealing with objects falling to the ground, we are dealing with a special case where the force of gravity acts on all objects with the same acceleration due to the mass of the Earth. I hope this helps clarify any confusion you may have had about this concept.
 

1. What is the relationship between mass and acceleration?

The relationship between mass and acceleration is described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that an object with a larger mass will require a greater force to accelerate it compared to an object with a smaller mass.

2. How does the mass of an object affect its acceleration?

The mass of an object directly affects its acceleration. The greater the mass of an object, the more inertia it has, meaning it will resist changes in its motion. This results in a smaller acceleration for the same amount of force applied, compared to an object with less mass.

3. Can two objects with different masses have the same acceleration?

Yes, two objects with different masses can have the same acceleration if they experience the same amount of force. This can be seen in free fall, where a feather and a brick will accelerate towards the ground at the same rate due to the force of gravity acting on them.

4. How does acceleration change with a change in mass?

Acceleration changes inversely with a change in mass. This means that if the mass increases, the acceleration will decrease, and vice versa. This relationship is seen in the formula F=ma, where mass is in the denominator, indicating the inverse relationship.

5. How does the acceleration of an object change if the net force acting on it changes?

The acceleration of an object changes proportionally with a change in the net force acting on it. This means that as the net force increases, the acceleration will also increase, and vice versa. This relationship is seen in the formula F=ma, where acceleration is directly proportional to the net force.

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