Free falling object due to gravity

[robax25]

Homework Statement

The reason why the heavy stone and light stone fall equally because of the ration of force to mass is same. can you explain it please what is ratio of force to mass is same?.

Homework Equations

F=ma and F=Gm1m2/r²

The Attempt at a Solution

As their acceleration is same, they fall to Earth equally.

 

[lekh2003]

Homework Statement

The reason why the heavy stone and light stone fall equally because of the ration of force to mass is same. can you explain it please what is ratio of force to mass is same?.

Homework Equations

F=ma and F=Gm1m2/r²

The Attempt at a Solution

As their acceleration is same, they fall to Earth equally.

If you calculate the actual acceleration due to gravity using the formulas you listed, where is the mass of the object involved?

 

[robax25]

They have different mass and different weight as well. m=F/a. Heavy object has greater force than small object but to get same acceleration heavy object needs twice force compare to light object.

 

[PeroK]

They have different mass and different weight as well. m=F/a. Heavy object has greater force than small object but to get same acceleration heavy object needs twice force compare to light object.

Is there a question here?

 

[robax25]

yes, Actually , I do not understand that what is ratio of fore to mass same?

 

[ehild]

yes, Actually , I do not understand that what is ratio of fore to mass same?

The gravitational force on a mass m is proportional to that mass:

F=GmM/r².

 

[PeroK]

yes, Actually , I do not understand that what is ratio of fore to mass is same?

1) What is the ratio of force to mass for a heavy stone, of mass $m_1$.

2) What is the ratio of force to mass for a light stone, of mass $m_2$?

Assuming they are both the same distance from a large object like the Earth.

 

[robax25]

F1=m1/a and F1=Gm1m2/r² are same value. it is also valid for m2,But for m2(heavy stone) you will get higher value than light stone. F2>F1 so how ratio of force to mass is same? they are different from object to object

 

[Let'sthink]

1) What is the ratio of force to mass for a heavy stone, of mass $m_1$.

2) What is the ratio of force to mass for a light stone, of mass $m_2$?

Assuming they are both the same distance from a large object like the Earth.

Neglecting air resistance, answer to both is observed acceleration, g or = GM/r2, where M is the mass of earth
However I can guess what is at the back of your mind.

Suppose I have an object and we do not know its mass. We go on applying different forces, F on it and note down different accelerations, a. Then we find the ratio F/a for a corresponding pair of F and a. I will get some value. I call it mass of the object, let us call it m.

Now I do entirely different experiment. I measure how much force I must apply on the object so that the force acting due to Earth is completely annulled. Suppose I call that force f. Now I divide this by the the acceleration, g due to gravity of Earth which is independent of mass of the object hence property of earth. If I want I can repeat such an experiment on any other planet or on moon say. Now the ratio of such corresponding f and g will have the dimensions of mass and what ever I get let me call it m'. The first one is called inertial mass and the latter one is called gravitational mass. These two are found to be equal. Or in other words the universal acceleration due to gravity for any mass shows that these two kinds of masses are equal.

I do not know whether I am right. Only this can explain your surprise at the fact which you knew very well still you were asking us to tell the ratio of force to mass!

 

[mjc123]

Are you confused by writing F = Gm1m2/r²? Here m1 and m2 are the two masses that attract each other, e.g the Earth and a stone. But you also seem to be using m1 and m2 for the masses of two stones, one light and one heavy. If we write M for the mass of the earth,
F1 = m1a1 = GMm1/r²
F2 = m2a2 = GMm2/r²
Now see whether a1 and a2 are the same.