Free falling object due to gravity

In summary: They are not, because a stone of mass m1 is heavier than a stone of mass m2. So the ratio of F1/F2 is not the same as the ratio of m1/m2.In summary, the ratio of force to mass is the same for both the heavy and light stones because they fall to the ground at the same rate due to the gravitational force.
  • #1
robax25
238
3

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.
 
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  • #2
robax25 said:

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?
 
  • #3
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.
 
  • #4
robax25 said:
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?
 
  • #5
yes, Actually , I do not understand that what is ratio of fore to mass same?
 
  • #6
robax25 said:
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.
 
  • #7
robax25 said:
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.
 
  • #8
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
 
  • #9
PeroK said:
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!
 
  • #10
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.
 
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Likes PeroK

1. What is a free falling object due to gravity?

A free falling object due to gravity is any object that is falling towards the Earth's surface under the influence of gravity alone. This means that there are no external forces acting on the object, such as air resistance or propulsion.

2. How does the acceleration of a free falling object due to gravity change?

The acceleration of a free falling object due to gravity is constant and does not change, regardless of the mass or size of the object. This acceleration is equal to the acceleration due to gravity (9.8 m/s^2) and is always directed towards the center of the Earth.

3. What factors affect the speed of a free falling object due to gravity?

The speed of a free falling object due to gravity is affected by the height from which it is dropped, the acceleration due to gravity, and the presence of air resistance. Objects with a smaller mass will fall slower than objects with a larger mass, but both will experience the same acceleration due to gravity.

4. How is the distance traveled by a free falling object due to gravity calculated?

The distance traveled by a free falling object due to gravity can be calculated using the formula d = 1/2gt^2, where d is the distance in meters, g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds. This formula assumes that the object is dropped from rest and there is no initial velocity.

5. Can the acceleration due to gravity change for a free falling object?

No, the acceleration due to gravity does not change for a free falling object. This is a fundamental constant in physics and is independent of the mass or size of the object. However, the acceleration may appear to change if other forces, such as air resistance, are present.

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