Newton's Force: Same Distance, Different Masses?

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In summary, the formula for force given by Newton is correct because it takes into account the acceleration due to gravity, which is independent of mass. This means that even if two objects with different masses fall from the same distance and time, they will still experience the same acceleration. This is because the force due to gravity is proportional to the mass, meaning that the heavier object will also have a greater force acting on it, but it will also require a greater force to accelerate it. Therefore, the acceleration remains the same, regardless of the mass.
  • #1
sambarbarian
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hi! i wanted to ask that if all the things fall in the same time from the same distance .. how can the formula for force given by Newton be correct ?

for example . if i take two balls with masses 10:1 .. then by the formula the force/acceleration should be 98 m/s^2 for 1st ball and 9.8 for the other .

i am sure that there is an explanation , or I am wrong :)

this may be a silly question for some people but i would like to know the answer :)
 
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  • #2
hi! i wanted to ask that if all the things fall in the same time from the same distance .. how can the formula for force given by Newton be correct ?
Because the balls experience different forces. (The heavy ball experiences a stronger force - that's what "heavy" means.)

Newton's law is F = ma
The force due to gravity (close to the Earth's surface) is F = mg where g=9.8N/kg

This becomes mg = ma and the masses cancel out giving you a = g = 9.8m/s/s no matter what the mass is.

It also works with the full formula for gravity:[tex]F=\frac{GMm}{r^2}=ma[/tex]... again the masses cancel out (comparing little m's).
 
  • #3
just to add on to that:

calculating the gravitational field strength (it's rate of acceration) if a fairly simple calculation:

g= -GM/d^2
(note the negative sign is due to the fact that gravity is an attractive force)

g=gravitation field strength
G=universal gravitational constant
M=mass of body
d=distance from center of "M"
 
  • #4
One way to think of it is that the heavier mass has a greater force acting on it BUT it also needs a greater force to accelerate it. Net result is that acceleration is independant of mass.
 
  • #5
... rereading post #1, OP seems to be equating force with acceleration ... easy to do because of the way we commonly talk about gravity. Notice how he has the heavier mass having the greater acceleration?

Taking what was written at face value: force/acceleration = mass (but I don't think OP means the "/" to indicate division.)
 
  • #6
Simon Bridge said:
Taking what was written at face value: force/acceleration = mass (but I don't think OP means the "/" to indicate division.)

yeah , it was just a slash .
 
  • #7
force-slash-acceleration doesn't work well either though ... which is why I thought it may have been a pointer to greater understanding. You OK with the acceleration due to gravity being independent of mass now?
 

FAQ: Newton's Force: Same Distance, Different Masses?

1. What is Newton's Force: Same Distance, Different Masses?

Newton's Force: Same Distance, Different Masses is a concept in physics that explains the relationship between mass and force. It states that if two objects with different masses are placed at the same distance from each other, the object with a greater mass will exert a greater force on the other object.

2. Who is Newton and why is this concept named after him?

Sir Isaac Newton was an English physicist and mathematician who is widely recognized as one of the most influential scientists of all time. He developed the laws of motion and gravitation, which form the basis of this concept and many other principles in physics. This concept is named after him in recognition of his contributions to the field of physics.

3. How does this concept relate to Newton's other laws of motion?

This concept is closely related to Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. It also ties in with Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Both of these laws help to explain why an object with greater mass exerts a greater force on another object at the same distance.

4. Can you provide an example of this concept in action?

One example of this concept is when a heavy weight and a lighter weight are placed on opposite ends of a seesaw. The heavier weight will cause the seesaw to tilt towards it, exerting a greater force on the lighter weight and causing it to move upwards. This is because the heavier weight has a greater mass and therefore exerts a greater force on the seesaw.

5. Are there any exceptions to this concept?

This concept holds true in most situations, but there are a few exceptions. One exception is when one of the objects is significantly larger than the other, causing the distance between their centers of mass to be different. In this case, the concept would not apply as the distance between their centers of mass would also affect the force exerted between the two objects.

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