Inertial Mass

[rahuldandekar]

Inertial mass is the inertia of a body, the ratio of the force applied to the acceleration. Now, all wonder why the inertial mass is equal to the gravitational mass.

Now, normal forces that we apply are electromagnetic in origin. The Electromagnetic force also obeys the inverse square law, like gravity, on normal scales. So, the same force that gravity applies, if applied by a normal object on another one, should prodce the same acceleration as that produced by gravitation.

So why should anybody wonder, before Einstein. why the two are equal?

Thanks in advance.

[antoniseb]

Originally posted by rahuldandekar@Dec 6 2004, 04:04 PM
Now, normal forces that we apply are electromagnetic in origin. The Electromagnetic force also obeys the inverse square law, like gravity, on normal scales.
I don't know what you're talking about here. If I take my hand and push an object [a baseball for example], I am applying a force to it and accelerating it. You can say that at a microscopic level electromagnetic forces come into play in this force, as the electron clouds in my skin are repelling the electron clouds in the surface of the baseball, but there are also other forces involved, and none of these are inverse square law forces, even the EM ones in my hand.

That being said, I don't follow how this relates to inertial mass and gravitational mass equivalence [before or after Einstein].

[rahuldandekar]

Sorry, But I have read in several books about normal forces being electromagnetic. That's why I asked the question.

[Gwen]

Rahuldandekar,
Hi, of course if the columb force is equal to the gravitational force you will see the same acceleration, (using g=GM/r(sq) ) if as i say it is equal to kqq/r(sq) however when you are saying normal force i think you are talking about normalizing a E field or E potential, this normalized force is not the same thing as a Normal force considered in classical mechanics.
Hopefully this helps somewhat.

[ferg.c.]

Originally posted by rahuldandekar@Dec 6 2004, 04:04 PM
So, the same force that gravity applies... should prodce the same acceleration as that produced by gravitation.


I think this is rather self-evident, don't you?
Ferg :)

[ferg.c.]

Hi Rahul,

Here's the inverse square law:

First, the story:
The Interplanetary Forestry Comission just replanted a forest, taking all the trees from Planet X (diameter of 10 km) and planting them on planet Y (diameter 20km). As they suspected the forest was a quarter as dense on the new planet. This is also an application of the inverse square law which as you can see has nothing to do with light or gravity.

Now for the math:
Anything radiating spherically from a single point like light, gravity etc. follow a pattern. Imagine the surface of a sphere as representing the influence of the radiation at a distance r in all directions. Then the total influence is

4pi * r^2 (the surface area of the sphere).

if we take a solid angle from the centre "theta" and find the area of influence within this angle at the surface when the angle tends to 0 ( we are looking now at a straight line coming from the centre) we find

A= 2theta * r^2

so the ratio of this surface to the total surface area is

(2theta * r^2)/(4pi * r^2)

dividing through by 2r^2 we get

theta/2pi

if the radius of the original sphere is increased by a coeficient "a" then the surface area of the new sphere is

4pi * r^2 * a^2

and since our line cross section will be the same at any distance, the ratio of this surface area to the new sphere will be

(2theta * r^2)/(4pi * r^2 * a^2)

or

theta/(2pi * a^2) or (theta/2pi) * 1/a^2

so you can see that the ratio of the total influence from the first sphere to the second at any point on thier surfaces is decresed by the inverse of the square of the radial coefficient.

Now go re-work that for the trees in the forestry comission story and you wont have any more nightmares about the inverse square law.

Cheers
Ferg :)