F=ma and F=mg whats the differece?

Question

What is the differece between "inertial mass" as in F=ma, and "gravitational mass" as in F=mg?

Also does it matter if we designate diatance as "x" or "d"?

Answer 1

Both types of masses are equivalent, but not Equal in quality. (Save the relativity). Magnetic force does not depend on mass, yet it entails units of mass (ML^2T-^2).

Gravitational Mass: It, whether being absolute or active, is quantity of matter of an object when measured in the given gravity (or weight equivalent). Being measured vis-à-vis “g”, it automatically pertains to accelerated or non-inertial frame of reference (tool-kit arrangement with observer). F= m * g .

Inertial mass: It is quantity of matter of an object when measured in an inertial (non-accelerated or uniformly-paced, or under-rest or obeying-inertia). This the actual mass determined experimentally without any influence of gravity. This mass can be measured even in the absence of gravity (weightlessness) or micro-gravity created artificially. It will be same even on different planets.
F= m * a

I am not going into relativity domain. But, there is a very peculiar characteristic of the “inertial mass”:

Force = mass * acceleration or F= m * a ----- (1)

In inertial conditions, when experiments were done to measure the relationship of m, a and F, we did not have the DEFINITION of UNITS-OF-FORCE or word NEWTONS was not assigned to any physical quantity.

It revealed that F makes ‘m’ to accelerate. When ‘m’ increases acceleration decreases. Also, that acceleration varies inversely with the mass. Thus, it was postulated that
F is proportional to “m” and F is proportional to “a”
So F = k (m*a) till then Units of F were not known.

As it was found that 1 kg mass always ACTUALLY produced 1meter/sec^2 acceleration, therefore, it was decided that let the amount of F be 1 Newton so that k=1. And, constant of proportionality (k) was made dimensionless.

This is very first definition of force 1N = 1 kg-meter/sec^2.

Everywhere else (including that in F=m*g) constant of proportionality (G) has dimensions because now one-NEWTON is defined.

You may not find such aspects of force in any tom-dick-harry’s book. Or even if it is written, we tend to jump over it. It needs self-analysis because it is too tiny a fish to spoil the stream (grades in exams).

*** As regards, denoting distance by “d” or “x”, there is not any hard-and-fast rule, yet there exists an unsaid convention whereby distance is denoted by “d” as a scalar quality and “x” when vector analog is meant or small elemental section is being worked on (dx) for overall calculation over time limits.

Answer 2

There's no real difference, only a specification. You may be confusing things just a little.

The "m" in each equation refers to the mass, and it is the same for both equations. Mass is mass. What you may be confusing is that the equation F=mg is often called the WEIGHT of an object. But again, for emphasis, the mass in each equation is the same.

The "a" in the first equation refers to acceleration of any type, whereas the "g" in the 2nd version refers to the acceleration of gravity. The second equation is a more specfic version of the first.

Other "types of a" are wind resistance acceleration (usually proportional to velocity squared), spring acceleration (usually proportional to how much the spring is compressed or expanded from its natural state), etc. They are all forms of acceleration that can replace the "a" in the first equation.

As for using x or d, it generally doesn't matter if it's a 1-dimensional problem. However, if you're working in 2-d (you can go up and down as well as left and right), then "x" is more appropriate because "y" is, by convention, the vertical axis of a 2d problem.

Answer 3

There is a difference because; mass multiply by a-acceleration is used for moving objects regardless of the gravitational force. F=mg on the other had require the gravitational force to be calculated.
The symbols for the designated distance dose not matter as long as your teacher agrees with it. I mean different teachers may have different opinions.
Hope this would help.... Please read what others have say as well.

Answer 4

Inertial mass and gravitational mass are exactly the same. And it does not make a difference changing x to d as long as you know your coordinate system.

Answer 5

In physics its all about the reference frame you choose. if you choose an accelerating frame of reference neglecting the earth's influence then F=ma is more convenient. if however you choose the earth as a whole and want to particularly measure the accn due to gravity in particular then F=mg is the more practical choice

and it doesnt really matter how u designate distance or any other quantity. its more for the sake of convenience and simplicity that a particular value is selected. bcos if everyone started using their own symbols, then it'd turn out to be one big mess.

Answer 6

Gravity causes an acceleration, that why you can use g or a, it is defined in m/s^2 (meters per seconds square)
Make sure you put what "they"want you to put on your exam paper,
some teachers are really over zealous about applying the exact formula and will add or subtract a point or two depending on the way you write your formula!

ie: for a falling object you better put g even if you know that g is an acceleration.

Some use x instead of d, but I find using d more use full, in the sense that you know it is defined in meters.

Answer 7

"a" is acceleration. it's not a constant. whereas "g" is a constant, which is 9.81. they both have same unit, which is ms^-2.
get it?

Answer 8

their is none lol haha. cant you see lol