Question

what is difference between these two equations :-
(a)F=MA
(b)F=PA
is meaning of FORCE different in these equations
F stands for force
M stands for mass
P stands for pressure
in equation (a)
A stands for acceleration
in equation (b)
A stands for area

Answer 1

There are two equations being mixed in that expression that are often mistaken to be an expression of the same thing.

One of them, F=maF=ma, is a simplified form of Newton’s second law of mechanics:

F=dpdtF=dpdt

which states that the resulting force to which a body is submitted is equal to the rate of change of its momentum with time, which is to say, how much its “movement” is changing. Only when we consider the mass of a body to be constant is that it reverts to its well-known form. In certain situations, though, the mass of a body is also changing with time, and therefore we need to take that into account (for example, a rocket will expel the products of the combustion of its fuel to propel itself, and therefore its mass will change as it is consumed).

The resulting force, in turn, is the result of the combination of all forces that act upon that body - no matter their source. It can be from gravity, from contact with other bodies, magnetic force, and so on.

This is a law that seeks to explain how movement works in the physical world - and it does a wonderful job of doing that. From this apparently simple relation between momentum and force springs the whole of mechanics, with all the results that come from it. Allying it with mathematical principles we can do some very beautiful physics.

The second equation is F=mgF=mg, which is an expression of the force a body will be subject to when in the vicinity of a massive body (such as the Earth or the Sun). It describes one particular force, the gravitational pull that arises between two bodies, which is described by another law that was also published by Newton:

F=GMmr2F=GMmr2

where MM and mm are the masses of the two bodies, rr is the distance between them and GG is the gravitational constant, which is an expression of the strength of the gravitational force itself. In this situation, when we compare the two equations, we end up with

g=GMr2g=GMr2

which is the intensity of the gravitational field at the point where body mm is located. In this sense, even though it has the same basic units of acceleration, g is more accurately described as the field strength at point A, and instead of measuring it as m/s2m/s2, it is better described with N/kgN/kg.

Now, in certain circumstances, when we add up all the forces acting on a body, it turns out that the gravitational pull is much larger than all the other ones, by so much that we can actually discard the contributions from other interactions and use only the force from gravity without having any sensible difference in the end result. When that happens (e.g. free fall in a vacuum) we can actually start working out the problem by assuming that the resulting force on a body is merely the gravitational force, and thus

ma=mgma=mg

which immediately tells us that the body will fall with a rate of acceleration that is equal to g=9,8m/s2g=9,8m/s2 (in the proximity of Earth’s surface).

Answer 2

Hi friend ,

I will explain it in a simple way.

(1) The first equation is the newtons second law of motion.

F∝m (mass of the substance)
F∝a(acceleration due to gravity) (a=9.8m/s²)

(2) The second force condition is used in pressure concepts.

P∝F/A
When area decreases pressure increases.

This equation only becomes
F= PA

F∝P(pressure)
F∝A(area).

Hope this helped you a little!!!
If you have any further dout please contact me!!!