Question

Prove. That. F. =. Mg

Answer 1

Derivation no. 1:

Force is change in momentum per unit time.

Or,

Force is directly proportional to (mv - mu)/t

Taking “m” as common.

F directly proportional to {m(v-u)}/t

Now, acceleration = (v-u)/t

Thus,

F directly proportional to m × a

Now we need a constant ‘k’ to convert it into an equation, where k is taken as 1 according tl C.G.S. system.

Hence F = ma

Derivation no. 2:

Force is directly proportional to acceleration.

Or, F directly proportional to ‘a’.

Now, we need a constant ‘k’ to convert this into an equation, where ‘k’ is taken as mass of the moving object om which force is applied.

Hence,

F = m × a
★★★★★★★★★★
Force = mass * acceleration of gravity
Newtons = kilograms*metres/second^2
the gravitational constant for acceleration is 9.81m/s^2 (if i remember correctly)
As an object falls towards earth it will accelerate at 9.81m/s^2 until it reaches terminal velocity at point it will cease to accelerate. Acceleration is the change of speed for a certain time.

This is an equation that uses one of Newtons laws; F=ma, force= mass*acceleration. Another law is for every reaction there is an equal and opposite reaction, so if something was moving through space where there is no force on it at all it would continue to move in that same direction forever (law of inertia) unless affected by force of another object. Also energy cannot be created or destroyed, just converted from one form of energy to another.

Answer 2

hey friend

The expression “F=mgF=mg” or “Force = (mass * gravitational acceleration)” is a specific application of Newton’s second law of motion as defined in 1686. When we use F=mgF=mg, we specifically define an object’s weight.
More generally the second law is written “F=maF=ma” or “Force is equal to the product of mass and acceleration.” It applies to forces due to any acceleration, not only those due to gravitational acceleration. However, even this is a specific application of Newton’s second law.
The most general form of Newton’s second law states:
F=ddt(mv)F=ddt(mv)
The expression “mvmv” — the product of mass and velocity — is simply an object’s momentum pp.
p=mvp=mv
Now what is the ddtddt part all about? That’s part of differential calculus which, incidentally, Newton developed himself (over breakfast one morning so the story goes) to better describe physical phenomena like force.
ddt(mv)ddt(mv) simply means that we are describing how momentum changes with time. What is the rate change of momentum? This is how Isaac Newton defined force. Force is equal to a body’s rate of change in momentum. Because mass is usually constant, we can usually take it out:
F=mddtvF=mddtv
Force is equal to mass times the rate change in velocity. Well, the change in velocity is simply acceleration, so we’re back to the original equation:
F=maF=ma
Okay, so where did all this about mass and momentum come from? As it turns out, Newton had to define that in his first law, or his law of inertia.

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force.

Newton had to create this law to define what inertia is. Inertia is a property of matter that resists change. He then quantified inertia in the second law by calling it mass. An object’s mass is a measure of its inertia. An object’s momentum is a property of a body defined by the product of its inertia and velocity. That’s basically the first law.
Then, still in the first law, Newton stated force is something that changes momentum (“…will continue with the same speed and direction unless acted upon by an external force”). The force of an object is defined as the rate at which it changes momentum. That’s the second law.
Isaac Newton defined all these things with his laws of motion to help us understand the workings of nature. Basically, F=maF=ma because that is how force is defined.