Question

Explain equation of force.

Answer 1

Hint: In order to solve this question, we are going to first define what a force is and how it is expressed mathematically, also to derive the various forms of the equations of the force and the units of force that include the SI unit of the force and the various non-SI units too.

Formula used:
The equation of the force is given by
$ F = mass \times acceleration \\$
$ \Rightarrow F = ma \\ $

Complete step-by-step answer:
Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction. The direction towards which the force is applied is known as the direction of the force and the application of force is the point where force is applied. Mathematically, the force is defined as the product of the mass and acceleration. The unit of force is kilogram metres per second square. The SI unit of the force is newton \[\left( N \right)\]. Other units of force are dyne, pound-force, kilo pound.

$ F = mass \times acceleration \\$
 $ \Rightarrow F = ma \\ $
Now the acceleration is given by\[a = \dfrac{v}{t}\],
Where,
$ v = velocity \\$
$ t = time\,taken \\$
Thus, force can also be written as
\[F = \dfrac{{mv}}{t}\]
Now as the momentum formula is given by
\[p = mv\]
Thus, another form of equation of force is
\[F = \dfrac{p}{t}\]
Now, if there is a small change in momentum \[dp\] in a period of time \[dt\], therefore, the equation of force becomes
\[F = \dfrac{{dp}}{{dt}}\]

Note: It is important to note that The Force can be measured using a spring balance. The force basically changes the motion of the body which is defined as a change in speed or change in direction. The work done on a body can also be determined from the force by multiplying it by displacement.