The Potential Theory Of Power

Introduction:

We know that what is force. To determine the value of force, we use this formula: F=ma. If we know the value of object’s momentum, mass and displacement, we can determine the force which was applied on the object. 

Abstract: 

Force is which thing can change the shape of an object. Here we will discuss about the relationship between force, momentum, mass and displacement. 

Method: 

We know that- v²=u²+2as

                     Or, v²= 2as          [u=0]

                     Or, 2as= v²          [Transforms]

                     Or, a= v²÷2s.       [Transforms]

                    So, a= v²÷2s__________(i)

We know that- F=ma

                          =m× v²÷2s

                          =mv²÷2s

                          =m²v²÷2ms  

                          =p²÷2ms

So, F=p²÷2ms__________(ii)

If p= 2p then-

               F'= (2p)²÷2ms

                  = 4p²÷2ms

F'÷F= (4p²÷2ms)÷(p²÷2ms)

       = (4p²÷2ms)×(2ms÷p²)

       = 4

So, F'= 4F

If p= ½p then-

              F’= (½p)²÷2ms

                  = ¼p²÷2ms

                  = p²÷8ms

F'÷F= (p²÷8ms)÷(p²÷2ms)

       = (p²÷8ms)÷(2ms÷p²)

       = ¼

So, F=¼F

If the square value of the momentum of an object increases, then the value of the force of the object increases proportionally. If the square value of the momentum of an object decreases, then the value of the force of the object decreases proportionally.

So, p²∞F_______(iii)

If ms= 2ms then-

   P'= p²÷2(2ms)

      = p²÷4ms

So, P'÷P= p²÷4ms ÷ p²÷2ms

              = p²÷4ms × 2ms÷p²

              = ½

So, P'= ½P

Again, If ms= ½ms then-

   P'= p²÷2(½ms)

      = p²÷ms 

So, P'÷P= p²÷ms ÷ p²÷2ms

              = p²÷ms × 2ms÷p²

              = 2

So, P'=½P

If the value of object’s mass and displacement  increases, the value of the force  of that object decreases. Again, the value of object’s mass and displacement decreases, the value of force  of that object increases. 

So, P∞1÷2ms________(iv)

The graph of iii no. equation- 

The graph of iv no. equation- 

From iii and iv no. equation- 

        p²∞F_______(iii)

        F∞1÷2ms________(iv)

So, F∞p²×1÷2ms

Or, F∞p²÷2ms

Or, F=kp²÷2ms

So, F=kp²÷2ms________(v)

If k=1 then-  F=p²÷2ms

Result: 

So, we can say that- 

The value of object’s force is proportional to the square value of the momentum of that object and disproportional to the value of its mass and displacement.

Conditions of this law: 

There are some conditions of this law. They are-

i) The object should be a moving object. 

ii) This formula applies to moving objects in a plane. This formula does not apply to tilted surfaces, freely falling objects and stationary objects.

Conclusion: 

So, if we know the value of object’s momentum, mass and displacement , we can find out the force  of that object.