Physics Spl

Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that distance. That is: F = kX, where k is a constant factor characteristic of the spring: its stiffness, and X is small compared to the total possible deformation of the spring.
The law is named after 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis (As the extension, so the force or the extension is proportional to the force).
Hooke's equation holds in many other situations, where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, and the filling of a party balloon. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.

Newton's second law of motion is F = MA. Thus, Ft = mv - mu.
Now, when F = 0, then v = u. In the absence of force, the object continues to move with same velocity throughout.
Now, when F = 0 and u = 0, then v = 0. That is, an object at rest will remain at rest if no force is acting on it. Thus, Newton's first law is derived from second law.
Now, let us consider a system of 2 bodies 1 and 2, and consider that there is no external force acting. Now, let F12 be the force acting on 2 by 1 & F21 be the force acting on 1 by 2.
The rate of change of momentum of 1 = dp1/dt and rate of change of momentum of 2 = dp2/dt. Thus, according to Newton's second law of motion F12 = dp2/dt and F21 = dp1/dt
Adding both the above equations, we get
F12 + F21 = dp2/dt + dp1/dt = d(p2+p1)/dt
We know that, no force is applied. Thus, momentum change will also be 0 because no change in velocity occurs.
Thus, d(p1 + p2)/dt = 0
Therefore, F12 + F21 = 0
That is, F12 = - F21.
Thus, Newton's third law is proved with Newton's second law.