Derive the second law of motion
The second law of motion can be derived by applying Newton's laws of motion. The statement of the second law is: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be represented as:
F = ma
Where:
F = net force acting on the object
m = mass of the object
a = acceleration produced by the net force
To derive this equation, let's consider a scenario where a force F is applied to an object of mass m, and it causes an acceleration a.
According to Newton's first law of motion, if no net force acts on an object, it will remain at rest or continue to move with a constant velocity. So, the initial velocity (u) of the object is zero, and after a certain time t, it attains a final velocity (v).
Using the basic equation of motion:
v = u + at
Since the initial velocity is zero, the equation simplifies to:
v = at
Now, by using the definition of acceleration:
a = (v - u)/t
Substituting the value of v from the earlier equation, we have:
a = (at - 0)/t
a = a
This equation shows that the acceleration of the object is equal to the acceleration produced by the net force.
Now, according to Newton's second law, the acceleration is directly proportional to the net force and inversely proportional to the mass. Mathematically, this can be written as:
a ∝ F/m
Introducing a constant of proportionality, we get:
a = k(F/m)
Simplifying further, we find:
F = ma
This equation is known as Newton's second law of motion, where the net force acting on an object is equal to the product of its mass and acceleration.