State newton's second law of motion and prove that newton's first law of motion is a special case of newton's second law of motion
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Newton's law of motion:-
1st law:-
Object in motion tends to stay in motion and object at rest tends to stay at rest unless acted upon by an unbalanced force.
2nd law:-
Force equal mass times acceleration(F=MA)
3rd law:-
For every action there is an equal and opposite reaction.
Newton’s first law of motion
Balanced and unbalanced force
‘An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it.’
When an object is at rest or in uniform motion along a straight line, it does not mean that no force is acting on it. Actually there are a number of forces acting on it, but they cancel one another so that the net force is zero. Newton’s first law explains the phenomenon of inertia, i.e. the inability of an object to change its state of motion on its own. It also explains the unbalanced forces which cause a change in the state of an object at rest or in uniform motion.
All instances of inertia are examples of Newton’s first law of Motion.
Newton’s second law of motion
Momentum (P)
Momentum (P) : Momentum is the product of mass and velocity of an object. P = m v.
Momentum is a vector quantity.
‘The rate of change of momentum is proportional to the applied force and the change of momentum occurs in the direction of the force.’
Suppose an object of mass m has an initial velocity u. When a force F is applied in the direction of its velocity for time t, its velocity becomes v.
The initial momentum of the object = mu,
Its final momentum after time t = mv
Rate of change of momentum =Change of momentum/ Time.
= mv- mu/ t
= m(v-u)/ t
= ma
According to Newton’s second law of motion, the rate of change of momentum is proportional to the applied force.
F = k ma (k = Constant of proportionality and its value is 1).
F = m × a