derivation of newton second and third law of motion
Answers
DERIVATION OF NEWTON'S SECOND LAW
According to Newton’s second law: F⃗ =dP⃗ /dt,
where P⃗ = momentum and P⃗ =mv⃗
If the time interval for the applied force is increased, then the value of the applied force will decrease. In cricket players use this while catching the ball. They pull their hands back so that time of contact with ball increases and they would experience less attack due to the motion of the ball.
From Newton’s second law of motion,
F⃗ ∝dP⃗ /dt
F⃗ =k×dP⃗ /dt=kma⃗
For simplicity, the constant of proportionality (k) is chosen to be 1, therefore
F⃗ =ma⃗
DERIVATION OF NEWTON'S THIRD LAW
Second law:-
According to this law, rate of change of linear momentum is directly proportional to the external force applied on a body and this change takes place in direction of force applied.
Let, m=mass of the body
->v=velocity of the body
p=mv=liner momentum of the body
F=external force acting on the body
ΔP=change in linear momentum in the time interval Δt sec.
The derivations is in the pic.
Third law of motion:-
According to this law, every action has equal and opposite reaction. But action acts on one body reaction on another body.
Or,
Every action has equal and opposite reaction and they do not cancel each other.
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