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MOMENTUM
Momentum of a particle (p) is equal to the mass of the particle (m) times velocity of the particle (v). So, p = mv
NEWTON LAWS OF MOTION
(i) First Law (Law of Inertia): Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state.
(ii) Second Law: The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.
So, F = dp/dt
This results force acting a body F is equal to the mass of the body m times acceleration of the body a.
So, F = ma
(iii) Third Law: To Every action there is an equal and opposite reaction.
F_{AB} =  F_{BA}
So, J = Ft
= mv – mu
(a) The lift possesses zero acceleration (fig1): W = m
(b) The lift moving upward with an acceleration a (fig2):
W = mg + ma
W= mg + mg
W= 2 mg
(c) The lift moving downward with an acceleration a (fig3):
W = mg – ma
W = mg – mg
W = 0
NOTE
When the velocity of a body is comparable to the velocity of light, inertial mass changes with velocity in accordance with following formula,
m_{i} = m_{i0}/√(1v^{2}/c^{2})
Here m_{i0} is the rest mass of body, v is the velocity of body and c is the velocity of light.
(b) Driven body moving horizontally:
Acceleration of the system, a = (M /M+m) g
Tension in the string, T= (Mm/M+m) g
The force on the pulley, F= [√2 (Mm) /M+m] g
Here g is the free fall acceleration.
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