State the Newtons' laws of motion. Derive the 2nd law. Show that 2nd law is the real law of motion.
Answers
According to Newton's 1st law of motion-A object at the state of rest or at at the state of motion wants to remain in the same state unless and until an external force is applied.
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According to Newton's 2nd law of motion, the force applied to an object is directly proportional to mass, acceleration and linear momentum of the object.
DERIVATION-Let their be an object of mass m and velocity v
F is directly proportional to dp/dt where p=linear momentum
F=kdp/dt where k=proportionality constant
F=kdmv/dt
F=kma
Since 1 N force is required to move 1 kg mass at 1m/s²
So k=1
Therefore F=ma
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According to 3rd law of motion, every action has an equal and opposite reaction. Action and reaction act on two different bodies.
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Explanation:
Newton’s second law of motion can be stated as the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.Here we see that, the initial momentum
p1 = m × u
the final momentum
p2 = m × v
The change in momentum is
p2 – p1 = (m × v) – (m × u)
p2 – p1 = m (v – u)
The rate of change of momentum with respect to time is proportional to the applied force. The applied force is
F ∝ m (v – u)/t
or
F ∝ m × a
a = Rate of change of velocity/Time
F = k × m × a
k = proportionality constant.
Hence from the second law of motion, we get force is the product of mass and acceleration i.e F = ma.