derivation of second law of motion. no spaming
Answers
Answer:
Let us derive the relation of force F = ma from Newton’s second law:
According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.
It means that the linear momentum will change faster when a bigger force is applied.
Consider a body of mass ‘m’ moving with velocity v.
The linear momentum of a body is given by:
p = mv
Now According to Newton’s 2nd Law of Motion:
Force is directly proportional to rate of change of momnetum, that is
F α dp/dt
F = k dp/dt
F = k d(mv)/dt
F = k md(v)/dt
F = k ma
Experimentally k =1
F = k ma
Which is the required equation of force.
Answer:
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Derivation:
Suppose an object of mass m has an initial velocity u. When a force F is applied in the direction of it's velocity for time t, it's velocity becomes v.
•°• The initial momentum of the object = mu
It's final momentum after time t = mv.
•°• Rate of change of momentum = (Change of momentum) / Time
•°• Rate of change of momentum =
(mv- mu) / t
= m(v - u) / t
= m × a .........(v - u / t = a)
P = ma.
According to Newton's second law of motion, the rate of change of momentum is directly proportional to applied force.
•°• ma α F
•°• F = K ma
F = ma
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