Q.State and explain Newton's second law of motion.
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Start your 14-day free trial to unlock the full solution →Newton's second law states that force equals the rate of change of momentum (F = dp/dt), which simplifies to F = m a when the mass of the body stays constant.
Statement: The rate of change of linear momentum of a body is directly proportional to the applied net external force, and this change in momentum takes place in the same direction as the applied force.
Mathematical form: If a body of mass m has momentum p = m v, and a net force F acts on it, then:
F is proportional to dp/dt
Introducing a constant of proportionality k (made equal to 1 by suitable choice of units, such as the newton):
F = dp/dt = d(mv)/dt
If the mass m of the body remains constant while its velocity changes:
F = m (dv/dt) = m a
where a = dv/dt is the acceleration produced in the body.
Explanation: This law quantifies the idea introduced qualitatively by the first law (that a net force is needed to change a body's state of motion) - it tells us exactly how much a given force changes the momentum, and hence the velocity, of a body of a given mass. A larger force produces a proportionally larger rate of change of momentum (and hence, for constant mass, a larger acceleration); a larger mass requires a proportionally larger force to produce the same acceleration. The direction of the acceleration produced is always along the direction of the net applied force. This law also reduces correctly to Newton's first law: if F = 0, then dp/dt = 0, i.e. momentum (and hence velocity, for constant mass) stays constant.
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