Q.State and explain Newton's 2nd law of motion. Prove that 2nd law of motion is real law of motion.
You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
Start your 14-day free trial to unlock the full solution →Newton's second law, F = dp/dt = ma, is the fundamental law of motion because the first and third laws both follow from it as special/derived cases.
Statement: The rate of change of linear momentum of a body is directly proportional to the net external force applied on it, and this change takes place in the direction of the applied force.
F proportional to dp/dt, so F = k (dp/dt). With SI units chosen so that k = 1:
F = dp/dt
Since p = m v, for a body of constant mass m:
F = d(mv)/dt = m (dv/dt) = m a
which is the familiar form F = ma.
Explanation: This law quantifies how much a given force changes a body's motion — a larger force produces a proportionally larger rate of change of momentum (or, for constant mass, a proportionally larger acceleration), and a larger mass means a smaller acceleration for the same force (inertia).
Proof that the 2nd law is the real law of motion:
- Contains the 1st law: If the net external force F on a body is zero, then from F = dp/dt = 0, we get p = constant, meaning the body's momentum (and velocity, for constant mass) does not change — it continues in its state of rest or uniform motion in a straight line unless acted upon by a force. This is exactly Newton's first law (the law of inertia), so it is a special case (F=0) of the second law.
- Contains the 3rd law: Consider two isolated bodies A and B interacting only with each other (no external forces), so the total momentum of the system p_A + p_B is conserved (constant) at every instant: d(p_A + p_B)/dt = 0, so dp_A/dt = -dp_B/dt By the second law, dp_A/dt is the force F_AB exerted on A by B, and dp_B/dt is the force F_BA exerted on B by A. So: F_AB = -F_BA which is exactly Newton's third law (action and reaction are equal and opposite) — derived here from the second law together with conservation of momentum of an isolated system. Since both the first and third laws can be obtained as consequences of the second law, the second law is regarded as the most fundamental, or 'real', law of motion, with the other two being special/derived cases. …
Unlock everything free for 14 days
- Full step-by-step solutions
- Concept-first explanations
- Methods, shortcuts & mistakes
- PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.