derive third law of motion through second law
Answers
Answer:
Explanation:
Newton's second law states that the net force applied on a body is equal to the rate of change in its momentum. Mathematically, ... the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction).
,Derivation of Newton’s third law of motion from Newton’s second law of motion Consider an isolated system of two bodies A & B mutually interacting with each other, provided there is no external force acting on the system. Let FAB, be the force exerted on body B by body A and FBA be the force exerted by body B on A. Suppose that due to these forces FAB and FBA, dp1/dt and dp2/dt be the rate of the change of momentum of these bodies respectively. Then, FBA =
d
p
1
dt
dp1dt ---------- (i) => FAB =
d
p
2
dt
dp2dt ---------- (ii) Adding equations (i) and (ii), we get, FBA + FAB =
d
p
1
dt
dp1dt +
d
p
2
dt
dp2dt ⇒ FBA + FAB =
d(
p
1
+
p
2
)
dt
d(p1+p2)dt If no external force acts on the system, then
d(
p
1
+
p
2
)
dt
d(p1+p2)dt = 0 ⇒ FBA + FAB = 0 ⇒ FBA = - FAB---------- (iii) the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction