Why can't we combine Newtons 3rd and 2nd law of motion?
Answers
Explanation:
Newton's second law of motion is F=ma
That is we have:-
F=m(v−
t
u
) thus, Ft=mv−mu.
Now,When F=0, then v=u. That is the absence of force,The object continue to move with same velocity
throughout.
Now,when F=0 and u=0, then v=0. That is , an object at rest if no force is acting on it.
Thus,
Newton's first law is derived from the second law.
Now let us consider a system of 2 bodies 1&2 and considers that there is no external force acting.
Now let F
12
be the force acting on 2 by 1 and F
21
be the force acting on 1 by 2.
The rate of change of momentum of 1=
dt
dp
1
and rate of change of momentum of 2=
dt
dp
2
Thus, according to Newton second law of motion F
12
=
dt
dp
2
and F
21
=
dt
dp
1
Adding both the above equation, we get:-
F
12
+F
21
=
dt
dp
2
+
dt
dp
1
=d(p
2
+p
1
)/dt
We know that, no force is applied.
Thus momentum change will also be 0 change in velocity occurs.
Thus
dt
d(p
1
+p
2
)
=0
Therefore, F
12
+F
21
=0
That is F
12
=−F
21
Thus, Newton's third law is proved with Newton's second law.
Hence,
Explanation:
Newton's second law of motion is F=ma
That is we have:-
F=m(v−
t
u
) thus, Ft=mv−mu.
Now,When F=0, then v=u. That is the absence of force,The object continue to move with same velocity
throughout.
Now,when F=0 and u=0, then v=0. That is , an object at rest if no force is acting on it.
Thus,
Newton's first law is derived from the second law.
Now let us consider a system of 2 bodies 1&2 and considers that there is no external force acting.
Now let F
12
be the force acting on 2 by 1 and F
21
be the force acting on 1 by 2.
The rate of change of momentum of 1=
dt
dp
1
and rate of change of momentum of 2=
dt
dp
2
Thus, according to Newton second law of motion F
12
=
dt
dp
2
and F
21
=
dt
dp
1
Adding both the above equation, we get:-
F
12
+F
21
=
dt
dp
2
+
dt
dp
1
=d(p
2
+p
1
)/dt
We know that, no force is applied.
Thus momentum change will also be 0 change in velocity occurs.
Thus
dt
d(p 1 +p 2 ) =0
Therefore, F 12 +f 21 =0
That is F
12
=−F
21
Thus, Newton's third law is proved with Newton's second law.
Hence,