newton's fundmental law...ie, newton's second law---how can the third law be derived from it?

Question

its said both newton's 1st n 3rd laws can be derived from the second law ...i have figured out for the first law...but what about the third one...everytime i try to prove it,something outsied the fundamental law comes in...

see,...alst time i asked a physics Q,some ppl answered wrongly...plz dont do that...answer only if u know it for sure...or u guess it can be right--i have no problem with that...we have to go wrong to straighten oursleves!

i am n the 10th...:15 years....
this is not given in my text book..it was just stated in it that this is so...i have figured rest of the things by myself

i must thank u,enem21

the basic problem is that cute girl...how did u say that conservation of momentm came from second law of motion?

excuse moi! mr.everyone_utki...i would be surprised is u know what the law states even...thats what i said..dont give wrong answers coz if they are wrong...maybe i will know it...but the others who might see it may get confused...so plz dear..i dint mean to be rude but i asjed for answers that ppl might possibly think correct...i told not to answer if u dont even know what the law is...th elaw u r provong is the second law...

Answer 1

I. If a body (M) is going a constant velocity (v), then its momentum is P = Mv. Therefore its change in momentum is dP/dt = M dv/dt + dM/dt v ; so that dP/dt = M*0 + 0*v = 0 since both M and v are assumed constant. This is Newt's first law because we see that without a change in velocity (called acceleration), there can be no change in momentum (called force). This leads us to:

II. dP/dt = F = Ma + dM/dt v = M dv/dt + dM/dt v; where F = force. This is really just a restatement of Newt's Law I, as you can see above. That is, because it requires a force to change momentum, we have to have F = Ma = dP/dt (which is the simplified form that assumes M = const.). Now, old number three:

III. Equal and opposite reaction...what does that mean? In terms of math it means all the forces acting on a body at rest or in uniform motion (Law I) must add vectorally to zero. Why? Because that body is not changing its momentum when at rest or moving at a constant velocity; so, dP/dt = 0 and the only way that can happen is for the net forces acting on that body to be zero. And the only way that can happen is for the sum of the forces to cancel each other out...equal and opposite reactions.

Let's look at a simple EXAMPLE: a free falling body in an atmosphere.

Assume you jump out of an airplane at 10,000 feet without a parachute. How fast would you hit when you splat all over the ground? The first thing you need to do is sum up all the forces on you while you are falling.

Gravity is acting to pull you downward (speed you up); so we have W = Mg; where W = your weight on Earth, M is your mass, and g = 9.81 m/sec^2 the acceleration due to gravity on Earth's surface.

Drag force is acting to pull you up (slow you down); so we have Fd = 1/2 Cd rho A v^2; where Cd is the drag coefficient, rho is the density of the air at the altitude you happen to be when you do the calculation, A is your cross sectional area, and v = the velocity you're falling at when you do the calculation.

Thus the sum of forces is f = W - Fd = Ma; so, as long as your weight (W) is greater than the drag force (Fd), you will be accelerating (a) downward in your fall to Earth. (a is positive in the downward direction) As you accelerate downward, your velocity increases and you gain kinetic energy (KE), which is the stuff that causes the splat when you hit the ground.

So where does the equal and opposite (Newt's III) come in? It comes in when your velocity (v) while falling gets large enough to produce a drag force equal to your weight so that f = W - Fd = Ma = 0. And there you have it, your weight is equal and opposite to the drag force; thus, you are in constant, uniform motion and there are no net forces acting on your soon to be dead body. When you reach that uniform, constant velocity you are said to be in terminal velocity.

In sum, Newt's I leads us to Newt's II; and Newt's I and II, combined, lead us to Newt's III. In reality, they are all one law based on the physics involved with the change of momentum (dP/dt = M dv/dt + dM/dt v). By the way the dMdt v term is not zero when working with rocket propulsion, for example. Part of a rocket's mass (M) is its fuel, which is getting less and less as the rocket reaches for the Moon. Thus, the dM/dt accounts for the loss in total mass as the fuel burns away.

Answer 2

Newton's laws contain more than what meets the eye.
The first law is more concerned with inertia than with forces. The second law holds only in inertial frames which is asserted by the first law.
You cannot derive the 3rd law from the second.
The significance of the 3rd law is that you cannot isolate external forces - forces are mutual, you need interaction. Without the 3rd law the 2nd would be meaningless! This is because you could always argue that some body is spontaneously accelerating because you failed to isolate it etc.

Answer 3

catty, like some others showed here, the 1st law can be derived from the 2nd: when F=0, a=0, ie, dv/dt = 0, so v doesnt change.

But I think, to get the 3rd law, one needs the law of conservation of momentum also. consider 2 billiards balls colliding. The sum of ther momentum before and after colliding is the same (law of conservation of momentum). p1+p2=const before and after. Now, diferentiate wrt time: dp1/dt + dp2/dt = 0. From 2nd law, F1+F2 =0. => F1 = -F2. This the 3rd law. So, to get 3rd law from the 2nd, i think one needs the law of conservation of momentum also.

Answer 4

Newton's third law of motion states that to every action, there is equal and opposite reaction. This law is also known as law of conservation of momentum.Equation is:m1u1+ m2u2= m1v1+m2v2.

Answer 5

change in linear momentum = force * time
change in linear momentum of B = F1$T1
change in linear momentum of A = F2$T2

Acc. to newton second law when no external force is applied
force applied to the body
F1$T + F2$T = 0
F1$T = - F2$T
F1 = - F2
ACTION = REACTION
$ represents DELTA

Answer 6

i think that ur in 9. hi, iam too in 9. and i prefer you to refer the text of science 1

Answer 7

third law of motion according to newton says that,
Acceleration is proportional to Force
Acceleration is inversly-proportional to Mass

combining both
A is proportional to F/M
A=k*F/m(where k is any constant)
F=k*M*A______(1)
if A=1 m/(s*s)
F=1 Newton
M=1 kg
putting the values in equation(1)
K=1__________(2)
Putting k's value in F=KMA
F=MA

proved

Answer 8

check out this link - http://www.lhup.edu/~dsimanek/cutting/3rdlaw.htm it may be of help.