Please look at the image given.
The force in the x-direction is N" which is a component of the normal reaction force.Now the body starts sliding down the slope, even if I consider kinetic friction opposite to N" it is not equal to N" so Fnet is not equal to zero and momentum is NOT conserved.However many books still say that momentum is conserved.Can anyone explain how?
NOTE:The inclined plane is fixed
How could you say component of kinetic friction (kN) opposite to horizontal component of N let's say (kN.cosx) is not equal to horizontal component of N i.e. (N.sinx)?
Where 'x' is angle of inclined plane with horizontal. And if the x and coefficient of friction (k) is such that
kN.cosx = N.sinx
&
N.cosx + kN.sinx = Mg
then the net force acting on the block would be zero and it will slide down with constant velocity and hence momentum would be conserved. But if there exists a net force such that the block accelerates then no momentum is conserved.
No books, or more specifically, no correct books, would say that momentum is conserved in this situation.
Momentum is conserved when the change in momentum is 0. When the mass of a system is constant, as it is here, the change in momentum is equal to the net force. If the net force is not 0 (that is to say, the mass is accelerating), the change in momentum is also not 0, and thus momentum is not conserved.
So is the momentum of your system conserved?
You need to take care when you apply the principle of conservation of momentum, as it always holds true only for an entire system of interacting bodies, and not for a subset of them. If a body accelerates down a ramp fixed to the Earth, its own momentum is clearly not fixed; however, its acceleration imparts an infinitesimal recoil to the ramp and the Earth, so the overall momentum is conserved.
You also need to take account of friction. At a macroscopic level, if a body is decelerated by frictional forces such as air resistance, the macroscopic momentum of the body is not conserved; however, were you able to observe and measure the effects of the countless collisions between the body and the individual molecules of air, you would find that the momentum lost by the body had been transferred to the air molecules, so momentum overall was conserved.
