Help on law of conservation of linear momentum?

Carmelina Enoch: This is a good question!First let's look at the Momentum (P):The trolley with load, I presume, has a mass of 20kg; so the initial momentum P is given by:(1) P = M * V = 20V kg·mI don't see any difference between having the sand trickle out vs. its falling off (or "through" the bottom of) the trolley. So let's assume, for the sake of simplicity, that the bag of sand falls off the trolley all at once.Now, to anthropomorphize a bit: The trolley does not "know" where the bag goes when it falls off--it could hit the ground and eventually come to a halt because of friction with the ground. Or . . . let's say that it is ejected onto a cart which is moving along side of the trolley.If you look at the "forward" momentum of the system = Trolley + Bag + Cart, it hasn't changed: All three were initially moving at velocity V, and afterwards that's still true; and their masses haven't changed, either. Let's look at the mechanical energy ME of the syst! em: It hasn't changed, either; it is still:(2) ME = ½ * (Mt + Mb + Mc) * V²True, the total ME has been redistributed (repackaged) from ½ * ((Mt + Mb) + Mc) * V² to ½ * (Mt + (Mb + Mc)) * V², so the cart now has the sandbag and the trolley doesn't.OK, back to the momentum: If the bag had simply fallen off the trolley, it takes Pb = Mb * V momentum with it and transfers it to the earth when it hits the ground.From an energy point of view, the fall transforms the Potential Energy PE of its height into KE at impact with the earth, and its translational KE into the "damage" it does when it hits the earth.Anyway, the velocity of the trolley V will not change when it loses the 10kg of sand. If its velocity increased because of some "conservation of momentum", then the trolley's increase would have to occur at the expense of a decrease in the velocity of the bag of sand. But that doesn't happen: At the instant when the sandbag has left the trolley (! and before it hits the ground or touches anything else) its ve! locity is still V and its momentum Pb is:(3) Pb = 10Vand that of the trolley Pt is(4) Pt = 10V,and (5) Pb + Pt = (Mb + Mt) * V = P of (1), the total initial momentum.When you apply these conservation laws, you have to make sure the System you look at initially must include the same components as the final System.....Show more

Cherry Stampka: Internal forces can lead to an increase the acceleration of a system. Net external force would be zero for an isolated system.Consider for example a unstable Uranium atom at rest, for argument sake. When the atom explodes into tinier atoms, the split atoms will each run away into opposite directions with their speeds inversely proportional to their masses.Similar is the case here. Since the sand flies away in the opposite direction, the remaining trolley system will gain velocity because of this....Show more