Question about centre of mass 
Example 9.4 in the essential university physics: Jumbo, a 4.8-t elephant, is standing near one end of a 15-t railcar, which is at rest, all by itself, on a frictionless horizontal track. Jumbo walks 19m toward the other end of car. How far does the car move?

I have several questions about this example


*

*If the system including jumbo and the car, then the centre of mass of this system is not moving since there is no external net force. So is the cm not moving relative to the ground?

*Does the car move because the elephant exerts a friction to the car toward left?

*If taking the car itself as the system, then does it has a external net force which is the friction? If it is, then will it run to the left forever? If it will, how can the centre of mass not moving?
Thanks ahead.
 A: Yes, the centre of mass of the system(elephant and railcar) does not change(it stays at the same point with respect to ground) as there is no net external force on it.
The elephant is able to move towards the right due to the friction between it and the surface of the railcar. The force due to friction acts towards the right on the elephant and towards the left on the railcar. This causes both of them to move. However as these are internal forces for the system, there is no net change in momentum and hence position of the centre of mass remains the same(the elephant and the railcar will have equal and opposite momentum). Note that although the net momentum hasn't changed the the kinetic energy of the system has increased.
If on reaching the end of the railcar if the elephant jumps down and continues its rightward motion, both the elephant and the railcar will keep on moving endlessly(assuming that no other forces will act on them, such as the friction between them and the ground). The velocity of the centre of mass of a system is defined as $$\frac{\sum_{i=1}^n m_i\vec{v_i}}{\sum_{i=1}^nm_i}$$ which is nothing but the summation of the momenta of individual bodies in the system divided by the total mass of the system. This is how we can mathematically show that the centre of mass is not moving. In this example as  the elephant is coming to rest after reaching the end of the railcar, the velocity of the railcar also becomes zero.
