# 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?

1. 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?

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

3. 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?

• Hi Cathy, welcome to PSE. You stand a better chance of getting a hint to your question if you write out your own thoughts and calculations, because PSE is not a homework-like question solving site. You really need to show some research or effort that you have done yourself to solve this. – user176049 Nov 29 '17 at 0:48
• It is not homework, it is an example form textbook – Cathy Nov 29 '17 at 0:52
• The center of mass of the car-elephant system will change as the elephant moves. When Jumbo is at one end of the car, (assuming the CM of the car is its center point) the CM of Jumbo AND the car will be somewhere in between them. Then when Jumbo moves over the center point of the car, the CM will be directly aligned on the vertical axis. This to me sounds like a conservation of momentum question. The car should move if Jumbo begins to move, and the friction between Jumbo and the car will apply a net force to the system as a whole. – bleuofblue Nov 29 '17 at 4:56
• The book said: we're asked about the car's motion, but we can interpret this problem as being fundamentally about the centre of mass. We identify the relevant system as comprising Jumbo and the car. Because there'e no net external force acting on the system, its centre of mass can't move. – Cathy Nov 29 '17 at 6:03
• Hi Cathy, I wish you all the best with your question, but just in case you submit any more, it's homework like, not simply pure homework : you should read this for the best chance in future: physics.meta.stackexchange.com/questions/714/… – user176049 Nov 29 '17 at 9:52

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.

• Thanks so much. Just one thing I still not quite understand, for "as the elephant is coming to rest after reaching the end of the railcar, the velocity of the railcar also becomes zero". The elephant stops itself, but how exactly the railcar stops? Since when the elephant stops, the car is still moving, and there is no any forces on the railcar, shouldn't it keep this velocity and moves forever? – Cathy Dec 1 '17 at 0:50
• @Cathy The elephant and the railcar stop the same way they started moving...friction. The elephant can't stop all by itself (an external force for the elephant should act on it, which in this case is friction between it and the railcar). Frictional force will be towards the left side on the elephant and an equal and opposite force acts on the railcar towards the right thus causing both of them to come at rest. – Atharva Kulkarni Dec 1 '17 at 5:10