Why can't we push a bus from inside?

Now that we are all outing for a picnic. The bus driver shouts as there's a failure in the engine's start-up. We will do what all we can do! Some will panic while some will make others panic and some will shout at the driver and the rest will look cool undisturbed. The most optimistic approach to this situation is pushing the bus till it starts up. We all know that. While everyone is trying to push the bus, what if one pushes the bus from inside??

It's absurd idiot-ism. But "Why actually we  can't move a bus from inside?" Hmm?? Let us give it a try.

According to Newton's first law of motion, "Every body continues to be in the state of rest or in uniform motion, until an external force acts upon it".

Newton has well described the law by including the term "external" which says that there is no change of position of the object( or its centre of mass) without the application of an external force. But what exactly is this "external force"? Well, any "unbalanced" force acting on the system is said to be an external force. 

In order to get a clear picture, we shall compare the properties of internal and external forces. Generally speaking, any internal force is "balanced", i.e, there are forces whose resultant is zero, whereas there is a finite resultant in case of an external force.

When we are pushing the bus from inside, our hands are providing a finite force on the walls of the bus, while our legs are pushing the floor of the bus with more/less the same force. These forces are normal(perpendicular) to each other.

These forces cancel and the resultant comes out to be zero. Hence we cannot move the bus. 

However if there is no friction and if we run from one end of the bus to the other end, the bus moves in the opposite direction so as the keep the centre of mass in the same place. In the absence of any other force, a system tries to keep the centre of mass in the same place despite the action of a small force.

Try running from the back of the bus and jumping into the front side such that your legs hit the front surface in karate style. As no part of your body is in contact with the bus at the instant when you hit the bus, your force is purely external and moves the bus. 

And that's the same reason "why we can't lift the chair in which we are sitting". 

Can you lift yourself?? Just give it a try.