Confusion about an example of inertia related to bus

Question

When the bus is stationary the passengers are also stationary. When the bus starts moving the part of the body (lower part) in contact with bus starts moving, but due to inertia the upper part remains stationary and thus he gets reclined back. If he is standing he will fall backward.

I cannot understand that how lower part starts moving while upper part remains stationary? My understanding is that our complete body is at rest - rather an unbalanced force acts on us in backward direction when bus starts?

Can anyone explain the scenario?

Answer 1

If you were a rigid metal pole welded to the floor of the bus, there would be no bending / lag of the upper section of the pole moving forward as the bus moves forward; it would all accelerate together with the bus.

So this clearly has something to do with the "floppiness" of people. Therefore let's consider an extreme case.

Imagine an ice block on the floor of the bus. As the bus moves off, the ice block would not move with the bus, but it would instead, to an observer on the bus, appear to slide to the rear.

If the bus had no windows, someone on the bus could make the honest observation of some kind of "backwards force", as you put it, that accelerates the block to the back of the bus.

As a matter of fact, it is clear from an observer on the pavement that the block is in fact remaining completely stationary relative to the road. You can almost imagine it floating in mid air and the bus just moving away from underneath it.

So in this case, due to the lack of friction between the floor of the bus and the ice block, the block does not even notice the bus moving off.

The same thing happens to the upper half of a person's body. Their feat can be considered to be like a rigid metal pole welded to the floor - firmly held in place by a strong friction force. But as you move up the body, this frictional force is transmitted less and less between vertebrae and other bones. By the time we consider our head, it is very weakly supported - just the muscles in our neck.

So it is clear that the further up our body we go, the more our body behaves more like the ice cube. That is to say that it is not being "pushed backwards" by the bus, but merely remaining more and more fixed in place relative to the road.

Of course, we are not just a pile of bones - our muscles are trying their hardest to keep our head and arms above our feat and not lag behind, so to speak. It is now clear why we subconsciously step back, and why people get whiplash. We step back to try and help our muscles - give them more of a structure to push off and keep our hips moving forward with the bus, and people get whiplash when the muscles in the neck aren't strong enough to keep our wobbly head moving along with the rest of our body - the head stays still and our body is jerked forwards/backwards. Note that the head is not experiencing a force when someone gets whiplash, it is experiencing an absence of a force as the person's body gets pulled along by the bus / car in a harsh period of acceleration.

Answer 2

I cannot understand that how lower part starts moving while upper part remains stationary?

First of all, the person is not rigid body. It can flex and bend in response to forces acting and not acting on different parts of the body.

Given that, the static friction force between the standing persons feet and floor of the bus (or between the sitting persons buttocks and the seat of the bus) keeps the lower part of the body stationary in the reference frame of the bus (enables it to accelerate with the bus).

The upper part of the body has no horizontal forces acting on it, so it is not so restrained. Since the persons body is not a "rigid body" (it can bend in the middle), per Newton's first law in the inertial frame of an observer standing on the road looking into the windows of the bus, the upper part of the body remains stationary, whereas in the frame of the bus, the non-inertial (accelerating) frame, it appears to move backwards due to some unknown (pseudo) force.

Hope this helps.

Answer 3

The bus floor makes an horizontal force on the feet of the people. As the point of application of the force is at some distance from the centre of mass, there is a torque.

To an inertial frame outside the bus, people inside are not falling backwards, they are tilting, what is the consequence of a torque.