Ball in an Accelerating Bus moves backwards

[Sabellic]

I know for a fact that whenever I am standing on the platform of a bus that starts accelerating from zero I have a tendency to go backwards. The friction on my shoes prevent from going backwards of course and I do the slightest stumble.

However, what causes the body in an accelerating bus to move backwards? I know that it happens, but I am having trouble constructintg the logic.

Let's forget about friction for the moment, and think of a ball (a sphere) on the floor of the bus. Why does the ball move backwards? Is it the Third Law? Or is it inertia?

I tried to get the answer by working backwards: I thought that if the bus makes a sudden stop (sudden negative acceleration), the ball will continue to move forward after the bus has stopped. The logic behind this is easy: prior to the deceleration, the ball had been moving at the same velocity as the bus, but while the bus stopped, the ball continued to move at the same velocity at the point of the bus just prior to its deceleration. It's the law of Inertia (a body in motion will have a tendency to stay in motion in an unchanged velocity unless acted upon by external force).

So, now that we have the situation of a decelerating bus made clear, what is the situation of the accelerating bus? I tried working the logic of the decelerating bus backwards but this didn't work out so well. When the ball rolls backwards during the acceleration process is it due to inerita (Newton's first law) or Newton's third law? Can anyone help me on this?

 

[xArcherx]

I believe it is Newton's first law. A body in motion tends to stay in motion and a body at rest tends to stay at rest. It's inertia in both cases.

 

[pantaz]

Keep in mind, you (and the ball) do not actually move "backwards". You are just accelerating more slowly than the bus.

 

[Sabellic]

Okay, I agree. It is Inerita.

However, this doesn't explain the processes of what is going on. Thanks for the reply though.

Actually, while I was waiting for a reply I did some more thinking. I think I am on to something here. Please bear with me as you read the following explanation:

You know, the same concept applies to a ball on a bus that is moving at a constant, unchanging velocity. What is the ball's velocity at this point? It is the same as the bus. So the bus and the ball are at one (so to speak) when the velocity is constant. However, when the bus suddenly decelerates the ball keeps moving, and the bus stops. There is a sudden point of Separation! The ball starts moving relative to the bus. With acceleration, it is the opposite happening: the bus is moving relative to the ball. (This is why you move backwards when somebody pulls a carpet from under your feet).

So my conclusion is that we have 3 distinct scenarios (not considering friction):
1. During acceleration of the bus = the bus moves relative to the ball (which initially stayed still).

2. During decleration of the bus = the ball moves relative to the bus (the ball moves at an unchanging velocity equal to that of the bus prior to its decleration)

3. During constant velocity = the ball moves at the same speed as the bus; and the bus moves at the same speed as the ball. There is no relative motion between the two.

 

[Quisquis]

1. During acceleration of the bus = the bus moves relative to the ball (which initially stayed still).

2. During decleration of the bus = the ball moves relative to the bus (the ball moves at an unchanging velocity equal to that of the bus prior to its decleration)

3. During constant velocity = the ball moves at the same speed as the bus; and the bus moves at the same speed as the ball. There is no relative motion between the two.

You're making it too complicated. Number one and two on your list are no different from each other; the ball has a velocity that is different from the bus, and so moves differently. Which one is moving with respect to the other is only a matter of your viewpoint.

 

[shamrock5585]

you remembered the law that a body in motion will stay in motion but you forgot that a body at rest will stay at rest... when the bus starts accelerating the ball wants to stay at rest and the bus moves... but the force from friction makes the ball move slower and eventually move with the bus... objects will always resist moving when a force is applied... when a force is applied and the reaction force is equal and opposite it will not move. force and acceleration are proportional

 

[swraman]

Maybe if you think of it like this:

Use the ground as your reference frame instead of the bus. If there is no friction and the bus starts moving, someone standing in the bus will NOT move relative to the bus.
The same goes if the bus is accelerating or decelerating.

Assuming the bus is at constant velocity AND the object in the bus is at constant velocity, both will move with the velocity V relative to the ground. If the bus begins to stop, the busses velocity will decrese, but he ball will still move with velocity V.
Again this is if there is no friction.

 

[Integral]

Consider a "bus" with a frictionless floor. Set on this frictionless floor a block. Now when the "bus" accelerates there is no force acting on the block so it remains motionless. However the rear of the bus is will approach the motionless block if your only frame of reference is the bus the block will appear to move, however if you are standing outside the bus you will clearly see a motionless block in a moving bus.

 

[Sabellic]

Thank you very much, everyone, for your replies!