Forces in inertial and non-inertial frame of reference

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In an inertial frame of reference, a man standing on a bus that begins to brake does not experience a force accelerating him forward; instead, he continues moving due to his initial motion. The force of friction opposes his motion but does not cause it. If the floor were slippery, reducing friction to zero, he would still move forward relative to the bus because no negative acceleration acts on him directly. The change in his position relative to the bus is a result of the bus's acceleration, not a force acting on him. This analysis clarifies that discussions of motion should focus on the inertial frame without conflating it with the bus's dynamics.
ChessEnthusiast
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Imagine such situation:
A bus is moving at constant speed, a man is standing on the bus and is not holding to anything - he is simply standing.
Now, the bus starts breaking with constant negative acceleration and so the man will change his relative position due to the force of inertia.
Now, let's say we don't believe in the existence of the force of inertia and want to solve this problem in an inertial frame of reference.

The only force of contact between the man and the bus is the force of friction.
The man will move forward due to braking.
Therefore, is the force of friction the force causing his motion relative to the floor on the bus?
 
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ChessEnthusiast said:
Therefore, is the force of friction the force causing his motion relative to the floor on the bus?
What do you think would happen if we made the floor very slippery* so the friction force was 0? Would he still move relative to the bus or not?

*perhaps he should not remain standing for this portion of the experiment, it might be difficult to pass the ethics committee review!
 
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Right, the force of friction was not the right guess.
However, there are no more forces in the x direction.

What about this analysis:
There is no force acelerating him towards the windshield, there is simply a force opposing his motion - the force of friction. The fact that this man starts moving is wrong - the man simply KEEPS moving because he was in motion and no negative acceleration was applied directly to him.
 
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ChessEnthusiast said:
Right, the force of friction was not the right guess.
However, there are no more forces in the x direction.

What about this analysis:
There is no force acelerating him towards the windshield, there is simply a force opposing his motion - the force of friction. The fact that this man starts moving is wrong - the man simply KEEPS moving because he was in motion and no negative acceleration was applied directly to him.
Yes. Don't talk about "relative to the bus" if you decided to use the inertial frame.
 
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ChessEnthusiast said:
The fact that this man starts moving is wrong - the man simply KEEPS moving because he was in motion and no negative acceleration was applied directly to him.
Yes, exactly. In the inertial frame the bus is accelerating, not the man. The change in relative position is due to the bus’ acceleration
 
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