Think outside the box

A box is on the floor in a train that is accelerating. The box does not move. Which horizontal forces are acting on the box?

My thoughts: If there were no friction between the box and the floor, the box would slide to the back of the train. What stops it is the force of friction. Since the box does not move there must be an equal, but opposite horizontal force to the friction. What is this force called and what causes it?

7 Responses to “Think outside the box”

  1. I don’t think it’s called anything. If it were an ever-present force, putting a box on the floor of a stopped train would cause the box to slide off to front!

  2. Jan Nordgreen says:

    I posted the same question on Aardvark last night. After 3 and 6 minutes I had two answers. Please see

  3. Aha! It’s called INERTIA, since it’s an accelerating reference frame.

    The Aardvarkers missed the simplest part of the explanation. Instead of speeding up the train, think about the train, with box, moving at a constant velocity. Then put on the brakes and Voila! an accelerating reference frame. What force gets applied to the box?

  4. Michael says:

    I concur. Inertia and friction are the two forces at play here.

  5. If by “the box does not move.” you mean “the box does not move with respect to the train”, then I see only one force: friction, which accelerates the block forwards w.r.t. the ground.

    “Inertia” isn’t really a force. It’s just an artefact of trying to explain the motion (or the lack of motion) of the box w.r.t. an accelerating frame of reference.

  6. Robert Bell says:

    I have to agree with Richard: if the box does not appear to move, i.e. it is stationary relative to the floor of the train, then it must have a resultant force acting on it in order to accelerate along with the train. This force is provided by friction between the floor and the box. Should the acceleration be so great that limiting friction is unable to provide the necessary force, the box will slide towards the rear of the train until it encounters some rigid object that is able to provide a reaction force to enable the box to accelerate along with the train.
    Inertia is the property of mass which relates to an object’s “reluctance to change its motion”. It is not a force itself, but is a measure of the “force required to obtain unit acceleration”.

  7. John Smith says:

    Really guys?…the horizantal force is gravity. Gravity is always constant…as far as we know lol. If there were no firction between the two the box would still be pulled towards the floor of the train. If the train were moving the box would still be on the floor, but at the back of the train do to a pocket of air between the two (Casimir effect) and even if not that then the fact that with no friction that would imply that all the molecules in both the floor and the box were aligned perfect enough to repell each other to keep each other apart. None the less the box would still be on the floor due to gravity…otheriwse, if not, the box would be floating in the air and in some strange way youd have antigravity lol. Inertia is the result of a force apllied to an object. If friction were still in play then the only thing that would send the box to the back of the train, like Robert said, would be the force of the train over coming the friction between the floor and the box. Same result if the train stopped. If it stopped slow enough the box wouldnt move. If it stopped faster the the inertia gained from the train moving then the box would fly forward at the speed of its inertia minus the friction that was tryin to keep it on the floor….jus me but i wouldnt wana stand in its way if it does lol.

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