# A person weighing 100 N stands on some bathroom scales in a lift. If the scales show a reading of 110 N, which way is he going

• Moving downwards and decelerating.
• Moving downwards with a constant velocity.
• Moving upwards and decelerating.
• Moving upwards with a constant velocity.
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I'm sure this has been answered before, but I can't see it in a search for "lift".

Anyhow the forum rules say we can't answer homework questions, but just discuss the concepts involved. You know from Newton's first law, F = ma, that if there is a force on a body it will accelerate, and it will accelerate in the direction of the force. So the question is, is there a net force on the person in the lift, and in which direction is the force?

The force downwards is just due to gravity, and the force upwards is the force being applied to the person by the floor of the lift. The scales are measuring the force being applied to the person by the floor of the lift. That should be all you need to answer the question.

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Another trick that may help you visualise this is the psuedoforce. The psuedoforce enables you to imagine stuff in an accelerated frame easily. It's the "pressing" you feel in a plane during takeoff, etc. It's also the "pressing" you feel in an ascending lift.

I realised that I've already written a sizeable chunk on psuedoforces, so I'll just blatantly copy it from this answer of mine.:

Whenever we view a system from an accelerated frame, there is a "psuedoforce" or "false force" which appears to act on the bodies. Note that this force is not actually a force, more of something which appears to be acting. A mathematical trick, if you will.

Let's take a simple case. You are accelerating with $\vec{a}$ in space, and you see a little ball floating around. This is in a perfect vacuum, with no electric/magnetic/gravitational/etc fields. So, the ball does not accelerate.

But, from your point of view, the ball accelerates with an acceleration $-\vec{a}$, backwards relative to you. Now you know that the space is free of any fields, yet you see the particle accelerating. You can either deduce from this that you are accelerating, or you can decide that there is some unknown force, $-m\vec{a}$, acting on the ball. This force is the psuedoforce. It mathematically enables us to look at the world from the point of view of an accelerated frame, and derive equations of motion with all values relative to that frame. Many times, solving things from the ground frame get icky, so we use this. But let me stress once again, it is not a real force.

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Depending on the instructions of your professor, this problem can be solved two different ways: in the inertial and the non-intertial frame of reference.

In the inertial frame of reference, you are watching the lift, the scale and the person within it, from outside. You see that the all three are traveling with a constant acceleration up or down. Just two forces are acting on the person, the force of gravity and the force of the scale. You do the 2nd Newton law. Important: The scale is nothing but a simple force gauge showing the actual force with which it supports the person (of course this is transformed on the scale into the mass under the assumption of the gravity acceleration).

In the non-inertial frame of reference, you are standing in the lift, so the scale and the person seem to be at rest. However, now three forces are acting on the person, force of gravity, force of the scale and fictitious or pseudo force. Fictitious force equals mass of the person multiplied by the acceleration of the lift and is acting in the opposite direction of the actual acceleration of the lift. So in this case you do the 1st Newton law.

In both frames of references, you should get the same result. Moreover, when lift is not accelerating, both frames of reference are inertial and you should use even the same calculation procedure (the first one).

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Uhh, don't do that, write a complete answer and then submit. Unless you've already written a sizeable chunk which self-sufficiently solves the problem, and leave a note that you will add more later. –  Manishearth Apr 21 '12 at 11:18
I'm sorry. The process of writing answers is complex for my head, I cannot think right unless I see the answer and the question one next to other. So I do this some kind of iteration process that usually ends in few minutes, but sometimes lasts for days :) –  Pygmalion Apr 21 '12 at 11:50
You do know that answers are saved as drafts--you can write half an answer and come back later (to the same question) to improve it without submitting. Also, you can always open the question in another tab. –  Manishearth Apr 21 '12 at 11:57
I do not know about those drafts. Do drafts appear next to the question, just like answers do? –  Pygmalion Apr 21 '12 at 11:58
No, they appear in the "compose answer" box. Try it, start writing an answer for a random question. Wait a while (draft saving is every 30 seconds IIRC), close the page. Come back whenever you want, your half-written answer will still be there, at the bottom of the page in the answerbox. The same applies for questions, but you can have only one question draft at a time (since there's only one "ask question" page, but there are many pages with an answerbox) –  Manishearth Apr 21 '12 at 12:02

Moving downwards and decelerating.

Let the lift in free fall from high (with the teacher inside to better understand the problem). The weigth is 0 (no units needed, because 0 is shared in the same way in all scales) because he is in free fall (and because he is not very very very very very tall I will assume the acceleration in his head equals the one at the feet level , uniform field approximation in a radial non uniform field ).

Now the lift smash in the concrete floor. The weight will increase under the decceleration, during the impact, in such a way that the bones eventually break.
The teacher will not survive if the de/acceleration is above 40g , give or take some *g*s.
To describe the evolution of the weigth during the impact is complicated. Firdt he foot first add, only after the body progressively will add, and finally the head. The teacher instead of jumping out and open the parachute, will die still waiting for the numeric answer.
The number 110 is above 100, it is all that matters to decide the answer because 'accelerating and going up' gives also an increase of weight but is not in the candidate answers.

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Please only give hints and partial solutions to homework problems, not a full solution. –  Manishearth Apr 22 '12 at 11:12
After the comments I saw in other answer I was antecipating comments and downvotes like this one, and precisely because of this I confined the theacher in the elevator, and let him smash ;). The professor is not the one that in the others answers is assumed to exist, but the authors of the others answers that do not explain nothing at all. When I try to explain simple issues I do not use equations, nor laws, I use simple facts of the quotidien, go to limiting situations for instance. And if I do not limit the way you express your sagesse, I ask the same back, even if this is not happening. –  Helder Velez Apr 22 '12 at 18:13
That's fine, just don't give the final answer. :) –  Manishearth Apr 22 '12 at 18:28