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Consider a mother and her child are in a elevator going down from the 100th floor to the first floor traveling at say 5MPH (or whatever speed). If the mother decides to pick up the child in her arms while going down, would she need to apply more lifting force or less? How about the opposite - going from first to the 100th?

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closed as unclear what you're asking by peterh says reinstate Monica, Jon Custer, ACuriousMind, user36790, Bosoneando Oct 8 '16 at 18:44

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ What are your thoughts? Please share. $\endgroup$ – FreezingFire Oct 7 '16 at 17:08
  • $\begingroup$ My thought is if by going down there is less gravity for both mother and the child, then less force needs to applied. If opposit, then more. But we should ask Newton. $\endgroup$ – Zuzlx Oct 7 '16 at 17:14
  • $\begingroup$ What do you mean by less gravity? (Please don't mind me asking so much, I'm trying to make you understand). Also, try to draw a free body diagram for the baby. Think about all the forces acting on the baby. Then think of its acceleration. What is the link between the two? $\endgroup$ – FreezingFire Oct 7 '16 at 17:24
  • $\begingroup$ First off, thank you. My train of thought was a free-falling body has less weight (although the same mass). If less weight, then less force. But I think the key here is acceleration and depends when it happens. At the beginning or when both bodies have constant speed...no? $\endgroup$ – Zuzlx Oct 7 '16 at 17:57
  • $\begingroup$ But are they really in a "free-fall"? Here they are moving with a constant velocity. What happens in a free fall? Keep thinking! (Just keep it simple.) Oh, and at the beginning of the motion, things will be a whole lot more complicated. For now, just imagine that they are currently moving at a constant speed. Forget about how they reached that state. $\endgroup$ – FreezingFire Oct 7 '16 at 18:01
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The baby and its mother are in a lift moving at a constant speed. So the baby itself (and its mother) are also moving at a constant speed. This means that their acceleration is zero (because the velocity is constant). Because $\vec{F\,} = m\cdot \vec{a\,}$, and $\vec{a\,}=0$, so the net force on the baby ($\vec{F\,}_{\text{net,baby}}$) must be zero. But the baby is experiencing the force of gravity ($m \vec{g\,}$), so we must have: $$\large \vec{F\,}_{\text{net,baby}}=m\vec{g\,} + \vec{F\,}_{\text{mother,baby}}=0$$ Thus, $$\large \vec{F\,}_{\text{mother,baby}}=-m\vec{g\,}$$

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    $\begingroup$ Thank you again FrezingFire. I'm going to think about this and chew on this a bit. You get the accepted answer since your answer has arrows and Ken G doesn't. $\endgroup$ – Zuzlx Oct 7 '16 at 21:39
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Ask yourself this question: what would be different to your question, if anything, if you were the one in the elevator, and the mother and child were in the hallway outside? Does it matter which of you is moving, to determine the force the mother needs? It's obvious that it doesn't matter your motion, so this question becomes, what does it mean to say the mother is moving at 5 mph? Moving with respect to the Earth? Then the question becomes, does the force of gravity depend on motion with respect to the Earth? The only way to answer that is to look at what works: Newton's law of gravity. Does it depend on motion with respect to the Earth? Then look at F=ma. Does it depend on motion with respect to the Earth? If the answer to both of those questions is "no", then what is the answer to your question?

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All velocities are relative, according to Galileo's principle. In the context of classical mechanics, we have, as the Second Law:

$$ \sum_i \textbf{F}_i = m\textbf{a} $$

In your problem, the elevator is going at a constant speed, thus its acceleration is zero. The, we can affirm that the mother, standing still inside the elevator, also has constant speed. Because of this, it doesn't matter the speed you see them moving: as long as they aren't accelerating, the mother will need the same amount of force to lift the baby the same height.

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