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I am reviewing for a Physics exam, and have come across the following example question:

If I weigh 200 pounds, but a scale I'm standing on reads 400 pounds, then I am accelerating upward at

  1. 1g
  2. 2g
  3. 3g
  4. 4g

(1) 1g is marked as the correct answer. How can this be so? If I am standing on a scale and it registers twice the weight, shouldn't my upward acceleration be -2g?

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closed as off-topic by stafusa, M. Enns, John Rennie, Kyle Kanos, ZeroTheHero Feb 14 at 17:40

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  • $\begingroup$ What is your upward acceleration when the scale reads 200 pounds? $\endgroup$ – BowlOfRed Feb 13 at 23:35
  • $\begingroup$ @BowlOfRed Is it not -1g? $\endgroup$ – Gerardo Hemingway Feb 13 at 23:43
  • $\begingroup$ In this wording, the gravitational force does not count as acceleration. $\endgroup$ – noah Feb 13 at 23:55
  • $\begingroup$ "If I am standing on a scale and it registers twice the weight, shouldn't my upward acceleration be -2g?" - That's correct if you're assuming that there is not also gravity acting on you. Are you assuming that there is gravity or not? From the question, I would guess that it's implying that there is gravity. $\endgroup$ – Samuel Weir Feb 13 at 23:59
  • $\begingroup$ hyperphysics.phy-astr.gsu.edu/hbase/elev.html $\endgroup$ – BowlOfRed Feb 14 at 0:22
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The wording of the problem is a bit misleading. The scale is being accelerated upward with the person, imagine that the person and the scale are on a lift. The problem also assumes that you are near the Earth's surface, so you are experimenting a force equal to $F_z=-mg$ due to gravity. The normal force between the scale and the person is responsible for the person's upward acceleration. Due to Newton's Third Law, while the scale exerts a normal force over you (upward), you are exerting the same force over the scale (downward).

The scale measures the normal force you are acting over it, so we now know that the normal force is $N=2mg=400 pounds\cdot g$. Applying Newton's second law, we can deduce the acceleration:

$$N+F_z=ma$$

$$a=2g-g=g$$

Side note: your science teacher should really considerate teaching science using the SI.

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