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I am holding a book in my hand and standing on a scale, the scale reads X Newtons. Then at t=1 second, I start to move the book, and by t=2 seconds, the book is at rest 0.5 m higher than its initial position. How did the reading of the scale change in those 2 seconds? The key concern I am having is if the book accelerates upward, then the scale reading should increase, but if it moves with a constant velocity, the reading should stay the same, so I am unclear about which one of these two possibilities is correct. Which one is it and how is the reading affected?

P.S. I tried this at home on my scale but my scale doesn't update its value fast enough.

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It depends on the acceleration profile. The number will change whenever the book is being accelerated (i.e. whenever the speed is changing). For instance, if the book is rapidly accelerated then moves at a constant velocity before being rapidly accelerated, the scale will spike up, return to normal, and then spike down. If the acceleration is more gradual, you'll see something else.

You can see a similar effect much more easily if you bring a scale into an elevator. I've seen some physics departments that put a scale of some sort in their elevators to demonstrate this effect.

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  • $\begingroup$ So this question, was one that I recently saw on an exam, and I haven't been able to stop thinking about it. What would you assume was happening, if the question was worded exactly like it is above? $\endgroup$ – ArnavT Feb 1 '18 at 1:34
  • $\begingroup$ @ArnavT All you can say is that the number on the scale goes up above $X$, then down below $X$, and then back to $X$. The time-averaged number on the scale is still $X$. You can't say exactly how high it goes, how low it goes, or how long each part is without more information. $\endgroup$ – Chris Feb 1 '18 at 1:51

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