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Any weighing machine records our weight by calculating the normal reaction that it applies on our body. So when we place the weighing machine on a smooth bedsheet, we must read a weight whose magnitude will be less than what when the machine is placed on a floor. Am I right? If yes, then we must ensure the machine is placed on the hardest possible surface to get a more accurate value. Am I correct? This being the case, what I have been thinking about my weight all these years is actually wrong (they are wrong, as the weight depends on the type of floor too).

I am attaching the pictures. One with a weighing machine on a floor and another on a bed sheet.

Weighing machine on plain floor

Weighing machine on bed sheet

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Good question, but actually no. You only have to wait until the pillow has finished sinking in and the scale is not moving anymore; then the scale shows the correct value again.

Because, while the scale and you are sinking into the pillow, you are braking and slowing down - in other words decelerating.

Nomatter the surface, when you are not accelerating downwards, the normal force equals your weight. This is Newton's 1st law. The scale exerts this normal force and shows it on the display.

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  • $\begingroup$ Thanks for the answer. mg - ma = m'g. Here m is real mass, m' is the mass of body on bed sheet, g is acceleration due to gravity, a is acceleration of body on smooth bedsheet. I am just modelling things based on what I understood from your answer. My m=57 kg,m' was 54kg. On solving I get the acceleration of the body on bedsheet is 0.701 m/(sec^2). But this 0.7 seems to be too big for describing the motion. While on pullow, I am not increasing my speed by 0.7 m every second. Did I misunderstand your answer and model it in wrong way? $\endgroup$ – user3219492 Nov 26 '16 at 6:32
  • $\begingroup$ @user3219492 Where do you get those numbers from? And also remember that the pillow is slowing down the motion, not speeding it up - when you jump onto a pillow, it compressed and you fall a bit down into the pillow. Afterwards all is still again. Nothing moves. So there is no $a$ anywhere. $\endgroup$ – Steeven Nov 26 '16 at 10:04
  • $\begingroup$ Oops. It must be -a (as decelerating). Recently I myself tried with a weighing machine and recorded the above values. When the bed sheet can no more be compressed, my body won't be moving. If that is the case, then the weighing machine must have recorded 57 Kg right? Why did it say 54 Kg? $\endgroup$ – user3219492 Nov 26 '16 at 11:09
  • $\begingroup$ @user3219492 Was the scale 100 % horizontal? $\endgroup$ – Steeven Nov 26 '16 at 11:57
  • $\begingroup$ Yes. I ensured that the scale was not inclined so that the force doesn't get resolved into cos and sin components. $\endgroup$ – user3219492 Nov 26 '16 at 14:32

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