# Weight on carpet vs. hard floor

Will the scale say I weigh more, less, or the same on a carpet as compared to a hard floor?

You can assume the scale works via spring mechanism. Free body diagrams encouraged!

According to what I understand you will show as weighing more on a carpet than on a hard floor. From what I understand it is due to the way the hard floor affects the feet of the scales.

Here is a article that explores that question: http://www.newscientist.com/article/dn2462-people-weigh-less-on-a-hard-surface.html

The new scientist article is one sided approach. My scale shows more on rigid surface. I tried to put a higher support in the middle under the scale, like on the second image below, and the scale showed much more.

So why shows less the scale on soft carpet? I guess more percentage of the force get on the perimeter than on the spring, and there is more deflection in the bottom of the scale. So the shape of the scale on a flat soft surface is the opposite than I drawed on my second image.

How scale works: http://home.howstuffworks.com/inside-scale.htm

My explanation:

Obviously you weight the same. On a soft carpet your weight is distributed to more contact area than a hard floor. Hence pressure, which is force per unit area is greater on a hard floor than soft carpet.

Suppose $A$ is the area of contact in case of a carpet and $a$ is the same for hard floor. $A$ > $a$ . Your weight is same in both cases. It is $Mg$ where $M$ is your mass and $g$ is the acceleration due to gravity. Pressure in case of a carpet is $p$ $=$ $\frac{Mg}{A}$ and pressure in case of hard floor is $P$ $=$ $\frac{Mg}{a}$

Since $A > a$ it follows $P > p$

By Newton's third law the same pressure is applied to you.

Therefore the soft carpet feels comfortable but as far as the weight is concerned any good scale will show that your weight being same in both cases. If they deffer then it is manufacturer's fault. (Normally a manufacturer calibrates weight scales on a hard surface)

If the carpet floor and the hard floor are in different locations then a spring scale also needs a gravity map to calibrate the result to perfection. The possibility exists that a mineralization anomaly starts beneath the carpeted room in your house and that the results could be reversed;-)

## protected by Qmechanic♦Jun 1 '13 at 20:39

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