# Challenge: measure body weight without bathroom scales

1. ### Jefficus

3
I have teenaged daughters, and like many of their peers, they're obsessed with their body weight. Unfortunately, since I have access to accurate scales at my gym, I've never bothered buying a bathroom scale at home, and this is now becoming a source of friction.

Rather than simply surrender, however, I'd rather turn this into a teaching opportunity by finding some reasonable way to exploit the laws of physics in computing their mass.

The simplest solution would be to hang some kind of beefed-up Newton spring scale from the ceiling, but I'm hoping to find something a bit more inventive. (And less invasive to my plaster.)

I considered using an adjustable-fulcrum balance beam and having them balance themselves against a 50 kg bag of potatoes, but that seemed bulky and inconvenient. (They'd have to go out to the garage to weigh themselves, and with the near-arctic winters we have Saskatchewan, that plan would be rejected by my users for half the year. :-)

I also considered water displacement in the bathtub, but this seems unlikely to produce accurate results in practice. (Plus it uses a lot of water and requires getting wet.)

So, I'm running out of ideas. Does anybody else have a suggestion? Remember: the goals are practicality, accuracy (say, within 1%) and educational value, with super bonus points for jaw-dropping elegance.

Jefficus

2. ### mgb_phys

8,952
Option 1, Stand on raft in bath/pool - measure change in displacement + given density of water.
(also works for how do you weigh a jumbo jet without scales interview question)

Option 2, give up and buy a Wii + Wii fit board thingy

3. ### LostConjugate

842
The fit board is more expensive than a scale.

4. ### jack action

761
You don't need a 50 kg counterweight to make a fulcrum scale, it is just a matter of lever arm lengths. The scale in the doctor's office use this principle and the counterweight is just a few 100s grams.

Also, you could use pressure. Stand on a piston, with a known area A, which is acting on a fluid (liquid or gas) and measure the pressure P. W = P X A

5. ### LostConjugate

842
Simplest method I can think of. Take their height and divide it by their waist circumference. If they increase and/or maintain this ratio to the extent that is healthy, their weight, figure, and athletic performance will all fall in line.

The body stores most of the unwanted fat weight in the mid section. The total weight of the body is not very informative.

6. ### Jefficus

3
I've already considered the water displacement method but it is not practical for a single individual to both stand on a raft AND measure the displacement. You also have accuracy problems because the relatively large surface area of a bath tub makes for small displacement magnitudes giving a precision error problem, and surface turbulence creates accuracy error. Then you have to multiply both errors together to get your answer.

As for the fulcrum scale, I agree that we could use a smaller reference weight, but then you get a larger multiplicative error, especially with the crude mechanics that are likely to be involved in a home-built system.

The piston solution will also work, but it works much better in theory than in practice, since you have to create a fluid-tight (or gas tight) housing. And again, this would entail a cumbersome setup in the garage, which makes it impractical.

There's got to be something more elegant out there.

7. ### Jefficus

3
The height/circumference ratio is an excellent suggestion in terms of psychology and health, something that interests me from the parenting perspective, but it neatly side-steps the intended physics lesson. :-)

8. ### pallidin

This has got to be a "trick question"
Solution: take them over to your gym and let them weigh themselves.

18. ### mender

563
How about a scale that uses the deflection of a steel tube? You could build a cheap but accurate scale and demonstrate beam strength at the same time.

Cantilevered beam made from say 1 x 2 x .095 wall rectangular tubing, an old swing seat that has a single hook at the top, a dial indicator at the unsupported end. Use a known weight (you) to calibrate the beam, weigh the kids at several different points along the beam, note the deflection, calculate the weights.

Surely you have a few lengths of steel and a MIG welder handy. That's standard equipment on the farm isn't it?

19. ### gmax137

894
How about a see-saw or teeter-totter with one daughter on each end, then have the lighter daughter move out till they're balanced. Mark the board and repeat each morning. This way you encourage the competition between the two, with the first one to reach the end of the board winning the future anorexic contest.

You should think carefully before you encourage your daughters to focus on their weight...

20. ### gmax137

894
Hey, I'm sorry about my previous reply - it sounds kind of mean seeing it 'in print.' If the moderator wants to remove it, please do.