# Challenge: measure body weight without bathroom scales

1. Apr 26, 2010

### Jefficus

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. Apr 26, 2010

### mgb_phys

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. Apr 26, 2010

### LostConjugate

The fit board is more expensive than a scale.

4. Apr 26, 2010

### jack action

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. Apr 26, 2010

### LostConjugate

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. Apr 26, 2010

### Jefficus

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. Apr 26, 2010

### Jefficus

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. Apr 26, 2010

### pallidin

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

Or, go to Walmart and buy a $10 scale. Duh.... 9. Apr 26, 2010 ### mgb_phys Do they ice-skate? You could have one swing the other around by the legs and use conservation of angular momentum 10. Apr 26, 2010 ### LostConjugate Well here is an idea. You may be able to build a large variable capacitor out of rubber and tin foil in such a way that there is a slight change in voltage when different weights compress the insulator. Not sure. 11. Apr 28, 2010 ### Buckleymanor Four ice cubes of the same size placed in four cups. Chair with four long legs placed on top of ice cubes. The room in which the chair is placed is allways at the same temperature. Person sits in chair and you time how long it takes for the ice cubes to melt or the chair legs touch the bottom of the cups. 12. Apr 28, 2010 ### LostConjugate I am baffled, how does the pressure make the ice melt faster? 13. Apr 28, 2010 ### Buckleymanor Won't more weight make it melt faster. 14. Apr 28, 2010 ### LostConjugate I don't know, you tell me :D Instinctively I would say no. 15. Apr 28, 2010 ### Buckleymanor More weight applied to the ice equals more work done which raises the temperature. So the ice melts quicker. 16. Apr 28, 2010 ### LostConjugate No work can be done by sitting in a chair. Work is Force x Distance 17. Apr 28, 2010 ### Gordianus Interesting idea. The melting point of ice varies with pressure. I imagine de chair and the ice cubes in a room at 0 Celsius (the ice shouldn´t mel). Once I put the chair (and the person), the legs go through the ice cube (try this with an ice cube and a knife, it´s beautiful to watch). From the time it takes to travel trough the ice cube we may calculate the weight. This is extremely funny but insane. A bathroom sacle costs$ 10. Anyway, I enjoy the post.

18. Apr 28, 2010

### mender

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. Apr 29, 2010

### gmax137

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. Apr 29, 2010

### gmax137

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.