# Scale Design Using an Angle Measurement for Weight

1. Apr 7, 2013

### BamaChemE

1. The problem statement, all variables and given/known data
I have to design a scale to weigh something under 1kg and all am given is a yard stick, 10 ft of fishing line, a 500g known standard mass, and a protractor.

Use an angle measurement for weight. Don't just balance weights on a see-saw

2. Relevant equations
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3. The attempt at a solution
I'm not looking for someone to do it for me. Just trying to figure out exactly what he means by using an angle measurement for weight. Any hints, examples, and pushes in the right direction would be appreciated.

2. Apr 7, 2013

### Staff: Mentor

Welcome to the PF.

Think about the two techniques for balancing forces that you use in solving many mechanical problems. One is to add up all of the forces on a body, and they sum to zero if there is no acceleration, right? What about summing moments (torques) on a hinged body? Same kind of thing, right?

So I would start with that, and think about how a mechanical beam balance works. BTW, the technique I'm thinking of does not require a protractor, it just requires the meter stick to be horizontal in balance. Does the solution of the problem require the use of the protractor?

3. Apr 7, 2013

### BamaChemE

He said there are many ways we can go about this. He is not strict on any sort of specific solution. As long as we solve the problem in the given parameters. So we don't HAVE to use everything given. I've done plenty of moment summing before in this class. Just his statement about using angle measurements for weight seemed to imply it wasn't that simple.

4. Apr 7, 2013

### BamaChemE

Correct me if I interpret what you say wrong, but it seems like you are encouraging the use of moments and setting them equal to each other adjusting the pivot point. In which case that seems like it goes against the requirement of not simply balancing them on a see-saw. Or am I completely off track of what you were saying?

5. Apr 7, 2013

### Staff: Mentor

A see-saw is a particular type of machine. You can avoid that type of machine by making it one-sided. Does that hint help? Please share your thoughts and efforts toward a solution of this question. The PF works best when you are talking out loud and trying to figure out the problem...

EDIT -- one more visual hint... What do you do when you step on a balance at the Gym to measure your weight. What do you move?

6. Apr 7, 2013

### nckalx

Hi, I'm in the same class as BamaChemE and I've been having the same problem. Every solution I've been able to come up with thus far in some way utilizes having the sum of the moments of both sides equal to zero, but never has any need for a protractor. Our professor told us that the scales in doctor's offices and chemistry labs (triple beam balance I assume), use angles measurements.

However, the best I've been able to come up is a scale where the yardstick is divided into two arms, one longer than the other, with the 500 gram counterweight tied to the shorter arm. The mass being weighed would be tied to the longer arm and could slide along the arm until the beam is horizontal. But this uses the sum of moments and is too similar to the see-saw my professor was describing.

I am just having trouble seeing how the angle measurement plays into this whatsoever

7. Apr 7, 2013

### BamaChemE

Not sure if this is what you were trying to hint at. I think it at least partially is. I will wedge one end of the meter stick into a wall and make that the fulcrum. The object of unknown weight will be placed at a point on this stick. The other end will be held in the air with the wire going up, around a pulley (possibly using protractor or finger as pulley), and back down to the hanging known 500g weight. Moment=Force x Distance. Sum of the moments = 0. I can figure out M2 from 500g, gravity, and d2 measurement. Then solve for the unknown mass knowing gravity, d1 measurement, and what M1 must equal for the system to be at rest. Thus we will move the unknown around until we find a position that leaves the counterweight unmoved. Sound like it will work? Did you have something different in mind?

^
|...........................d2..........................Fulcrum
| - ----------------------------------------|
500g
.........................unknown
..............................|
..............................|
..............................V..............d1..........Fulcrum
..............................|---------------------|

8. Apr 7, 2013

### BamaChemE

nckalx I know what you mean. I figured out a viable solution that isn't a see saw. But just uses our generic sum of moments =0 and I don't know if that will be okay since he seemed to push the angular measurement. I may send him an email...

9. Apr 7, 2013

### nckalx

I think I'll send an email as well... after looking at this link, I feel like I have a pretty good understanding of how triple beam balances, the kind we use in chemistry, work, but in no way are angle measurements or protractors used. Maybe if enough of us send emails, he'll clarify what he means.

http://www.ohaus.com/input/tutorials/tbb/TBBtheory.html [Broken]

Last edited by a moderator: May 6, 2017
10. Apr 8, 2013

### barryj

How about something like this. As the weight to be measured gets greater, the angle of the wire from the vertical will increase.

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11. Apr 9, 2013

### qomsday

Will the vertical wire stay vertical when there is no weight on the other end and the 500g mass in place under the vertical wire?
I feel like the triangle would be off vertical to begin with

12. Apr 9, 2013

### barryj

The wire might not be vertical due to the yardstick being off to the side, but one could add another vertical wire when there was no weight to be measured. The idea here is that the weight could be measured by using the angle of the protractor located where the wires connected to the ceiling or other support.

13. Apr 9, 2013

### qomsday

So the angle that is being measured is the angle between the wire above the 500g mass and the vertical when there is no weight AND when there is weight?

14. Apr 9, 2013

### barryj

That is the idea.

15. Apr 9, 2013