Repeat History: Design a test to prove who is right spring

[wein7145]

Homework Statement

Not surprisingly there is an old forum post on this topic:
https://www.physicsforums.com/threads/proving-force.46215/
However it doesn't contain the answer.
Reposted:
Two physics students are having a debate about the best way to define a force scale using rubber bands. Each one is trying to convince you to do it their way. They have the following apparatus to use in tests:
A bunch of identical small rubber bands
10N spring scale
meter stick

Joe argues that: “It’s so much easier to use one rubber band to define a force scale than many. All I have to do is to stretch the rubber band by 1 cm to get one unit of force, then by 2 cm to get two units of force, and then by 3 cm to get three units of force and so on.”

Larry counters: “We do not know whether or not rubber bands are linear. Maybe the force the rubber band exerts at 3 cm is not really three times than the force it exerts at 1 cm. I think it is absolutely necessary to use many identical looking rubber bands in parallel with each other to define a force.”

How could I design a test using the same apparatus Joe and Larry have to prove who is right?

Homework Equations

F=ma/Hooke's Law

The Attempt at a Solution

Quote "A way to create double and triple forces is to combine equivalent forces. You should start this investigation by pulling a single rubber band out to some predetermined length that you choose. You can name the unit of force associated with the pull after yourself or make up another name for it." At some point use a Newton spring scale (which is a known accepted unit) and make it equal to your rubber band at some distance. The Activity Book which for some reason now parallels the 15 page supplementary packet makes for the same problem twice with no solution and is driving me crazy. By the law of observation one rubber band shouldn't be enough to make a solid decision so I believe Larry correct in needing to test multiple rubber bands even multiple rubber bands at the same time. However Joe also seems to be correct since it is linear/proportional. This is just page 1 of the 15 pages due tomorrow. The internet exists to share the knowledge and united together we will do just that. I don't really care about the grades I care more about the knowledge but the grades are proportional to the knowledge so...

 

[mfb]

By the law of observation one rubber band shouldn't be enough to make a solid decision

That is a different point. In the context of the problem statement, I think you can assume that all rubber bands are exactly identical.

However Joe also seems to be correct since it is linear/proportional.

Is it? How do you know?

 

[HallsofIvy]

Since this is a question about "experiments" the only way to determine which experiment is better is to actually do the two experiments and compare the results to a known outcome.

As to what you say, "However Joe also seems to be correct since it is linear/proportional", that is NOT true. Any (differentiable) function can be approximated by a linear function over a sufficiently small region- that is what is done in basic Calculus with springs- one assumes that the region of extension is short enough that we can approximate it by a linear function. That is what Larry is saying. You cannot answer this just by saying "Larry is wrong" without giving a reason.

 

[wein7145]

However Joe also seems to be correct since it is linear/proportional.
Is it? How do you know?

By setting the units to Newtons 1 can equal X many cm stretched. We did this in the 2nd part of book. But you are right a conclusion can't be made unless it is proven, I'm just saying this: By using a spring scale measure the force at 1 rubber band per x length vs rubber band at 3 times the cm length and compare the results.