How Do You Calculate the Mass of a Single Screw from Multiple Cup Weights?

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Homework Help Overview

The problem involves determining the mass of a single screw based on the total weights of five cups, each containing a different number of screws. The context is related to basic principles of mass and assumptions regarding uniformity among the screws and cups.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to assume that all cups and screws have uniform weights. They explore potential common differences among the given masses and suggest testing various integer weights for the screws. Questions about the largest common factor and the implications of the cups having mass are also raised.

Discussion Status

The discussion is ongoing, with participants exploring various assumptions and interpretations. Some guidance has been offered regarding the need for assumptions, and there is an acknowledgment of the complexity introduced by the cups' weights. However, no consensus has been reached on a specific method or solution.

Contextual Notes

There is uncertainty regarding whether the cups have mass and how that affects the calculations. The problem is also complicated by the possibility of non-integer weights for the screws, leading to multiple potential solutions.

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I have been given the masses of 5 cups, each with a different amount of screws inside.
1st cup = 13g
2nd cup = 19g
3rd cup = 8g
4th cup = 26g
5th cup = 38g

I need to find the mass of a single screw.
I was not given any equations or data besides those masses
I have no clue how to approach this, we have not done anything like it before and therefore have no skills to solve this. Please help!
 
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first you have to make an assumption: all cups are the same weight and all screws are the same weight.

is there a common difference between these masses?

They're all integers right, so perhaps a screw weighs 1g? There's a mix of even and numbers so screw's can't weigh an even amount. Maybe they all weigh 3g, does that work? 5, 7 etc...?

Just mess around and see what you find, then in your answer explain the uncertainty and put in all the things you think it could be.
 
What is the largest common factor of those numbers? A screw cannot weigh more than that.
 
are you given the mass of the cup? if the cups are not massless then there will be a lot of possibilities for answers. and if the mass of the screws are allowed to be non integers, the question will have an infinite numbers of answers.
 
Last edited:
tim_lou said:
the question will have an infinite numbers of answers.
infinite possible answers.


Clearly the answer will have to include some assumptions and some logic to determine the most reasonable value. Given that all the data supplied are integers, I think we can manage to not overcomplicate the problem.
 
Thanks! I finally figured it out.
 
Could you please share with us how you figured it out? I'm interested in knowing

:cool:
 

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