Assistance: Large uncertainties making it difficult to plot slopes

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The discussion centers on challenges in plotting slopes due to significant uncertainties in data related to the cosine of an angle versus temperature. A participant questions the validity of a maximum boiling water temperature of 360K at an altitude of 2,000 feet, noting that water typically boils at lower temperatures at higher altitudes. The original poster expresses frustration with high equipment uncertainty affecting their practical report and seeks guidance on accurately representing slopes that encompass all uncertainties. Another contributor suggests considering whether the uncertainties are independent, as a constant source of uncertainty might not significantly impact the slope. Overall, the conversation highlights the complexities of data representation in experimental contexts.
Physicist_2
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Homework Statement
This isn't a textbook problem, but rather I am currently writing my practical report and have encountered several problems due to a high equipment uncertainty which has led me to a standstill. Attached is a diagram of my graph with the appropriate uncertainties, however, I am finding it difficult to draw the max and min slopes which encompass all the uncertainty. I would appreciate any guidance. Thank you
Relevant Equations
Thank you
Screen Shot 2019-07-17 at 8.21.24 pm.png
 
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Can you explain a bit more in detail what you are plotting and how you estimated your uncertainties? If you are plotting the cosine of an angle vs. temperature, the point at, say 335 K shows an uncertainty from -0.5 to 1.0 in the cosine which corresponds to an angle uncertainty from 0 to 120 degrees. Is that consistent with what you observed?
 
And how can the max temperature of your boiling water be 360K (~ 87C)? I must be misunderstanding this...
 
berkeman said:
And how can the max temperature of your boiling water be 360K (~ 87C)? I must be misunderstanding this...
According to Wikipedia at an altitude of 12,000 ft water boils at 87.6 ##^o \rm{C}##.
:oldsmile:
 
kuruman said:
According to Wikipedia at an altitude of 12,000 ft water boils at 87.6 ##^o \rm{C}##.
:oldsmile:
Hmm, I used my Mentor superpowers just now to check the OP's location, and unless he went on a road trip to conduct this experiment, he was right around 2000 feet in altitude...

:smile:
 
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Physicist_2 said:
Problem Statement: This isn't a textbook problem, but rather I am currently writing my practical report and have encountered several problems due to a high equipment uncertainty which has led me to a standstill. Attached is a diagram of my graph with the appropriate uncertainties, however, I am finding it difficult to draw the max and min slopes which encompass all the uncertainty. I would appreciate any guidance. Thank you
Relevant Equations: Thank you

View attachment 246749
Further to @kuruman 's comments in post #2, consider whether the uncertainties are independent. Quite possibly there is a source of uncertainty which would have a roughly constant affect across all datapoints, so would not affect the slope much.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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