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My textbook is Essential University Physics by Richard Wolfson. I'm attending Illinois Central College, and my course is Engineering Physics 1: Mechanics. It's calculus based.
From the Text:
"A florist asks you to make a window display with two hanging pots as shown in the diagram. The florist is adamant that the strings be invisible as possbile, so you decide to use fishing line but you want to use the thinnest line you can. Will fishing line that can withstand 100N of tension work?"
Original given diagram and my free body diagrams are attached.
(edit: I had an ascii diagram worked out that didn't work in the preview, but when i scrapped it i forgot to change my angle notation, so I'm just arbitrarily naming the angles 1, 2, and 3)
Mass of A = 3.85 kg
Mass of B = 9.28 kg
Angle 1 = 13.9 degrees
Angle 2 = 54.0 degrees
Angle 2 = 68.0 degrees
Force of Gravity = 9.8 m/(s^2)
Tensions : T(a1), T(a2), T(b1), T(b2) = ??
I know this problem is of net forces to find string tensions. I started first trying to find the x and y components of each string tension assuming that the objects weren't in motion so the sum of y components would equal the inverse of gravity, but I figured that I couldn't assume that because I don't know if the string is actually breaking or not (if it were breaking, gravity's force would be larger, no?), and if I did assume that, I don't know the distribution of gravity between the y components (if the angles were equal, the y components would balance the forces equally, making this problem infinitely easier). Maybe I'm thinking too much about it (I tend to do that), or maybe I'm missing something from the basic concepts, or maybe i'm just really bad at remembering trigonometry.
So far:
F=ma
Movement isn't considered, so (for both objects)
T(1) + T(2) + G = 0
Tension of the string between objects A and B
T(b2) = T(a2)
This is where i start to get fuzzy
Y components (for both objects)
T(1y) + T(2y) + G = 0
X components (for both objects)
T(1x) + T(2x) = 0
I was still working out an equation. I tried some trig functions, but they didn't seem to work out in my mind because of the conceptual problems I stated earlier. There was a similar, simpler example problem in the text that had a single mass hanging from a rope and equal angles that it was hanging from, and it gave me ideas, but the different angles in my problem keep screaming at me that there's something different at play, something I'm missing.
4. Closing remarks
What I'm asking here is not the answer. I just want a little help getting on the right track. Am I missing anything? Do I have too much of anything that is tripping me up? And for goodness sake, what is the secret gravity is hiding?
Many thanks to any help whatsoever.
Homework Statement
From the Text:
"A florist asks you to make a window display with two hanging pots as shown in the diagram. The florist is adamant that the strings be invisible as possbile, so you decide to use fishing line but you want to use the thinnest line you can. Will fishing line that can withstand 100N of tension work?"
Original given diagram and my free body diagrams are attached.
(edit: I had an ascii diagram worked out that didn't work in the preview, but when i scrapped it i forgot to change my angle notation, so I'm just arbitrarily naming the angles 1, 2, and 3)
Mass of A = 3.85 kg
Mass of B = 9.28 kg
Angle 1 = 13.9 degrees
Angle 2 = 54.0 degrees
Angle 2 = 68.0 degrees
Force of Gravity = 9.8 m/(s^2)
Tensions : T(a1), T(a2), T(b1), T(b2) = ??
I know this problem is of net forces to find string tensions. I started first trying to find the x and y components of each string tension assuming that the objects weren't in motion so the sum of y components would equal the inverse of gravity, but I figured that I couldn't assume that because I don't know if the string is actually breaking or not (if it were breaking, gravity's force would be larger, no?), and if I did assume that, I don't know the distribution of gravity between the y components (if the angles were equal, the y components would balance the forces equally, making this problem infinitely easier). Maybe I'm thinking too much about it (I tend to do that), or maybe I'm missing something from the basic concepts, or maybe i'm just really bad at remembering trigonometry.
Homework Equations
So far:
F=ma
Movement isn't considered, so (for both objects)
T(1) + T(2) + G = 0
Tension of the string between objects A and B
T(b2) = T(a2)
This is where i start to get fuzzy
Y components (for both objects)
T(1y) + T(2y) + G = 0
X components (for both objects)
T(1x) + T(2x) = 0
The Attempt at a Solution
I was still working out an equation. I tried some trig functions, but they didn't seem to work out in my mind because of the conceptual problems I stated earlier. There was a similar, simpler example problem in the text that had a single mass hanging from a rope and equal angles that it was hanging from, and it gave me ideas, but the different angles in my problem keep screaming at me that there's something different at play, something I'm missing.
4. Closing remarks
What I'm asking here is not the answer. I just want a little help getting on the right track. Am I missing anything? Do I have too much of anything that is tripping me up? And for goodness sake, what is the secret gravity is hiding?
Many thanks to any help whatsoever.
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