Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and a length of 350 mm (the central mandrel has a diameter of 50 mm)?

Correct answer:

l =  313.4 m

Step-by-step explanation:

$$\begin{gathered} a=10\text{mm} \\ {D}_1=50\text{mm} \\ {D}_2=200\text{mm} \\ x=350\text{mm} \\ n=(D_2-D_1)/a=(200-50)/10=15 \\ o=\pi \cdot D \\ {x}_1=D_1=50\text{mm} \\ d=2\cdot a=2\cdot 10=20\text{mm} \\ {x}_2=x_1+(n-1)\cdot d=50+(15-1)\cdot 20=330\text{mm} \\ s=(x_1+x_2)/2\cdot n=(50+330)/2\cdot 15=2850\text{mm} \\ {l}_1=\pi \cdot s=3.1416\cdot 2850\doteq 8953.5391\text{mm} \\ {l}_2=l_1\to \text{m}=l_1:1000\text{m}=8953.5391:1000\text{m}=8.95354\text{m} \\ m=x/a=350/10=35 \\ l=m\cdot l_2=35\cdot 8.9535=313.4\text{m} \end{gathered}$$

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