Rope

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

Correct answer:

l =  313.4 m

Step-by-step explanation:

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

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