Winch drum

Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without hook). How long is the whole rope?

Correct result:

x =  22.3896 m

Solution:

D=20 cm m=20/100  m=0.2 m s=30 cm m=30/100  m=0.3 m s0=1 cm m=1/100  m=0.01 m  n=80 x0=3.54 m n0=s/s0=0.3/0.01=30  r0=D/2=0.2/2=110=0.1 m r1=r0+s0=0.1+0.01=11100=0.11 m r2=r1+s0=0.11+0.01=325=0.12 m  x1=2π r0 n0=2 3.1416 0.1 3018.8496 m x2=2π r1 n0=2 3.1416 0.11 3020.7345 m x3=2π r2 (n2 n0)=2 3.1416 0.12 (802 30)15.0796 m  x=x0+x1+s2+s3=3.54+18.8496+s2+s3=22.3896 m



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