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?

Result

x =  22.39 m

Solution:

D=20 cmm=20/100 m=0.2 m s=30 cmm=30/100 m=0.3 m s0=1 cmm=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+s322.389622.39 mD=20 \ cm \rightarrow m=20 / 100 \ m=0.2 \ m \ \\ s=30 \ cm \rightarrow m=30 / 100 \ m=0.3 \ m \ \\ s_{0}=1 \ cm \rightarrow m=1 / 100 \ m=0.01 \ m \ \\ \ \\ n=80 \ \\ x_{0}=3.54 \ \text{m} \ \\ n_{0}=s/s_{0}=0.3/0.01=30 \ \\ \ \\ r_{0}=D/2=0.2/2=\dfrac{ 1 }{ 10 }=0.1 \ \text{m} \ \\ r_{1}=r_{0}+s_{0}=0.1+0.01=\dfrac{ 11 }{ 100 }=0.11 \ \text{m} \ \\ r_{2}=r_{1}+s_{0}=0.11+0.01=\dfrac{ 3 }{ 25 }=0.12 \ \text{m} \ \\ \ \\ x_{1}=2 \pi \cdot \ r_{0} \cdot \ n_{0}=2 \cdot \ 3.1416 \cdot \ 0.1 \cdot \ 30 \doteq 18.8496 \ \text{m} \ \\ x_{2}=2 \pi \cdot \ r_{1} \cdot \ n_{0}=2 \cdot \ 3.1416 \cdot \ 0.11 \cdot \ 30 \doteq 20.7345 \ \text{m} \ \\ x_{3}=2 \pi \cdot \ r_{2} \cdot \ (n-2 \cdot \ n_{0})=2 \cdot \ 3.1416 \cdot \ 0.12 \cdot \ (80-2 \cdot \ 30) \doteq 15.0796 \ \text{m} \ \\ \ \\ x=x_{0}+x_{1}+s_{2}+s_{3}=3.54+18.8496+s_{2}+s_{3} \doteq 22.3896 \doteq 22.39 \ \text{m}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you want to convert length units?

 

 

Next similar math problems:

  1. Closed drum
    drum Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm . (π= 3.14)
  2. Pulley
    kladka On wheels with a diameter of 40 cm is fixed rope with the load. Calculate how far is load lifted when the wheel turns 7 times?
  3. Base
    rotunda Base of building is circle with diameter 25 m. Calculate the circumference of a circular trench witch diameter is 41 cm wider than the diameter of the base.
  4. Central angle
    obluk What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
  5. Circle - simple
    kruh The circumference of a circle is 930 mm. How long in mm is its diameter?
  6. The diameter
    circles The diameter of a circle is 4 feet. What is the circle's circumference?
  7. Wheel
    wheel_1 What is the wheel diameter if on the 0.38 km track turns 128 times?
  8. Coal mine
    koleso The towing wheel has a diameter of 1.7 meters. How many meters does the elevator cage lower when the wheel turns 32 times?
  9. Clock hands
    clocks2_16 The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
  10. Clock
    clock How long is trajectory of second hand of hours for day, if is 15 mm long?
  11. Customary length
    inch Convert length 65yd 2 ft to ft
  12. Athlete
    sportovec How long length run athlete when the track is circular shape of radius 120 meters and an athlete runs five times in the circuit?
  13. Circle
    circle_1 What is the radius of the circle whose perimeter is 6 cm?
  14. Curved surface area CSA
    cylinder_8 A cylinder 5cm high has a base radius(7/2) cm. Calculate the curved surface area.
  15. Bicycle wheel
    cyklo2_2 After driving 157 m bicycle wheel rotates 100 times. What is the radius of the wheel in cm?
  16. Circle - easy 2
    circle_3 The circle has a radius 6 cm. Calculate:
  17. Circle from string
    motuz Martin has a long 628 mm string . He makes circle from it. Calculate the radius of the circle.