Winch

The steel rope has a diameter of 6mm and a length of 20m.
We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?

Correct answer:

D₂ =  138 mm

Step-by-step explanation:

$$\begin{gathered} D_1=50\text{ mm } \\ {l}_1=60\text{ mm } \\ d=6\text{ mm } \\ {l}_2=20\text{ m}\to \text{ mm}=20\cdot 1000\text{ mm}=20000\text{ mm } \\ {r}_1=D_1\mathrm{/}2=50\mathrm{/}2=25\text{ mm } \\ {V}_1=\pi \cdot r_1^2\cdot l_1=3.1416\cdot 25^2\cdot 60\doteq 117809.7245{\text{mm}}^3 \\ {V}_2=d^2\cdot l_2+V_1=6^2\cdot 20000+117809.7245\doteq 837809.7245{\text{mm}}^3 \\ {V}_2=\pi \cdot r_2^2\cdot l_1 \\ {r}_2=\sqrt{{\displaystyle \frac{V_2}{\pi \cdot l_1}}}=\sqrt{{\displaystyle \frac{837809.7245}{3.1416\cdot 60}}}\doteq 66.6687\text{ mm } \\ {D}_3=2\cdot r_2=2\cdot 66.6687\doteq 133.3374\text{ mm } \\ {D}_2=d\cdot \lceil D_3\mathrm{/}d\rceil =6\cdot \lceil 133.3374\mathrm{/}6\rceil =138\text{ mm} \end{gathered}$$

Try another example

Related math problems and questions:

• 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 h
• 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)?
• Rainfall
  A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
• Diameter of a cylinder
  The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
• Engine pulley
  The engine has a 1460 rev / min (RPM). Disc diameter is 350 mm. What will be the disc peripheral speed in RPM? Pulleys on the engine has diameter 80mm, on a disc has diameter 160mm.
• The coil
  How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
• Aquarium volume
  The aquarium has a cuboid shape and dimensions a = 0.3 m, b = 0.85 m, c =? , V = ?. What volume has a body, if after dipping into the aquarium water level rises by 28 mm?
• Cu wire
  Copper wire has a length l = 820 m and diameter d = 10 mm. Calculate the weight if density of copper is ρ = 8500 kg/m³. Result round to one decimal place.
• AL wire
  What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
• How much
  How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
• Copper winding
  Calculate the current flowing through the copper winding at an operating temperature of 70°C. Celsius, if the winding diameter is 1.128 mm and the winding length is 40 m. The winding is connected to 8V.
• Rainwater
  6 mm of water rained on the garden with an area of 25 acres. How many 12 liter cans of water would we water this garden just as much?
• Kitchen
  Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
• The pot
  The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
• The square
  The square oak board (with density ρ = 700 kg/m³) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
• Sawdust
  How many cubic centimeters of wood sawdust is created by cut the tree trunk with a diameter of 66 cm and when the gap width is 5 mm?
• Steel tube
  The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m³. Calculate its length if it weighs 15 kg.