Question

a steel cable weighs 2450kg the cable has a uniform circular cross section of radius 0.85cm. the steel from which thecable is made has adensity of 7950kg/m3. find the length of the cabl

Answer 1

Answer:

1357.7 m

Step-by-step explanation:

The cable has a circular cross section, so the cable is shaped like a cylinder. The length of the cable is the height of the cylinder.

volume of cylinder = (pi)(r^2)h

where r = radius of cylinder, and h = height of cylinder.

First, we convert the radius into meters.

r = 0.85 cm = 0.85 cm * (1 m)/(100 cm) = 0.0085 m

Now we find an expression for the volume of the cable in cubic meters in terms of h, the unknown height which is the length of the cable.

volume = (pi)(0.0085 m)^2 * h

volume = 0.00022698 m^2 * h    <------  first expression for volume

Now we use the density and given mass to find the volume of the cable.

density = mass/volume

volume = mass/density

volume = (2450 kg)/(7950 kg/m^3)  <------  second expression for volume

Set the two expressions for volume equal and solve for h.

0.00022698 m^2 * h = (2450 kg)/(7950 kg/m^3)

h = [(2450 kg)/(7950 kg/m^3)]/(0.00022698 m^2)

h = 1357.7 m