Question

A steel rope has a 25 mm diameter and density of 5000 kg/m^3. The largest tension it can withstand is 320,000 N. What is the longest length of of this rope in m that can hang without breaking?

Answer 1

Answer:

longest length is 13304.05 m

Explanation:

given data

diameter = 25 mm

so radius r = 12.5 × $10^{-3}$ m

density = 5000 kg/m³

tension = 320000 N

to find out

longest length of of this rope

solution

we know that here tension is express as

T = m × g

and m is mass and g is  acceleration due to gravity

here mass = density × volume

and volume = π×r²×l

here r is radius and l is length

so T = density c volume  × g

put here value

320000 = 5000 × π×12.5² × $10^{-3}$ × l × 9.8

solve it we get length l

l = 13304.05

so longest length is 13304.05 m