The lifting capacity of a crane is 10 metric tonne . how thick should the steel rope be ? ( yield strenght of steel = 300×1000000 nm-² , g = 10ms-²
Answers
The lifting capacity of a crane is 10 metric tonne, then the steel rope be 6.48 mm thick.
Explanation:
The lifting capacity of the crane = 10 metric tonne= 10*1000 kg = 10000 kg
The yield strength of steel = 3 * 10⁸ N/m²
We know that the formula for ultimate stress is given by,
Ultimate stress = Load/ Area
⇒ 3 * 10⁸ = 10000 / Area ….. [substituting the given values]
⇒ Area = 0.33× 10⁻⁴ m …. (i)
Now,
Let the thickness i.e., the diameter of the rope be denoted as “d” m.
So, we can write, the formula for area of the base of the steel rope is given by,
Area = π/4 * (d)²
⇒ 0.33 * 10⁻⁴ = π/4 * (d)²
⇒ 0.33 * 10⁻⁴ = 0.785 * (d)²
⇒ d² = 0.42 * 10⁻⁴
⇒ d = 0.648 * 10⁻² meters
⇒ d = 6.48 millimeters
Thus, the thickness of the steel rope should be 6.48 mm.
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Answer:
approx.. 1 cm
Explanation:
Breaking stress=F/A
300×10^6=10×1000×10/A
A=3.3cm^2= Πr^2
r=1cm