Question

The cable of a hoist has a cross-section of 80 mm 2 . The hoist is used to lift a crate weighing 500 kg. What is the stress in the cable? The free length of the cable is 3 m. How much will it extend if it is made of steel (modulus 200 GPa)? How much if it is made of polypropylene, PP (modulus 1.2 GPa)?

Answer 1

Answer:

0.0009196875 m

0.15328125 m

Explanation:

Y = Young's modulus

Stress is given by

$\sigma=\dfrac{mg}{A}\\\Rightarrow \sigma=\dfrac{500\times 9.81}{80\times 10^{-6}}\\\Rightarrow \sigma=61312500\ Pa$

Change in length is given by

$\Delta L=\dfrac{L\sigma}{Y}\\\Rightarrow \Delta L=\dfrac{3\times 61312500}{200\times 10^9}\\\Rightarrow \Delta L=0.0009196875\ m$

The change in length of steel is 0.0009196875 m

$\Delta L=\dfrac{L\sigma}{Y}\\\Rightarrow \Delta L=\dfrac{3\times 61312500}{1.2\times 10^9}\\\Rightarrow \Delta L=0.15328125\ m$

The change in length of polypropylene is 0.15328125 m