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

0.0009196875 m

0.15328125 m

Step-by-step explanation:

Y = Young's modulus

Stress is given by

`\sigma=(mg)/(A)\\\Rightarrow \sigma=(500* 9.81)/(80* 10^(-6))\\\Rightarrow \sigma=61312500\ Pa`

Change in length is given by

`\Delta L=(L\sigma)/(Y)\\\Rightarrow \Delta L=(3* 61312500)/(200* 10^9)\\\Rightarrow \Delta L=0.0009196875\ m`

The change in length of steel is 0.0009196875 m

`\Delta L=(L\sigma)/(Y)\\\Rightarrow \Delta L=(3* 61312500)/(1.2* 10^9)\\\Rightarrow \Delta L=0.15328125\ m`

The change in length of polypropylene is 0.15328125 m