Question

A nylon rope that has a 0.73 cm radius and is 12 meters long is used to lift a 24 kg object straight up. If the object is lifted at constant velocity, how much is the rope stretched by? The Young's modulus of the nylon is 5.0 × 109 N/m2 and use 9.81 m/s2 for the acceleration of free fall. Express your answer in centimeters and round to the nearest hundredth.

Answer 1

The rope is stretched by 0.3373 cm

Step-by-step explanation:

As we know

Youngs Modulus (
`5.0 * 10^9` N/m2) is Stress divided by strain

Stress = force/Area = (65*9.8)/(pi * (7.3*10^-3)^2)

Starin = change in length/original length of the rope = l/12 meters

Substituting the given values we get

`5.0 * 10^9` N/m2 = {(
`((24*9.8)/(\pi *(7.3*10^(-3))^2) )/((\delta L)/(L) )`)

`5.0 * 10^9` N/m2 = {(
`((24*9.8)/(\pi *(7.3*10^(-3))^2) )/((\delta L)/(12) )`)

`(\delta L)/(12) = ((65*9.8)/(pi * (7.3*10^-3)^2) )/(5.0 * 10^9)`

The rope is stretched by 0.3373 cm