High School

We appreciate your visit to A 84 kg mountain climber hangs from a rope and stretches it by 26 cm If the rope was originally 37 4 m long and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A 84 kg mountain climber hangs from a rope and stretches it by

26 cm. If the rope was originally 37.4 m long and its diameter is

1.0 cm, what is Young's Modulus in N/m^2 for the rope? Use 3

significan

Answer :

Final answer:

The Young's Modulus for the rope is approximately 3.52 × 10^9 N/m^2.

Explanation:

To calculate Young's Modulus for the rope, we need to use the formula:

E = (F/A) / (ΔL/L)

First, let's calculate the force applied to the rope. The weight of the mountain climber can be calculated using the formula:

Weight = mass × acceleration due to gravity

Weight = 84 kg × 9.8 m/s^2 = 823.2 N

Next, let's calculate the cross-sectional area of the rope. The formula for the area of a circle is:

A = πr^2

Given that the diameter of the rope is 1.0 cm, the radius can be calculated as:

Radius = diameter / 2 = 1.0 cm / 2 = 0.5 cm = 0.005 m

Now we can calculate the area:

A = π(0.005 m)^2 = 7.85 × 10^-5 m^2

Next, let's calculate the change in length of the rope. The original length of the rope is 37.4 m and it stretches by 26 cm, so the change in length is:

ΔL = 26 cm = 0.26 m

Finally, we can plug these values into the formula for Young's Modulus:

E = (823.2 N / 7.85 × 10^-5 m^2) / (0.26 m / 37.4 m)

Calculating this expression gives us:

E ≈ 3.52 × 10^9 N/m^2

Learn more about young's modulus here:

https://brainly.com/question/29134671

#SPJ14

Thanks for taking the time to read A 84 kg mountain climber hangs from a rope and stretches it by 26 cm If the rope was originally 37 4 m long and. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada